You can back Sequent on Kickstarter starting at $189 for a watch.
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In an attempt to fix this, Sequent looked toward the automatic movements in traditional watches to create a kinetic battery system for its smartwatch.
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Lunar isn't the first hybrid smartwatch to try and solve the battery problem, either: a company called Sequent took a stab at it on Kickstarter earlier this year using kinetic charging, too.
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The general notion of sequent introduced here can be specialized in various ways. A sequent is said to be an intuitionistic sequent if there is at most one formula in the succedent (although multi-succedent calculi for intuitionistic logic are also possible). More precisely, the restriction of the general sequent calculus to single-succedent-formula sequents, with the same inference rules as for general sequents, constitutes an intuitionistic sequent calculus. (This restricted sequent calculus is denoted LJ.) Similarly, one can obtain calculi for dual-intuitionistic logic (a type of paraconsistent logic) by requiring that sequents be singular in the antecedent.
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Tableaux can be intuitively seen as sequent systems upside- down. This symmetrical relation between tableaux and sequent systems was formally established in (Carnielli 1991).
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The codebase also included an option to spread client connections among multiple processors on the Sequent multiprocessor system and to run simultaneously on multiple processors on a Sequent server. The database enhancements included several new areas, 50 player levels and 10 administrative levels. Notable MUDs running on the Sequent codebase include Sojourn and its successor, TorilMUD.
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This is equivalent to the sequent ' ⊢ ⊥ ', which clearly cannot be valid.
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A sequent is a formalized statement of provability that is frequently used when specifying calculi for deduction. In the sequent calculus, the name sequent is used for the construct, which can be regarded as a specific kind of judgment, characteristic to this deduction system. The intuitive meaning of the sequent \Gamma\vdash\Sigma is that under the assumption of Γ the conclusion of Σ is provable. Classically, the formulae on the left of the turnstile can be interpreted conjunctively while the formulae on the right can be considered as a disjunction.
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Sequent Energy Management is the company's Houston-based subsidiary primarily involved in asset optimization and energy marketing and trading. It was established in 2001. Sequent Energy Management provides clients in the eastern and southeastern United States ways to optimize energy programs and increase cost effectiveness from wellhead to burner-tip. Sequent offers solutions for large energy users looking to outsource their asset management activities.
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In mathematical logic, a sequent is a very general kind of conditional assertion. : A_1,\,\dots,A_m \,\vdash\, B_1,\,\dots,B_n. A sequent may have any number m of condition formulas Ai (called "antecedents") and any number n of asserted formulas Bj (called "succedents" or "consequents"). A sequent is understood to mean that if all of the antecedent conditions are true, then at least one of the consequent formulas is true.
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This style of conditional assertion is almost always associated with the conceptual framework of sequent calculus.
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The word "sequent" is taken from the word "Sequenz" in Gentzen's 1934 paper. Kleene makes the following comment on the translation into English: "Gentzen says 'Sequenz', which we translate as 'sequent', because we have already used 'sequence' for any succession of objects, where the German is 'Folge'.".
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Structads are an approach to the semantics of logic that are based upon generalising the notion of sequent along the lines of Joyal's combinatorial species, allowing the treatment of more drastically nonstandard logics than those described above, where, for example, the ',' of the sequent calculus is not associative.
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Sequent was a DikuMUD derivative codebase developed by Raja Kushalnagar ("Duke of Sequent"). It was a text-based online role-playing game that was an accessible DikuMUD based MUD. It added several new playing areas with shorter text descriptions that was designed to be accessible to users with sensory disabilities. It also supported more players online at the same time by being hosted on a Sequent multi-processor machine at the University of California, Berkeley, and was first started in March 1991.
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For System LK, System LJ, and System LL, uniform proofs are focused proofs where all the atoms are assigned negative polarity. Many other sequent calculi has been shown to have the focusing property, notably the nested sequent calculi of both the classical and intuitionistic variants of the modal logics in the S5 cube.
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Gerhard Gentzen discovered that a simple restriction of his system LK (his sequent calculus for classical logic) results in a system which is sound and complete with respect to intuitionistic logic. He called this system LJ. In LK any number of formulas is allowed to appear on the conclusion side of a sequent; in contrast LJ allows at most one formula in this position. Other derivatives of LK are limited to intuitionistic derivations but still allow multiple conclusions in a sequent. LJ'Proof Theory by G. Takeuti, is one example.
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For certain formulations (i.e. variants) of the sequent calculus, a proof in such a calculus is isomorphic to an upside-down, closed analytic tableau.
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IBM since the ruling states that Novell "is entitled, at its sole discretion, to direct SCO to waive its claims against IBM and Sequent".
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By studying the sequent occupance of New Zealand, students will be able to analyze the physical landscape and the cultural landscape of the country.
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"Sequent C'" is a short but memorable piece by Peter Baumann on flute, with tape echo. The sleeve design and cover painting are by Froese.
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A sequent of the form ' ⊢ α, β ', for logical formulas α and β, means that either α is true or β is true (or both). But it does not mean that either α is a tautology or β is a tautology. To clarify this, consider the example ' ⊢ B ∨ A, C ∨ ¬A '. This is a valid sequent because either B ∨ A is true or C ∨ ¬A is true.
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However, sequent calculus and cut- elimination were not known at the time of Herbrand's theorem, and Herbrand had to prove his theorem in a more complicated way.
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There are many formal derivation ("proof") systems for first-order logic. These include Hilbert-style deductive systems, natural deduction, the sequent calculus, the tableaux method and resolution.
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Propositional calculus is commonly organized as a Hilbert system, whose operations are just those of Boolean algebra and whose theorems are Boolean tautologies, those Boolean terms equal to the Boolean constant 1. Another form is sequent calculus, which has two sorts, propositions as in ordinary propositional calculus, and pairs of lists of propositions called sequents, such as A∨B, A∧C,... \vdash A, B→C,.... The two halves of a sequent are called the antecedent and the succedent respectively. The customary metavariable denoting an antecedent or part thereof is Γ, and for a succedent Δ; thus Γ,A \vdash Δ would denote a sequent whose succedent is a list Δ and whose antecedent is a list Γ with an additional proposition A appended after it. The antecedent is interpreted as the conjunction of its propositions, the succedent as the disjunction of its propositions, and the sequent itself as the entailment of the succedent by the antecedent.
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Since this early work, sequent calculi, also called Gentzen systems,, calls Gentzen systems LC systems. Curry's emphasis is more on theory than on practical logic proofs.. This book is much more concerned with the theoretical, metamathematical implications of Gentzen-style sequent calculus than applications to practical logic proofs., defines Gentzen systems and proves various theorems within these systems, including Gödel's completeness theorem and Gentzen's theorem., gives a brief theoretical presentation of Gentzen systems.
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They had long been working with Sequent Computer Systems, and were sceptical that the BiiN systems would deliver anything that the Sequent systems could not. Eventually Intel and Siemens could not agree on further funding, and the venture ended. Several pre-orders on the books were cancelled, and the technology essentially disappeared. With the closing of the project, Intel used the basic RISC core of the CPU design as the basis for the i960 CPU.
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To this ends, the program is symbolically executed with the resulting changes to program variables stored in so-called updates. Once the program has been processed completely, there remains a first-order logic proof obligation. At the heart of the KeY system lies a first-order theorem prover based on sequent calculus, which is used to close the proof. Interference rules are captured in so called taclets which consist of an own simple language to describe changes to a sequent.
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In proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. The first sequent calculi systems, LK and LJ, were introduced in 1934/1935 by Gerhard Gentzen, . as a tool for studying natural deduction in first-order logic (in classical and intuitionistic versions, respectively). Gentzen's so-called "Main Theorem" (Hauptsatz) about LK and LJ was the cut-elimination theorem,, gives a 5-page proof of the elimination theorem.
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Accordingly, the dual notion to paraconsistency is called paracompleteness, and the "dual" of intuitionistic logic (a specific paracomplete logic) is a specific paraconsistent system called anti-intuitionistic or dual-intuitionistic logic (sometimes referred to as Brazilian logic, for historical reasons).See Aoyama (2004). The duality between the two systems is best seen within a sequent calculus framework. While in intuitionistic logic the sequent : \vdash A \lor eg A is not derivable, in dual-intuitionistic logic : A \land eg A \vdash is not derivable.
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Using ' → ' instead of ' ⊢ ' and ' ⊃ ' instead of ' ⇒ ', he wrote: "The sequent A1, ..., Aμ → B1, ..., Bν signifies, as regards content, exactly the same as the formula (A1 & ... & Aμ) ⊃ (B1 ∨ ... ∨ Bν)".. : 2.4. Die Sequenz A1, ..., Aμ → B1, ..., Bν bedeutet inhaltlich genau dasselbe wie die Formel ::: (A1 & ... & Aμ) ⊃ (B1 ∨ ... ∨ Bν). (Gentzen employed the right-arrow symbol between the antecedents and consequents of sequents. He employed the symbol ' ⊃ ' for the logical implication operator.) In 1939, Hilbert and Bernays stated likewise that a sequent has the same meaning as the corresponding implication formula.. : Für die inhaltliche Deutung ist eine Sequenz ::: A1, ..., Ar → B1, ..., Bs, : worin die Anzahlen r und s von 0 verschieden sind, gleichbedeutend mit der Implikation ::: (A1 & ... & Ar) → (B1 ∨ ... ∨ Bs) In 1944, Alonzo Church emphasized that Gentzen's sequent assertions did not signify provability.
