110 Sentences With "derivable" | Random Sentence Generator

Yearning for a clear answer, derivable from constitutional text, is understandable.

In superintuitionistic and modal logics, a logic is structurally complete if every admissible rule is derivable.

An axiomatic system is complete if every tautology is a theorem (derivable from axioms). An axiomatic system is sound if every theorem is a tautology.

In propositional logic, the set of all true propositions is deductively closed. This is to say that only true statements are derivable from other true statements.

The name is not clearly derivable from history, although it is more or less clear that the village originates at least from 1166, under the name Millen or Mylle.

Gewirth is best known for his ethical rationalism, according to which a supreme moral principle, the "Principle of Generic Consistency" (PGC), is derivable as a requirement of "agential self-understanding".Deryck Beyleveld, A Theoretical Framework for Integrating Ethics and Law The principle states that every agent must act in accordance with his or her own and all other agents' generic rights. According to Gewirth's theory, the PGC, is derivable from the fact of human agency, but it is derivable only via a "dialectically necessary" mode of argumentation. The mode is "dialectical" in the sense that it presents the steps of the argument to the PGC as inferences made by an agent, rather than as statements true of the world itself.

Article 123(2) EPC provides that a European patent application, or European patent, may not be amended (both before and after grant) in such a way that it contains subject-matter which extends beyond the content of the application as filed. In other words, an amendment cannot go beyond the original disclosure of the application. The amended subject-matter must be directly and unambiguously derivable (i.e., clearly and unambiguously derivable) from the content of the application as filed.

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.

These are models derivable from oral traditional data and ethnographic resources. Such models, if carefully applied to archaeological situations, can greatly fill the gaps in our knowledge of the past of the Ibeku peoples.

2,5-Dimethylfuran is a heterocyclic compound with the formula (CH3)2C4H2O. Although often abbreviated DMF, it should not be confused with dimethylformamide. A derivative of furan, this simple compound is a potential biofuel, being derivable from cellulose.

The use of the plant for diabetes was the original stimulus for research. Effectiveness in the treatment of both Hodgkin's Disease and leukemia were discovered instead. The Hodgkin's lymphoma chemotherapeutic drug vinblastine is derivable from the rosy periwinkle.

It is common to include in a Hilbert-style deduction system only axioms for implication and negation. Given these axioms, it is possible to form conservative extensions of the deduction theorem that permit the use of additional connectives. These extensions are called conservative because if a formula φ involving new connectives is rewritten as a logically equivalent formula θ involving only negation, implication, and universal quantification, then φ is derivable in the extended system if and only if θ is derivable in the original system. When fully extended, a Hilbert-style system will resemble more closely a system of natural deduction.

BAN logic, and logics in the same family, are decidable: there exists an algorithm taking BAN hypotheses and a purported conclusion, and that answers whether or not the conclusion is derivable from the hypotheses. The proposed algorithms use a variant of magic sets.

THF can also be synthesized by catalytic hydrogenation of furan. This allows certain sugars to be converted to THF via acid-catalyzed digestion to furfural and decarbonylation to furan, although this method is not widely practiced. THF is thus derivable from renewable resources.

The Empty Set axiom in STZ is redundant, because the existence of the empty set is derivable from the axiom schema of Specification. Burgess's theory STCalled S' in Tarski et al. (1953: 34). is GST with Empty Set replacing the axiom schema of specification.

An axiom system is sound when all its axioms are valid and its inference rules are sound. An axiom system is complete when every valid formula is derivable as a theorem of that system. These concepts apply to all systems of logic including dynamic logic.

There are several ways of seeing that the system is nonholonomic. The dimension of the phase space is 5, which is odd. The constraint on the velocity is not derivable from a constraint on the coordinates. The motion of the system can be characterized simply.

Karl Haller, of FOGRA in Munich, proposed a different model, one in which dots with larger perimeters tended to exhibit greater dot gain than those with smaller perimeters. One result derivable from his work is that dot gains depend on the shape of the halftone dots.