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Nicor Enerchange is Sequent Energy Management's Illinois- based brand for providing Commercial and Industrial customers’ natural gas procurement services. Founded in 1998, Nicor Enerchange is a wholesale natural gas supplier to the Midwest market.
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The standard semantics of a sequent is an assertion that whenever every A_i is true, at least one B_i will also be true.For explanations of the disjunctive semantics for the right side of sequents, see , , , , and . Thus the empty sequent, having both cedents empty, is false. One way to express this is that a comma to the left of the turnstile should be thought of as an "and", and a comma to the right of the turnstile should be thought of as an (inclusive) "or".
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SCI was often used to implement non-uniform memory access architectures. It was also used by Sequent Computer Systems as the processor memory bus in their NUMA-Q systems. Numascale developed a derivative to connect with coherent HyperTransport.
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Serving the needs of utilities, marketers, energy poolers, municipalities and industrials in the southern and eastern United States from Texas to New York, Sequent focuses primarily on asset management and the wholesale marketing, gathering and transporting of natural gas.
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The sequent calculus was developed to study the properties of natural deduction systems.Shankar, N., Owre, S., Rushby, J. M., & Stringer- Calvert, D. W. J., PVS Prover Guide 2.4 (Menlo Park: SRI International, November 2001). Instead of working with one formula at a time, it uses sequents, which are expressions of the form :A_1, \ldots, A_n \vdash B_1, \ldots, B_k, where A1, ..., An, B1, ..., Bk are formulas and the turnstile symbol \vdash is used as punctuation to separate the two halves. Intuitively, a sequent expresses the idea that (A_1 \land \cdots\land A_n) implies (B_1\lor\cdots\lor B_k).
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In proof theory, Gerhard Gentzen developed natural deduction and the sequent calculus. The former attempts to model logical reasoning as it 'naturally' occurs in practice and is most easily applied to intuitionistic logic, while the latter was devised to clarify the derivation of logical proofs in any formal system. Since Gentzen's work, natural deduction and sequent calculi have been widely applied in the fields of proof theory, mathematical logic and computer science. Gentzen also proved normalization and cut-elimination theorems for intuitionistic and classical logic which could be used to reduce logical proofs to a normal form.
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Thus, swapping left for right in a sequent corresponds to negating all of the constituent formulae. This means that a symmetry such as De Morgan's laws, which manifests itself as logical negation on the semantic level, translates directly into a left-right symmetry of sequents — and indeed, the inference rules in sequent calculus for dealing with conjunction (∧) are mirror images of those dealing with disjunction (∨). Many logicians feel that this symmetric presentation offers a deeper insight in the structure of the logic than other styles of proof system, where the classical duality of negation is not as apparent in the rules.
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Sequent calculus is related to other axiomatizations of propositional calculus, such as Frege's propositional calculus or Jan Łukasiewicz's axiomatization (itself a part of the standard Hilbert system): Every formula that can be proven in these has a reduction tree. This can be shown as follows: Every proof in propositional calculus uses only axioms and the inference rules. Each use of an axiom scheme yields a true logical formula, and can thus be proven in sequent calculus; examples for these are shown below. The only inference rule in the systems mentioned above is modus ponens, which is implemented by the cut rule.
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In a general sequent of the form :\Gamma\vdash\Sigma both Γ and Σ are sequences of logical formulas, not sets. Therefore both the number and order of occurrences of formulas are significant. In particular, the same formula may appear twice in the same sequence. The full set of sequent calculus inference rules contains rules to swap adjacent formulas on the left and on the right of the assertion symbol (and thereby arbitrarily permute the left and right sequences), and also to insert arbitrary formulas and remove duplicate copies within the left and the right sequences.
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This is a pseudo-contraction since it has the syntactic form of a contraction on the right, but the actual formula doesn't exist i.e., in the interpretation of the proof in the focused system the sequent has only one formula on the right.
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Sequent Scientific Ltd. is a Pharmaceutical company, and has its manufacturing unit at Baikampady in Mangalore. Syngene International, a contract research arm of Biocon, has set up its manufacturing plant at Mangalore SEZ. Solara, a pharmaceutical company also has its manufacturing unit in Mangalore.
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Finally, sequent calculus generalizes the form of a natural deduction judgment to : A_1, \ldots, A_n \vdash B_1, \ldots, B_k, a syntactic object called a sequent. The formulas on left-hand side of the turnstile are called the antecedent, and the formulas on right-hand side are called the succedent or consequent; together they are called cedents or sequents. Again, A_i and B_i are formulae, and n and k are nonnegative integers, that is, the left-hand-side or the right-hand-side (or neither or both) may be empty. As in natural deduction, theorems are those B where \vdash B is the conclusion of a valid proof.
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In focused systems for classical and Intuitionistic logic, the use of backtracking can be simulated by pseudo-contraction. Let \uparrow and \downarrow denote change of polarity, the former making a formula negative, and the latter positive; and call a formula with an arrow neutral. Recall that \lor is positive, and consider the neutral polarized sequent \downarrow \uparrow \phi \lor \psi \implies \uparrow \phi \lor \psi, which is interpreted as the actual sequent \phi \lor \psi \implies \phi \lor \psi. For neutral sequents such as this, the focused system forces on to make an explicit choice of which formula to focus on, denoted by \langle \, \rangle .
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Historically, sequents have been introduced by Gerhard Gentzen in order to specify his famous sequent calculus., . In his German publication he used the word "Sequenz". However, in English, the word "sequence" is already used as a translation to the German "Folge" and appears quite frequently in mathematics.
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To clarify this, consider the example ' B ∧ A, C ∧ ¬A ⊢ '. This is a valid sequent because either B ∧ A is false or C ∧ ¬A is false. But neither of these expressions is a contradiction in isolation. It is the conjunction of these two expressions which is a contradiction.
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With its failure in office automation products, Informix refocused on the growing database server market. In 1994, as part of a collaboration with Sequent Computer Systems, Informix released its version 6.00 database server, which featured its new Dynamic Scalable Architecture, DSA. DSA involved a major rework of the core engine of the product, supporting both horizontal parallelism and vertical parallelism, and based on a multi- threaded core well suited towards the symmetric multiprocessing systems that Sequent pioneered and that major vendors like Sun Microsystems and Hewlett- Packard would eventually follow up on. The two forms of parallelism made the product capable of market-leading levels of scalability, both for OLTP and data warehousing.
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Lattner studied computer science at the University of Portland, Oregon, graduating in 2000. While in Oregon, he worked as an operating system developer, enhancing Sequent Computer Systems's DYNIX/ptx. He is married to compiler engineer Tanya Lattner, who co-founded and is president and COO of the LLVM Foundation since 2015.
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Consequently, it supports local and remote procedure call, rendezvous, message passing, dynamic process creation, multicast, semaphores and shared memory. Version 2.2 has been ported to the Apollo, DECstation, Data General AViiON, HP 9000 Series 300, Multimax, NeXT, PA-RISC, RS/6000, Sequent Symmetry, SGI IRIS, Sun-3, Sun-4 and others.
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There are several types of proof calculi. The most popular are natural deduction, sequent calculi (i.e., Gentzen type systems), Hilbert systems, and semantic tableaux or trees. A given proof procedure will target a specific proof calculus, but can often be reformulated so as to produce proofs in other proof styles.
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Algorithms for compression of sequent calculus proofs include Cut-introduction and Cut- elimination. Algorithms for compression of propositional resolution proofs include RecycleUnits,Bar-Ilan, O.; Fuhrmann, O.; Hoory, S. ; Shacham, O. ; Strichman, O. Linear-time Reductions of Resolution Proofs. Hardware and Software: Verification and Testing, p. 114–128, Springer, 2011.
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A screenshot of the login sequence from TorilMUD TorilMUD is set in the Forgotten Realms Dungeons & Dragons campaign setting. (Toril is the name of the planet where the continent Faerûn, which "Forgotten Realms" refers to, is located.) Its technical infrastructure is based on the Sequent derivative of the DikuMUD codebase.
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The modus ponens rule may be written in sequent notation as :P \to Q,\; P\;\; \vdash\;\; Q where P, Q and P → Q are statements (or propositions) in a formal language and ⊢ is a metalogical symbol meaning that Q is a syntactic consequence of P and P → Q in some logical system.
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Even Keima acknowledged her as a genius. But, because of her talent, there is nothing that truly interest her and thus creates a gap in her heart. After she is captured by Keima, from the sequent of events, she becomes addicted to gal games and becomes famous in gal game world as "".
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Entailment differs from implication in that whereas the latter is a binary operation that returns a value in a Boolean algebra, the former is a binary relation which either holds or does not hold. In this sense entailment is an external form of implication, meaning external to the Boolean algebra, thinking of the reader of the sequent as also being external and interpreting and comparing antecedents and succedents in some Boolean algebra. The natural interpretation of \vdash is as ≤ in the partial order of the Boolean algebra defined by x ≤ y just when x∨y = y. This ability to mix external implication \vdash and internal implication → in the one logic is among the essential differences between sequent calculus and propositional calculus.
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The rule of cut is different: it states that, when a formula A can be concluded and this formula may also serve as a premise for concluding other statements, then the formula A can be "cut out" and the respective derivations are joined. When constructing a proof bottom-up, this creates the problem of guessing A (since it does not appear at all below). The cut-elimination theorem is thus crucial to the applications of sequent calculus in automated deduction: it states that all uses of the cut rule can be eliminated from a proof, implying that any provable sequent can be given a cut-free proof. The second rule that is somewhat special is the axiom of identity (I).
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This section introduces the rules of the sequent calculus LK as introduced by Gentzen in 1934. (LK, unintuitively, stands for "klassische Prädikatenlogik".) A (formal) proof in this calculus is a sequence of sequents, where each of the sequents is derivable from sequents appearing earlier in the sequence by using one of the rules below.
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Scott Morton co-founded three companies in the fields of Information and Control Systems and is active as an Angel investor.Michael S. Scott Morton: Reflections of Decision Support Pioneers on dssresources.com. Accessed November 2013. He has previously served on the boards of Index Systems Inc; Emhart Corporation; ICL Plc; Sequent Computer Systems; Genrad Corporation, and Merrill Corporation.
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Gerhard Karl Erich Gentzen (November 24, 1909 – August 4, 1945) was a German mathematician and logician. He made major contributions to the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. He died of starvation in a Soviet prison camp in Prague in 1945, having been interned as a German national after the Second World War.
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Due to the deterministic behaviour, uniform proof-search has been used as the control mechanism defining the programming language paradigm of logic programming. Occasionally, uniform proof-search is implemented in a variant of the sequent calculus for the given logic where context management is automatic thereby increasing the fragment for which one can define a logic programming langue.
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Deep inference names a general idea in structural proof theory that breaks with the classical sequent calculus by generalising the notion of structure to permit inference to occur in contexts of high structural complexity. The term deep inference is generally reserved for proof calculi where the structural complexity is unbounded; in this article we will use non-shallow inference to refer to calculi that have structural complexity greater than the sequent calculus, but not unboundedly so, although this is not at present established terminology. Deep inference is not important in logic outside of structural proof theory, since the phenomena that lead to the proposal of formal systems with deep inference are all related to the cut-elimination theorem. The first calculus of deep inference was proposed by Kurt Schütte,Kurt Schütte.
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But neither of these expressions is a tautology in isolation. It is the disjunction of these two expressions which is a tautology. Similarly, a sequent of the form ' α, β ⊢ ', for logical formulas α and β, means that either α is false or β is false. But it does not mean that either α is a contradiction or β is a contradiction.
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The assertion symbol in sequents originally meant exactly the same as the implication operator. But over time, its meaning has changed to signify provability within a theory rather than semantic truth in all models. In 1934, Gentzen did not define the assertion symbol ' ⊢ ' in a sequent to signify provability. He defined it to mean exactly the same as the implication operator ' ⇒ '.
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In this interpretation the cut rule of the sequent calculus corresponds to composition in the category. Boolean and Heyting algebras enter this picture as special categories having at most one morphism per homset, i.e., one proof per entailment, corresponding to the idea that existence of proofs is all that matters: any proof will do and there is no point in distinguishing them.
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The firm has invested across multiple sectors over the years and is focused on enterprise software, IT security, consumer internet, mobile, e-commerce, healthcare, and IT-enabled healthcare services. Select portfolio companies include: Arkose Labs, Box, HeartFlow, HotelTonight, Inari Medical, Inspire Medical Systems, Intersect ENT, Luminate, Omada Health, Pluto TV, Prevoty, Sequent, ThreatMetrix and Zerto.“OUR PORTFOLIO.” USVP, www.usvp.com/portfolio/.
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Alliant Computer Systems was a computer company that designed and manufactured parallel computing systems. Together with Pyramid Technology and Sequent Computer Systems, Alliant's machines pioneered the symmetric multiprocessing market. One of the more successful companies in the group, over 650 Alliant systems were produced over their lifetime. The company was hit by a series of financial problems and went bankrupt in 1992.
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And furthermore: "A proof in a calculus of sequents can be looked upon as an instruction on how to construct a corresponding natural deduction."See , for this and further details of interpretation. In other words, the assertion symbol is part of the object language for the sequent calculus, which is a kind of meta-calculus, but simultaneously signifies deducibility in an underlying natural deduction system.
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Avron's research interests include proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of mathematical logic in computer science and artificial intelligence. Arnon made a significant contribution to the theory of automated reasoning with his introduction of hypersequents, a generalization of the sequent calculus. Avron also introduced the use of bilattices to paraconsistent logic, and made contributions to predicative set theory and geometry.
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John McAdam is a technology executive. McAdam holds a B.Sc. in computer science from the University of Glasgow, Scotland. From January 1995 until August 1999, he served as the president and chief operating officer of Sequent Computer Systems, a manufacturer of high-end open systems, which was sold to IBM in September 1999. McAdam then served as general manager of the web server sales business at IBM.
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California-based Intel, Oregon's largest private for- profit employer, has its largest concentration of employees in the county, mainly in Hillsboro. Other technology companies include Electro Scientific Industries, FEI Company, Qorvo, Tektronix, SolarWorld, Planar Systems, and EPSON. Nike, one of two Fortune 500 corporations based in Oregon, has its headquarters in Washington County. Until it was acquired by IBM, Sequent Computer Systems was headquartered near Nike.
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JapeRichard Bornat, "Proof and Disproof in Formal Logic: An Introduction for Programmers." is a configurable, graphical proof assistant, originally developed by Richard Bornat at Queen Mary, University of London and Bernard Sufrin the University of Oxford. It allows user to define a logic, decide how to view proofs, and much more. It works with variants of the sequent calculus and natural deduction. It is claimedC.
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Teradata acquired Britton Lee — renamed ShareBase — in June, 1990. Others disagree, considering appliances as a "disruptive technology" for Teradata Additional vendors, including Tandem Computers, and Sequent Computer Systems also offered MPP architectures in the 1980s. Open source and commodity computing components aided a re-emergence of MPP data warehouse appliances. Advances in technology reduced costs and improved performance in storage devices, multi-core CPUs and networking components.
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The disjunction introduction rule may be written in sequent notation: : P \vdash (P \lor Q) where \vdash is a metalogical symbol meaning that P \lor Q is a syntactic consequence of P in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic: :P \to (P \lor Q) where P and Q are propositions expressed in some formal system.
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Pomset logic was proposed by Christian Retoré in a semantic formalism with two dual sequential operators existing together with the usual tensor product and par operators of linear logic, the first logic proposed to have both commutative and noncommutative operators. A sequent calculus for the logic was given, but it lacked a cut- elimination theorem; instead the sense of the calculus was established through a denotational semantics.
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Fred Thiel (born 1960) is an American business executive and the current CEO of Thiel Advisors. Thiel is the former CEO of GameSpy, Local Corporation, and Lantronix. Thiel serves as chairman of the board of the Young Presidents' Organization's technology network and Fintech subnetwork. He also serves on the boards of several other companies including Marathon Patent Group, Dorner Manufacturing, Oden Technologies, and Sequent Software.
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In the sequent calculus for an intuitionistic logic, the uniform proofs can be characterised as those in which the upward reading performs all right rules before the left rules. Typically, uniform proofs are not complete for the logic i.e., not all sequents or formulas admit a uniform proof, so one considers fragments where they are complete e.g., the hereditary Harrop fragment of Intuitionistic logic.
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In August 2007, Gaille departed Oxy with private equity backing to found the Gaille Group (www.gaillegroup.com), which has launched and incubated a series of businesses in the energy and financial services sectors. The Gaille Group's ventures have included the founding of Sequent Asset Management, LLC ($400 million in assets raised from 2008-2010) and the acquisition of petroleum concession rights in several African nations.
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In the extreme case where the list of antecedent formulas of a sequent is empty, the consequent is unconditional. This differs from the simple unconditional assertion because the number of consequents is arbitrary, not necessarily a single consequent. Thus for example, ' ⊢ B1, B2 ' means that either B1, or B2, or both must be true. An empty antecedent formula list is equivalent to the "always true" proposition, called the "verum", denoted "⊤".
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The notion of analytic proof was introduced into proof theory by Gerhard Gentzen for the sequent calculus; the analytic proofs are those that are cut-free. His natural deduction calculus also supports a notion of analytic proof, as was shown by Dag Prawitz; the definition is slightly more complex--the analytic proofs are the normal forms, which are related to the notion of normal form in term rewriting.
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The Sequent DikuMUD enhanced both the codebase and database of the DikuMUD Gamma version. The codebase enhancements increased the number of spells and guilds, plus supporting multiple active zones, chat channels and guilds. It added several new playing areas with shorter text descriptions that was designed to be accessible to users with sensory disabilities. DikuMUD had been a great leveler and allowed people from diverse regions to connect and play together.
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The term tends to be used quite a bit when comparing computer hardware. During the latter 1990s, the price–performance ratios of midrange and large mainframe systems fell tremendously in comparison to a number of smaller microcomputers handling the same load. Many companies were forced out of the industry as this happened, including DEC, Data General and many multiprocessor vendors such as Sequent Computer Systems and Pyramid Technology.
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Sequent calculi and systems of natural deduction have been developed for several modal logics, but it has proven hard to combine generality with other features expected of good structural proof theories, such as purity (the proof theory does not introduce extra-logical notions such as labels) and analyticity (the logical rules support a clean notion of analytic proof). More complex calculi have been applied to modal logic to achieve generality.
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In sequent calculus, the completeness of atomic initial sequents states that initial sequents (where is an arbitrary formula) can be derived from only atomic initial sequents (where is an atomic formula). This theorem plays a role analogous to eta expansion in lambda calculus, and dual to cut- elimination and beta reduction. Typically it can be established by induction on the structure of , much more easily than cut-elimination.
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The court also ruled that "SCO is obligated to recognize Novell's waiver of SCO's claims against IBM and Sequent". After the ruling Novell announced they have no interest in suing people over Unix and stated "We don't believe there is Unix in Linux". In an order entered on September 21, 2007, Judge Kimball administratively closed the case of SCO v. IBM due to SCO filing for bankruptcy on September 14, 2007.
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Although doing little of practical value, the goal of making a microkernel was realized. This was soon followed by versions on the IBM RT PC and for Sun Microsystems 68030-based workstations, proving the system's portability. By 1987 the list included the Encore Multimax and Sequent Balance machines, testing Mach's ability to run on multiprocessor systems. A public Release 1 was made that year, and Release 2 followed the next year.
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Prior to 1993, Talwalkar held senior engineering and marketing management positions at Sequent Computer Systems (now part of IBM), Bipolar Integrated Technology and Lattice Semiconductor. Talwalkar served in many upper management positions at Intel from 1993 to 2005. His career at Intel started as a Server Development Engineering and Program manager in 1993. He then served as vice president and general manager for the Intel Enterprise Platform and Service Division.
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Gaille has frequently served as an executive and/or a member of the Board of Directors of both public and private companies, including as Managing Director & General Counsel of Sequent Asset Management and as the Chief Compliance Officer, General Counsel, and Corporate Secretary of a NASDAQ-listed energy company (ZaZa Energy Corporation). His legal practice (GAILLE PLLC - www.gaillelaw.com) focuses on outside general counsel representation for entrepreneurs and global energy law.
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Every cell type, especially cancer cells, are capable of undergoing apoptosis, a process in which the plasma membrane undergoes blebbing followed by orderly deconstruction of cells into apoptotic bodies. Cancer stem cells have the extraordinary ability to construct blebbishields from these apoptotic bodies by bleb-bleb fusion and form stem cell spheres/cellular transformation by sub-sequent blebbishield-blebbishield fusion.Jinesh GG, Kamat AM. Blebbishield emergency program: an apoptotic route to cellular transformation. Cell Death Differ.
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The disjunctive syllogism rule may be written in sequent notation: : P \lor Q, \lnot P \vdash Q where \vdash is a metalogical symbol meaning that Q is a syntactic consequence of P \lor Q, and \lnot P in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic: : ((P \lor Q) \land eg P) \to Q where P, and Q are propositions expressed in some formal system.
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The Geometry of Interaction (GoI) was introduced by Jean-Yves Girard shortly after his work on linear logic. In linear logic, proofs can be seen as various kinds of networks as opposed to the flat tree structures of sequent calculus. To distinguish the real proof nets from all the possible networks, Girard devised a criterium involving trips in the network. Trips can in fact be seen as some kind of operator acting on the proof.
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According to the rules in the sequent calculus, formulas are canonically put into one of two classes called positive and negative e.g., in LK and LJ the formula \phi \lor \psi is positive. The only freedom is over atoms are assigned a polarity freely. For negative formulas provability is invariant under the application of a right rule; and, dually, for a positive formulas provability is invariant under the application of a left rule.
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Kris Kortright, a developer from the MUD Black Knights Realm, founded Sojourn, set in the Forgotten Realms campaign setting for the Dungeons & Dragons role-playing game, in 1993, along with Tim Devlin and John Bashaw. Sojourn was based on the Sequent codebase, the Epic spell system, and areas from Black Knights Realm. The City of Waterdeep was the first zone built entirely for Sojourn. Brad McQuaid was an avid player of Sojourn.
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The big success of the Series 32000 was in the laser printer market, where the NS32CG16 with microcoded BitBlt instructions had very good price/performance and was adopted by large companies like Canon. By the mid-1980s, Sequent introduced the first SMP server-class computer using the NS 32032. This was one of the design's few wins, and it disappeared in the late 1980s. The MIPS R2000 (1984) and R3000 (1989) were highly successful 32-bit RISC microprocessors.
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Roloff worked as a computer programmer for Silicon Valley companies including Altos Computer Systems in the late 1980s. He sold systems software to Fortune 500 companies. A friend encouraged him to take a job with Sequent Computer Systems, which was headquartered in Beaverton, Oregon, in order to escape the long work hours and stress of Silicon Valley. Matt and his wife Amy relocated to the Portland area in 1990, while she was pregnant with twins Jeremy and Zachary.
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One sees here again a symmetry because of the disjunctive semantics on the right hand side. If the left side is empty, then one or more right-side propositions must be true. If the right side is empty, then one or more of the left-side propositions must be false. The doubly extreme case ' ⊢ ', where both the antecedent and consequent lists of formulas are empty is "not satisfiable".. In this case, the meaning of the sequent is effectively ' ⊤ ⊢ ⊥ '.
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In a series of seminars in 1961 and 1962 Prawitz gave a comprehensive summary of natural deduction calculi, and transported much of Gentzen's work with sequent calculi into the natural deduction framework. His 1965 monograph Natural deduction: a proof-theoretical study, . was to become a reference work on natural deduction, and included applications for modal and second-order logic. In natural deduction, a proposition is deduced from a collection of premises by applying inference rules repeatedly.
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Proof theory is the study of formal proofs in various logical deduction systems. These proofs are represented as formal mathematical objects, facilitating their analysis by mathematical techniques. Several deduction systems are commonly considered, including Hilbert-style deduction systems, systems of natural deduction, and the sequent calculus developed by Gentzen. The study of constructive mathematics, in the context of mathematical logic, includes the study of systems in non-classical logic such as intuitionistic logic, as well as the study of predicative systems.
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A deductive system is used to demonstrate, on a purely syntactic basis, that one formula is a logical consequence of another formula. There are many such systems for first-order logic, including Hilbert-style deductive systems, natural deduction, the sequent calculus, the tableaux method, and resolution. These share the common property that a deduction is a finite syntactic object; the format of this object, and the way it is constructed, vary widely. These finite deductions themselves are often called derivations in proof theory.
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The sequent layers consist of fortifications built by the Indo-Greek kings. A stone wall in Hellenistic style was built around the city, with equidistant quadrangular bastions, all according to Attic measurements. Ruins of palatial quarters as well as areas related to the Buddhist have been unearthed During the Kushan period, Barikot experienced rapid development with the creation of building dedicated to workmanship. Barikot has become a very important archaeological site, rivaling Taxila, for the study of history in northern Pakistan.
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Since every formula in the antecedent (the left side) must be true to conclude the truth of at least one formula in the succedent (the right side), adding formulas to either side results in a weaker sequent, while removing them from either side gives a stronger one. This is one of the symmetry advantages which follows from the use of disjunctive semantics on the right hand side of the assertion symbol, whereas conjunctive semantics is adhered to on the left hand side.
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Two systems were designed, the BiiN 20 was an entry-level machine with one or two processors, and an interesting battery-backed disk-cache. The larger BiiN 60 was similar, but supported up to eight CPUs. Both machines could be used in larger multi- machine systems. One interesting feature of the BiiN was that the CPU sets could be used to provide either fault tolerance, as in the Tandem systems, or parallel processing, as in the Pyramid and Sequent systems.
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Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions. In sequent calculi this property can be captured by an inference rule called weakening, or sometimes thinning, and in such systems one may say that entailment is monotone if and only if the rule is admissible. Logical systems with this property are occasionally called monotonic logics in order to differentiate them from non-monotonic logics.
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Noncommutative logic is an extension of linear logic which combines the commutative connectives of linear logic with the noncommutative multiplicative connectives of the Lambek calculus. Its sequent calculus relies on the structure of order varieties (a family of cyclic orders which may be viewed as a species of structure), and the correctness criterion for its proof nets is given in terms of partial permutations. It also has a denotational semantics in which formulas are interpreted by modules over some specific Hopf algebras.
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A sequent calculus is often shown to have the focusing property by working in a related calculus where polarity explicitly controls which rules apply. Proofs in such systems are in focused, unfocused, or neutral phases, where the first two are characterised by hereditary decomposition; and the latter by forcing a choice of focus. One of the most important operational behaviours a procedure can undergo is backtracking i.e., returning to an earlier stage in the computation where a choice was made.
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The conjunction elimination sub- rules may be written in sequent notation: : (P \land Q) \vdash P and : (P \land Q) \vdash Q where \vdash is a metalogical symbol meaning that P is a syntactic consequence of P \land Q and Q is also a syntactic consequence of P \land Q in logical system; and expressed as truth-functional tautologies or theorems of propositional logic: :(P \land Q) \to P and :(P \land Q) \to Q where P and Q are propositions expressed in some formal system.
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In mathematical logic, the cut rule is an inference rule of sequent calculus. It is a generalisation of the classical modus ponens inference rule. Its meaning is that, if a formula A appears as a conclusion in one proof and a hypothesis in another, then another proof in which the formula A does not appear can be deduced. In the particular case of the modus ponens, for example occurrences of man are eliminated of Every man is mortal, Socrates is a man to deduce Socrates is mortal.
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Novell ruled on summary judgment that Novell, not the SCO Group, is the rightful owner of the copyrights covering the Unix operating system. The court also ruled that "SCO is obligated to recognize Novell's waiver of SCO's claims against IBM and Sequent". After the ruling, Novell announced they have no interest in suing people over Unix and stated "We don't believe there is Unix in Linux". The final district court ruling, on November 20, 2008, affirmed the summary judgment, and added interest payments and a constructive trust.
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The disjunction elimination rule may be written in sequent notation: : (P \to Q), (R \to Q), (P \lor R) \vdash Q where \vdash is a metalogical symbol meaning that Q is a syntactic consequence of P \to Q, and R \to Q and P \lor R in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic: :(((P \to Q) \land (R \to Q)) \land (P \lor R)) \to Q where P, Q, and R are propositions expressed in some formal system.
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Block diagram of one example Different versions and derivatives of SCI were implemented by companies like Dolphin Interconnect Solutions, Convex, Data General AViiON (using cache controller and link controller chips from Dolphin), Sequent and Cray Research. Dolphin Interconnect Solutions implemented a PCI and PCI- Express connected derivative of SCI that provides non-coherent shared memory access. This implementation was used by Sun Microsystems for its high-end clusters, Thales Group and several others including volume applications for message passing within HPC clustering and medical imaging.
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In Los Angeles, Beyoncé gave a full-length performance of the song, dressed in a long sequent number that flowed straight down to her feet. It was executed with several female and male backup dancers, and live instrumentation. Jon Pareles of The New York Times praised the performance, stating: "Beyoncé needs no distractions from her singing, which can be airy or brassy, tearful or vicious, rapid-fire with staccato syllables or sustained in curlicued melismas. But she was in constant motion, strutting in costumes [...]".
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The biconditional introduction rule may be written in sequent notation: :(P \to Q), (Q \to P) \vdash (P \leftrightarrow Q) where \vdash is a metalogical symbol meaning that P \leftrightarrow Q is a syntactic consequence when P \to Q and Q \to P are both in a proof; or as the statement of a truth- functional tautology or theorem of propositional logic: :((P \to Q) \land (Q \to P)) \to (P \leftrightarrow Q) where P, and Q are propositions expressed in some formal system.
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The constructive dilemma rule may be written in sequent notation: : (P \to Q), (R \to S), (P \lor R) \vdash (Q \lor S) where \vdash is a metalogical symbol meaning that Q \lor S is a syntactic consequence of P \to Q, R \to S, and P \lor R in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic: :(((P \to Q) \land (R \to S)) \land (P \lor R)) \to (Q \lor S) where P, Q, R and S are propositions expressed in some formal system.
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The absorption rule may be expressed as a sequent: : P \to Q \vdash P \to (P \land Q) where \vdash is a metalogical symbol meaning that P \to (P \land Q) is a syntactic consequence of (P \rightarrow Q) in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as: :(P \to Q) \leftrightarrow (P \to (P \land Q)) where P, and Q are propositions expressed in some formal system.
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In single-conclusion sequent calculi, modus ponens is the Cut rule. The cut-elimination theorem for a calculus says that every proof involving Cut can be transformed (generally, by a constructive method) into a proof without Cut, and hence that Cut is admissible. The Curry–Howard correspondence between proofs and programs relates modus ponens to function application: if f is a function of type P → Q and x is of type P, then f x is of type Q. In artificial intelligence, modus ponens is often called forward chaining.
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Some recruits participated in CCP and sequent revolutionary movements in China. Outstanding members, like Le Hong Phong, Le Quang Dat, and Tran Phu, were even sent to Whampoa Military Academy or the University for the Toilers of the East (Soviet Union) for further military and political training. To propagandize their revolutionary ideas and attract young people, the League published pamphlets and periodicals (in Vietnamese) on different political subjects. The Road to Revolution (Duong Kach Menh), a training manual for the League's members, was a collection of Nguyen Ai Quoc's lecture notes for the training course.
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Many students from Cochinchina participated in the League, meeting up with their peers from Tonkin and Annam in Guangzhou. In March 1927, the fourth wave of trainees was gathering in Guangzhou; but unfortunately, Chiang Kai-shek’s April 12 coup and his sequent persecution of communists crushed their training. Nguyen Ai Quoc fled to Moscow in June 1927. Main leaders like Ho Tung Mau and Le Hong Son were imprisoned. To escape KMT’s repression, the headquarters of the Revolutionary Youth League had to be moved to Wuhan and later to Hong Kong (Kowloon).
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In 1996, X/Open and the new OSF merged to form the Open Group. COSE work such as the Single UNIX Specification, the current standard for branded Unix, is now the responsibility of the Open Group, which also controls the current POSIX standards. Since then, occasional bursts of Unix factionalism have broken out, such as the HP/SCO "3DA" alliance in 1995, and Project Monterey in 1998, a teaming of IBM, SCO, Sequent and Intel which was followed by litigation (SCO v. IBM) between IBM and the new SCO, formerly Caldera.
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TATA Elxsi was a minicomputer manufacturing company established in the late 1970s along with a host of other competitors (Trilogy Systems, Sequent, Convex Computer) in Silicon Valley, USA. The Elxsi processor was an Emitter Coupled Logic (ECL) design that featured a 50-nanosecond clock, a 25-nanosecond backpanel bus, IEEE floating-point arithmetic and a 64-bit architecture. It allowed multiple processors to communicate over a common bus called the Gigabus, believed to be the first company to do so. The operating system was a message based operating system called EMBOS.
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Analyzing the development of the natural sciences, he sought to uncover their specific "logic." According to Orlov, the laws of thought should be treated as formal rules, bounded by the laws of identity and contradiction. (When Orlov wrote this, the invention of natural deduction, the sequent calculus, and the semantic tableaux all lay in the future.) We must seek the semantic relation between antecedent and consequent. The main "contradiction of logic" manifests itself in the linkage of premise and corollary, and requires a logic different from the traditional one.
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Retrieved December 21, 2010. Schussel has authored the 1985 book Data Management: Past, present and future (Critical technology report), as well as co-authored the 1994 book Rightsizing Information Systems (Professional Reference). He has also authored or co- authored over 100 articles or columns in leading computer industry journals such as Computerworld, Datamation, Client Server Today and Data Based Advisor. During his time at DCI, Schussel was credited as having consulted major clients such as Cullinet, Computer Associates, Revelation Technologies, Hewlett Packard, Sybase, AT&T;/NCR, DEC, Sequent Computer Systems, Borland and IBM.
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After the trial in Changsha in September 2014, the company apologized to the Chinese people, and paid one of the biggest fines in Chinese history worth ¥3bn (£300m; €350m; $490m). 4 executives of the company, including Mark Reilly, the only foreign citizens involved, were sentenced to jail. Reilly was also deported from China. The sequent US Securities and Exchange Commission investigation was settled by GSK with a $20 million civil penalty in 2016, yet the UK Serious Fraud Office failed to finish the expensive investigation which was officially ended in 2019.
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Most of the developers had their background from high-speed computer buses. Representatives from companies in the computer industry and research community included Amdahl, Apple Computer, BB&N;, Hewlett-Packard, CERN, Dolphin Server Technology, Cray Research, Sequent, AT&T;, Digital Equipment Corporation, McDonnell Douglas, National Semiconductor, Stanford Linear Accelerator Center, Tektronix, Texas Instruments, Unisys, University of Oslo, University of Wisconsin. The original intent was a single standard for all buses in the computer. The working group soon came up with the idea of using point-to-point communication in the form of insertion rings.
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In mathematical logic, focused proofs are a family of analytic proofs that arise through goal-directed proof-search, and are a topic of study in structural proof theory and reductive logic. They form the most general definition of goal-directed proof-search—in which someone chooses a formula and performs hereditary reductions until the result meets some condition. The extremal case where reduction only terminates when axioms are reached forms the sub-family of uniform proofs. A sequent calculus is said to have the focusing property when focused proofs are complete for some terminating condition.
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In either case one can safely apply rules in any order to hereditary sub-formulas of the same polarity. In the case of a right rule applied to a positive formula, or a left rule applied to a negative formula, one may result in invalid sequents e.g., in LK and LJ there is no proof of the sequent B \lor A \implies A \lor B beginning with a right rule. A calculus admits the focusing principle if when an original reduct was provable then the hereditary reducts of the same polarity are also provable.
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Conjugate, or sequent, depths are the paired depths that result upstream and downstream of a hydraulic jump, with the upstream flow being supercritical and downstream flow being subcritical. Conjugate depths can be found either graphically using a specific momentum curve or algebraically with a set of equations. Because momentum is conserved over a hydraulic jump conjugate depths have equivalent momentum, and given a discharge, the conjugate to any flow depth can be determined with an M-y diagram (Figure 6). A vertical line that crosses the M-y curve twice (i.e.
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By this time a number of other vendors, notably Sequent Computer Systems, were also introducing similar machines. The lack of lock-in now came back to haunt DG, and the rapid commoditization of the Unix market led to shrinking sales. DG did begin a minor shift toward the service industry, training their technicians for the role of implementing a spate of new x86-based servers and the new Microsoft Windows NT domain-driven, small server world. This never developed enough to offset the loss of high margin server business however.
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The concepts of Fitch-style proof, sequent calculus and natural deduction are generalizations of the concept of proof.The Cambridge Dictionary of Philosophy, deduction The theorem is a syntactic consequence of all the well-formed formulas preceding it in the proof. For a well-formed formula to qualify as part of a proof, it must be the result of applying a rule of the deductive apparatus (of some formal system) to the previous well-formed formulas in the proof sequence. Formal proofs often are constructed with the help of computers in interactive theorem proving (e.g.
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Data storage considerations for HTS platforms, Invited talk given at the EMBRACE next generation sequencing workshop in Rome, November 2009.The NGS IT notes, invited talk given at the International Workshops on Bioinformatics - 2012, Center of Genomic Sciences, National Autonomous University of Mexico (UNAM). Prior working at the University of Oslo, Magklaras has worked in various technical and scientific positions for a number of companies and organizations, including those of Sequent Computer Systems, IBM UK and Tiscali. He has held a number of professional affiliations, including those of an IEEE affiliate member, USENIX, SAGE/LOPSA and Red Hat Certified Engineer.
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Gentzen's main work was on the foundations of mathematics, in proof theory, specifically natural deduction and the sequent calculus. His cut-elimination theorem is the cornerstone of proof-theoretic semantics, and some philosophical remarks in his "Investigations into Logical Deduction", together with Ludwig Wittgenstein's later work, constitute the starting point for inferential role semantics. One of Gentzen's papers had a second publication in the ideological Deutsche Mathematik that was founded by Ludwig Bieberbach who promoted "Aryan" mathematics.Dipl.Math. Walter Tydecks, Neuere Geschichte der Mathematik in Deutschland (in German) Gentzen proved the consistency of the Peano axioms in a paper published in 1936.
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Caspases (Caspase-3, caspase-8, caspase-9) are found to have important roles in contributing the formation of blebbishields as well as sub-sequent cancer stem cell spheres. Caspase-3 plays a dual role where it is needed for induction of proper apoptosis: to activate Bax and Bak by cleavage to kill the cells and also needed for transformation from blebbishields.Jinesh GG, Molina JM, Huang L, Laing NM, Mills GB, Bar-Eli M & Kamat AM. Mitochondrial oligomers boost glycolysis in cancer stem cells to facilitate blebbishield-mediated transformation after apoptosis. Cell Death Discovery 2016 Feb;2: 20163.
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By March 2001, however, "the explosion in popularity of Linux ... prompted IBM to quietly ditch" this; all involved attempted to find a niche in the rapidly developing Linux market and moved their focus away from Monterey. Sequent was acquired by IBM in 1999. In 2000, SCO's UNIX business was purchased by Caldera Systems, a Linux distributor, who later renamed themselves the SCO Group. In the same year, IBM eventually declared Monterey dead. Intel, IBM, Caldera Systems, and others had also been running a parallel effort to port Linux to IA-64, Project Trillian, which delivered workable code in February 2000.
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The oldest zone on TorilMUD, the Lava Tubes, comes from Copper II, and the Underworld and Alterian Wilderness zones are from Black Knights Realm. Sojourn was based on the Sequent codebase, the Epic spell system, and areas from Black Knights Realm. The City of Waterdeep was the first zone built entirely for Sojourn, and remains TorilMUDs most heavily populated hometown. Brad McQuaid, with Kris’ permission, used it as the model for the city of Freeport in EverQuest. Sojourn continued until 1996, when a difference in creative vision among the staff led to the project being forked into TorilMUD and Duris: Land of Bloodlust.
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Fluid Mechanics with Engineering Applications, McGraw-Hill, New York, NY. Despite the fact that there is an energy loss, momentum across a hydraulic jump is still conserved. This means that the flow depth on either side of the jump will have the same momentum, and in this way, if the momentum and flow depth on either side of the jump is known, it is possible to determine the depth on the other side of the jump. These paired depths are known as sequent depths, or conjugate depths. The latter is valid unless the jump is caused by an external force or outside influence.
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The biconditional elimination rule may be written in sequent notation: :(P \leftrightarrow Q) \vdash (P \to Q) and :(P \leftrightarrow Q) \vdash (Q \to P) where \vdash is a metalogical symbol meaning that P \to Q, in the first case, and Q \to P in the other are syntactic consequences of P \leftrightarrow Q in some logical system; or as the statement of a truth- functional tautology or theorem of propositional logic: :(P \leftrightarrow Q) \to (P \to Q) :(P \leftrightarrow Q) \to (Q \to P) where P, and Q are propositions expressed in some formal system.
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They were developed commercially during the 1990s by Unisys, Convex Computer (later Hewlett-Packard), Honeywell Information Systems Italy (HISI) (later Groupe Bull), Silicon Graphics (later Silicon Graphics International), Sequent Computer Systems (later IBM), Data General (later EMC), and Digital (later Compaq, then HP, now HPE). Techniques developed by these companies later featured in a variety of Unix-like operating systems, and to an extent in Windows NT. The first commercial implementation of a NUMA- based Unix system was the Symmetrical Multi Processing XPS-100 family of servers, designed by Dan Gielan of VAST Corporation for Honeywell Information Systems Italy.
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The destructive dilemma rule may be written in sequent notation: : (P \to Q), (R \to S), ( eg Q \lor eg S) \vdash ( eg P \lor eg R) where \vdash is a metalogical symbol meaning that eg P \lor eg R is a syntactic consequence of P \to Q, R \to S, and eg Q \lor eg S in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic: :(((P \to Q) \land (R \to S)) \land ( eg Q \lor eg S)) \to ( eg P \lor eg R) where P, Q, R and S are propositions expressed in some formal system.
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The second chapter introduces the sequent calculus, a method of making sound deductions in second-order logic, and its incompleteness. The third continues the topic of second-order logic, showing how to formulate Peano arithmetic in it, and using Gödel's first incompleteness theorem to provide a second proof of incompleteness of second-order logic. Chapter four formulates a non- standard semantics for second-order logic (from Henkin), in which quantification over relations is limited to only the definable relations. It defines this semantics in terms of "second-order frames" and "general structures", constructions that will be used to formulate second-order concepts within many-sorted logic.
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Speculatively, the Curry–Howard correspondence might be expected to lead to a substantial unification between mathematical logic and foundational computer science: Hilbert-style logic and natural deduction are but two kinds of proof systems among a large family of formalisms. Alternative syntaxes include sequent calculus, proof nets, calculus of structures, etc. If one admits the Curry–Howard correspondence as the general principle that any proof system hides a model of computation, a theory of the underlying untyped computational structure of these kinds of proof system should be possible. Then, a natural question is whether something mathematically interesting can be said about these underlying computational calculi.
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There is some freedom of choice regarding the technical details of how sequents and structural rules are formalized. As long as every derivation in LK can be effectively transformed to a derivation using the new rules and vice versa, the modified rules may still be called LK. First of all, as mentioned above, the sequents can be viewed to consist of sets or multisets. In this case, the rules for permuting and (when using sets) contracting formulae are obsolete. The rule of weakening will become admissible, when the axiom (I) is changed, such that any sequent of the form \Gamma , A \vdash A , \Delta can be concluded.
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For example, \Gamma\vdash\Sigma can be read as asserting that it cannot be the case that every formula in Γ is true and every formula in Σ is false (this is related to the double-negation interpretations of classical intuitionistic logic, such as Glivenko's theorem). In any case, these intuitive readings are only pedagogical. Since formal proofs in proof theory are purely syntactic, the meaning of (the derivation of) a sequent is only given by the properties of the calculus that provides the actual rules of inference. Barring any contradictions in the technically precise definition above we can describe sequents in their introductory logical form.
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A propositional proof system is given as a proof-verification algorithm P(A,x) with two inputs. If P accepts the pair (A,x) we say that x is a P-proof of A. P is required to run in polynomial time, and moreover, it must hold that A has a P-proof if and only if it is a tautology. Examples of propositional proof systems include Sequent calculus, Resolution, Cutting Planes and Frege system. Strong mathematical theories such as ZFC induce propositional proof systems as well: a proof of a tautology \tau in a propositional interpretation of ZFC is a ZFC-proof of a formalized statement '\tau is a tautology'.
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The court also ruled that "SCO is obligated to recognize Novell's waiver of SCO's claims against IBM and Sequent". After the ruling, Novell announced they have no interest in suing people over Unix and stated, "We don't believe there is Unix in Linux".Novell Won't Pursue Unix Copyrights 15 August 2007 SCO successfully got the 10th Circuit Court of Appeals to partially overturn this decision on 24 August 2009 which sent the lawsuit back to the courts for a jury trial.Novell.com 24 August 2009 On 30 March 2010, following a jury trial, Novell, and not The SCO Group, was "unanimously [found]" to be the owner of the UNIX and UnixWare copyrights.
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Alessio Guglielmi proposed a variation of Retoré's calculus, BV, in which the two noncommutative operations are collapsed onto a single, self-dual, operator, and proposed a novel proof calculus, the calculus of structures to accommodate the calculus. The principal novelty of the calculus of structures was its pervasive use of deep inference, which it was argued is necessary for calculi combining commutative and noncommutative operators; this explanation concurs with the difficulty of designing sequent systems for pomset logic that have cut-elimination. Lutz Strassburger devised a related system, NEL, also in the calculus of structures in which linear logic with the mix rule appears as a subsystem.
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On the large side, the 3B4000 (1986) was the first "snugly coupled" multiprocessor (the "network in a box"), containing the A-BUS which supported 16 large single-board computer (SBC) circuit panels, and featured the first SVR4 distributed UNIX kernel (codenamed "Apache", nothing to do with the open source project started in the 1990s). Although the SBCs did not share address space, the UNIX kernel was distributed across all SBCs in a single virtual image. The StarServer E ("Enterprise" or SSE) was an Intel-based symmetric multiprocessor (SMP), introduced just after the Sequent system, making the SSE the world's second SMP UNIX system, and the first to run System V.4. It featured 4 Intel i486 CPUs.
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Entailment as external implication between two terms expresses a metatruth outside the language of the logic, and is considered part of the metalanguage. Even when the logic under study is intuitionistic, entailment is ordinarily understood classically as two-valued: either the left side entails, or is less-or-equal to, the right side, or it is not. Similar but more complex translations to and from algebraic logics are possible for natural deduction systems as described above and for the sequent calculus. The entailments of the latter can be interpreted as two-valued, but a more insightful interpretation is as a set, the elements of which can be understood as abstract proofs organized as the morphisms of a category.
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Players with auditory disabilities were often not fluent in spoken or written English, and have a similar problem in that they are unable to read as fast as their hearing peers. As a result, an avid DikuMUD player who had friends with visual disabilities at University of California at Berkeley, enhanced the DikuMUD codebase and database to make it more accessible to people with visual and aural disabilities. This DikuMUD, called Sequent, improved accessibility in by creating an alternate description in each room that consisted of shorter and more direct descriptions of the world, which reduced the amount of text by about half. Players with visual disabilities could then quickly scan for relevant keywords, and act more quickly.
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There was a minor controversy in late 1999 and early 2000 regarding whether the commercial MMORPG EverQuest, developed by Verant Interactive, had derived its code from DikuMUD. It began at the Re:Game gaming conference in 1999, where the Director of Product Development for EverQuest, Bernard Yee, allegedly stated that EverQuest was "based on Dikumud". He did not specify whether he meant the code itself was derived from DikuMUD, or if it just had a similar feeling. Some attendees had understood it to mean the former, given that the chief designer, Brad McQuaid was an avid player of SojournMUD and TorilMUD that was based on the Sequent DikuMUD derivative, and reported to that effect on Usenet.
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Encore Computer was an early pioneer in the parallel computing market, based in Marlborough, Massachusetts. Although offering a number of system designs beginning in 1985, they were never as well known as other companies in this field such as Pyramid Technology, Alliant, and the most similar systems Sequent and FLEX. Encore was founded in 1983 by: Kenneth Fisher, former CEO of Prime Computer; Gordon Bell, an engineering vice president from Digital Equipment Corporation responsible for the development of the VAX; and, Henry Burkhardt III, co-founder of Data General and Kendall Square Research. Their goal was to build massively parallel machines from commodity processors; their first design, the Multimax, was released in September 1985.
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Functioning daughters consisted of different amino acid sequences. Whereas the iron–sulfur world identifies a circular pathway as the most simple, the thermosynthesis hypothesis does not even invoke a pathway: ATP synthase's binding change mechanism resembles a physical adsorption process that yields free energy, rather than a regular enzyme's mechanism, which decreases the free energy. The described first protein may be simple in the sense that is requires only a short sequence of conserved amino acid residues, a sequent sufficient for the appropriate catalytic cleft. In contrast, it has been claimed that the emergence of cyclic systems of protein catalysts such as required by fermentation is implausible because of the length of many required sequences.
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Semantic tableaux are a proof method for formal systems — cf. Gentzen's natural deduction and sequent calculus, or even J. Alan Robinson's resolution and Hilbert's axiomatic systems. It is considered by many to be intuitively simple, particularly for students not acquainted with the study of logic (Wilfrid Hodges for example presents semantic tableaux in his introductory textbook, Logic, and Melvin Fitting does the same in his presentation of first-order logic for computer scientists, First-order logic and automated theorem proving). One starts out with the intention of proving that a certain set \Gamma \, of formulae imply another formula \varphi\, , given a set of rules determined by the semantics of the formulae's connectives (and quantifiers, in first-order logic).
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See also Unix wars. Throughout the 1980s and early 1990s, AT&T-CS; produced many "firsts" in the computer world, besides the UNIX operating system itself. The 3B5 and 3B15 were the first computers to be designed with the 32-bit WE 32000 microprocessor, and the 3B15 was the first computer to run a demand-paging version of Unix. There was a project, codenamed "Alice", to develop the 3B5 into an asymmetric multiprocessor with 3 CPUs, but this was canceled in favor of the demand paging 3B15 project, and a few of the "Alice" participants left the company and went to Sequent Computer Systems. The 3B5, 3B15, and 3B20S and 3B20D were aimed at the former AT&T; subsidiaries the RBOCs.
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In a Hilbert system, the premises and conclusion of the inference rules are simply formulae of some language, usually employing metavariables. For graphical compactness of the presentation and to emphasize the distinction between axioms and rules of inference, this section uses the sequent notation (\vdash) instead of a vertical presentation of rules. The formal language for classical propositional logic can be expressed using just negation (¬), implication (→) and propositional symbols. A well-known axiomatization, comprising three axiom schemata and one inference rule (modus ponens), is: (CA1) ⊢ A → (B → A) (CA2) ⊢ (A → (B → C)) → ((A → B) → (A → C)) (CA3) ⊢ (¬A → ¬B) → (B → A) (MP) A, A → B ⊢ B It may seem redundant to have two notions of inference in this case, ⊢ and →.
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Intel owned all the silicon designs which were licensed to Siemens, while Siemens owned all the software and documentation and licensed them to Intel. BiiN aimed their designs at the high-end fault tolerant market, competing with Tandem Computers and Stratus Computer, as opposed to the parallel processing market, where Sequent Computer Systems, Pyramid Technology, Alliant Computer Systems and others were operating. In order to compete here they had to make sure their first designs were as powerful as the best from the other vendors, and by the time such a system was ready both Intel and Siemens had spent about 300 million with no shipping units. In 1989 Siemens underwent a reorganization, which brought UBE's own computer division into the mix.
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Wiederhorn lost the lawsuit, and found himself "something of a pariah" as a 2011 newspaper article described his situation. Fog Cutter owned a major position in Fatburger, a restaurant chain based in southern California, and because he needed to devote more attention to the restaurant chain, moved to Beverly Hills in 2009, saying that will make his commute to Fatburger's Santa Monica headquarters considerably easier and cheaper. His home in Portland, a mansion he and his wife dubbed "The Ivy", was put up for sale July 2011 for $5.7 million. Wiederhorn had acquired the mansion and its properties in a trade from Casey Powell, former CEO of Sequent Computer Systems in 1995, then spent $8.7 million constructing a new wing to the house and other improvements.
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Logo for Project Monterey Project Monterey was an attempt to build a single Unix operating system that ran across a variety of 32-bit and 64-bit platforms, as well as supporting multi-processing. Announced in October 1998, several Unix vendors were involved; IBM provided POWER and PowerPC support from AIX, Santa Cruz Operation (SCO) provided IA-32 support, and Sequent added multi-processing (MP) support from their DYNIX/ptx system. Intel Corporation provided expertise and ISV development funding for porting to their upcoming IA-64 (Itanium Architecture) CPU platform, which was yet to be released at that time. The focus of the project was to create an enterprise-class UNIX for IA-64, which at the time was expected to eventually dominate the UNIX server market.
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A converse direction is to use a program to extract a proof, given its correctness—an area of research closely related to proof-carrying code. This is only feasible if the programming language the program is written for is very richly typed: the development of such type systems has been partly motivated by the wish to make the Curry–Howard correspondence practically relevant. The Curry–Howard correspondence also raised new questions regarding the computational content of proof concepts that were not covered by the original works of Curry and Howard. In particular, classical logic has been shown to correspond to the ability to manipulate the continuation of programs and the symmetry of sequent calculus to express the duality between the two evaluation strategies known as call-by-name and call-by-value.
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However, states that the assertion symbol in Gentzen-system sequents, which he denotes as ' ⇒ ', is part of the object language, not the metalanguage., defines sequents to have the form U ⇒ V for (possibly non-empty) sets of formulas U and V. Then he writes: : "Intuitively, a sequent represents 'provable from' in the sense that the formulas in U are assumptions for the set of formulas V that are to be proved. The symbol ⇒ is similar to the symbol ⊢ in Hilbert systems, except that ⇒ is part of the object language of the deductive system being formalized, while ⊢ is a metalanguage notation used to reason about deductive systems." According to Prawitz (1965): "The calculi of sequents can be understood as meta-calculi for the deducibility relation in the corresponding systems of natural deduction.".
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As she was elected as an independent regional MSP, there could be no by-election and her seat remained vacant until the 2016 election. Peter Law was expelled from the Labour Party after standing against an official Labour candidate in Blaenau Gwent at the 2005 UK general election and became an independent in the National Assembly and UK Parliament. In 2006 Peter Law died from a brain tumour and his wife, Trish Law campaigned and took the seat as an independent candidate at the sequent by-election and held onto the seat again in the 2007 Welsh Assembly elections. In 2016, Nathan Gill as the then leader of UKIP Wales defected from the group to sit as an independent after a falling out with Neil Hamilton who was elected UKIP Assembly group leader.
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For a general study in this area, see Nicholas Schofield and Gerard Skinner, The English Cardinals (London: Family Publications, 2007)Michael Walsh Westminster Cardinals London: Burns & Oates, 2009 To highlight this historical continuity, dating back to Pope Gregory I's appointment of Augustine and his sequent bestowal of the pallium on the appointee, the installation rites of pre-Reformation Catholic Archbishops of Canterbury and earlier Archbishops of Westminster were used at the installation of the current Cardinal Archbishop of Westminster, Vincent Gerard Nichols.Elena Curti and Christopher Lamb, "Cathedral countdown to installation", The Tablet, 16 May 2009, 39.Lucy Wooding, "Binding Identities," The Tablet, 26 June 2011, 26" Archbishop of Westminster Vincent Nichols is made cardinal," The Telegraph, 22 February 2014 He also became the forty-third of the English cardinals since the 12th century.
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Similarly, in intuitionistic logic the sequent : eg eg A \vdash A is not derivable, while in dual-intuitionistic logic : A \vdash eg eg A is not derivable. Dual-intuitionistic logic contains a connective # known as pseudo-difference which is the dual of intuitionistic implication. Very loosely, can be read as "A but not B". However, # is not truth-functional as one might expect a 'but not' operator to be; similarly, the intuitionistic implication operator cannot be treated like "". Dual-intuitionistic logic also features a basic connective ⊤ which is the dual of intuitionistic ⊥: negation may be defined as A full account of the duality between paraconsistent and intuitionistic logic, including an explanation on why dual-intuitionistic and paraconsistent logics do not coincide, can be found in Brunner and Carnielli (2005).
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The quality of HYPO's results speak for themselves, in that a number of sequent legal reasoning systems are either directly based upon HYPO's mechanisms as in the case of Kowalski (1991),Kowalski, A., Case-based reasoning and the deep structure approach to knowledge representation, (1991) Proceedings of the 3rd international conference on Artificial intelligence and law, 21-30 TAX-HYPO, precedent case-based system operating in the statutory domain of tax law (Rissland and Skalak 1989), CABARET, a mixed-paradigm cases and rule system for the income tax law domain, (Skalak and Rissland 1992), CATO, IBP, developed for argumentation to make predictions based on argumentation concepts (Brüninghaus and Ashley 2003), or their creators at least pay homage to HYPO in their discussions (Henderson and Bench-Capon 2001Henderson, J. & Bench-Capon, T, Dynamic arguments in a case law domain, (2001) Proceedings of the 8th international conference on Artificial intelligence and law, 60-69.).
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Judgments are used in formalizing deduction systems: a logical axiom expresses a judgment, premises of a rule of inference are formed as a sequence of judgments, and their conclusion is a judgment as well (thus, hypotheses and conclusions of proofs are judgments). A characteristic feature of the variants of Hilbert-style deduction systems is that the context is not changed in any of their rules of inference, while both natural deduction and sequent calculus contain some context-changing rules. Thus, if we are interested only in the derivability of tautologies, not hypothetical judgments, then we can formalize the Hilbert-style deduction system in such a way that its rules of inference contain only judgments of a rather simple form. The same cannot be done with the other two deductions systems: as context is changed in some of their rules of inferences, they cannot be formalized so that hypothetical judgments could be avoided—not even if we want to use them just for proving derivability of tautologies.
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To perform a proof-search the best thing is to chose the left formula, since \lor is positive, indeed (as discussed above) in some cases there are no proofs where the focus is on the right formula. To overcome this, some focused calculi create a backtracking point such that focusing on the right yields \downarrow \uparrow \phi \lor \psi \implies \langle \phi \lor \psi \rangle, \uparrow \phi \lor \psi, which is still as \phi \lor \psi \implies \phi \lor \psi. The second formula on the right can be removed only when the focused phase has finished, but if proof-search gets stuck before this happens the sequent may remove the focused component thereby returning to the choice e.g., \downarrow \uparrow B \lor A \implies \langle A \rangle, \uparrow A \lor B must be taken to \downarrow \uparrow B \lor A \implies \uparrow A \lor B as no other reductive inference can be made.
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The approach was introduced by G. Japaridze inG.Japaridze, “Introduction to cirquent calculus and abstract resource semantics”. Journal of Logic and Computation 16 (2006), pp. 489–532. as an alternative proof theory capable of “taming” various nontrivial fragments of his computability logic, which had otherwise resisted all axiomatization attempts within the traditional proof-theoretic frameworks.G.Japaridze, “The taming of recurrences in computability logic through cirquent calculus, Part I”. Archive for Mathematical Logic 52 (2013), pages 173-212. G.Japaridze, “The taming of recurrences in computability logic through cirquent calculus, Part II” Archive for Mathematical Logic 52 (2013), pages 213–259. The origin of the term “cirquent” is CIRcuit+seQUENT, as the simplest form of cirquents, while resembling circuits rather than formulas, can be thought of as collections of one-sided sequents (for instance, sequents of a given level of a Gentzen-style proof tree) where some sequents may have shared elements. Cirquent for the "two out of three" combination of resources, inexpressible in linear logic The basic version of cirquent calculus inG.
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Since Soulcalibur II, every sequent game have hosted guest characters, usually from other Namco franchises, although more recent games have branched into titles developed by other companies, such as The Legend of Zelda, Spawn, Star Wars, God of War, Assassin's Creed and The Witcher. The guests, though, can only appear in one game due to licensing. Guest characters who have appeared in the series include Heihachi Mishima, Devil Jin, King, Ling Xiaoyu, Asuka Kazama, and Jun Kazama from Tekken (the latter five as attires for custom characters), Link from The Legend of Zelda, Spawn from Spawn, Lloyd Irving from Tales of Symphonia, KOS-MOS from Xenosaga (as an attire for custom characters), Darth Vader, Yoda, and The Apprentice from Star Wars, Kratos from God of War, Ezio Auditore da Firenze from Assassin's Creed, Geralt of Rivia from The Witcher, and 2B from NieR: Automata. Other than featuring characters from other series, the series' characters have also appeared in other video games as well, including the Ridge Racer series, Pac-Man Fever, Smash Court Tennis Pro Tournament 2, Queen's Gate: Spiral Chaos, Musou Orochi 2 Ultimate, as well as crossover titles such as Namco × Capcom and Project X Zone 2.
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