All this gives an impression somewhat different from Lord Peter Wimsey, and there may be an element of deliberate contrast. Sayers had a profound knowledge of the advertising world, as evidenced in Murder Must Advertise, and the milieu of Egg is derivable from this expertise and knowledge.

Popper argues that science should adopt a methodology based on "an asymmetry between verifiability and falsifiability; an asymmetry which results from the logical form of universal statements. For these are never derivable from singular statements, but can be contradicted by singular statements".Popper, Karl (2002). p. 19.

Z-relation on two pitch sets analyzable as or derivable from set 5-Z17Schuijer, Michiel (2008). Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts. University of Rochester. . , with intervals between pitch classes labeled for ease of comparison between the two sets and their common interval vector, 212320.

This highlights the specialness of four dimensions. Note further that the full Riemann tensor cannot in general be derived from derivatives of the Lanczos potential alone.E. Massa and E. Pagani, "Is the Riemann tensor derivable from a tensor potential?", General Relativity and Gravitation, 16 (1984) pp. 805–816.

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.

Information fluctuation complexity is an information-theoretic quantity defined as the fluctuation of information about entropy. It is derivable from fluctuations in the predominance of order and chaos in a dynamic system and has been used as a measure of complexity in many diverse fields. It was introduced in a 1993 paper by Bates and Shepard.

They are also often called proofs, but are completely formalized unlike natural-language mathematical proofs. A deductive system is sound if any formula that can be derived in the system is logically valid. Conversely, a deductive system is complete if every logically valid formula is derivable. All of the systems discussed in this article are both sound and complete.

For systems at constant pressure, with no external work done other than the work, the change in enthalpy is the heat received by the system. For a simple system, with a constant number of particles, the difference in enthalpy is the maximum amount of thermal energy derivable from a thermodynamic process in which the pressure is held constant.

For Frye, this kind of coherent, critical integrity involves claiming a body of knowledge for criticism that, while independent of literature, is yet constrained by it: "If criticism exists," he declares, "it must be an examination of literature in terms of a conceptual framework derivable from an inductive survey of the literary field" itself (Anatomy 7).

Phenomenological models have been characterized as being completely independent of theories,McMullin, Ernan (1968), “What Do Physical Models Tell Us?”, in B. van Rootselaar and J. F. Staal (eds.), Logic, Methodology and Science III. Amsterdam: North Holland, 385–396. though many phenomenological models, while failing to be derivable from a theory, incorporate principles and laws associated with theories.

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).

The origins of the distinction are less clear, and it concerns the origins of knowledge. A posteriori knowledge arises from, or is caused by, experience. A priori knowledge may come temporally after experience, but its certainty is not derivable from the experience itself. Saul Kripke was the first major thinker to propose that there are analytic a posteriori knowledge claims.

Perhaps there were features derivable from the original features that were important for identifying the ugly duckling. The set of booleans in the vector can be extended with new features computed as boolean functions of the k original features. The only canonical way to do this is to extend it with all possible Boolean functions. The resulting completed vectors have 2^k features.

This algebra is quotiented over by the ideal generated by the Euler–Lagrange equations. Then, this quotient algebra is converted into a Poisson algebra by introducing a Poisson bracket derivable from the action, called the Peierls bracket. This Poisson algebra is then \hbar-deformed in the same way as in canonical quantization. There is also a way to quantize actions with gauge "flows".

'Focus (abbreviated ') is a grammatical category that determines which part of the sentence contributes new, non-derivable, or contrastive information. Focus is related to information structure. Contrastive focus specifically refers to the coding of information that is contrary to the presuppositions of the interlocutor. The topic–comment model distinguishes between the topic (theme) and what is being said about that topic (the comment, rheme, or focus).

Data representations are structured forms suitable for computer-based transformations. These structures must exist in the original data or be derivable from the data themselves. They must retain the information and knowledge content and the related context within the original data to the greatest degree possible. The structures of underlying data representations are generally neither accessible nor intuitive to the user of the visual analytics tool.

Intuitively, givenness classifies words and information in a discourse that are already known (or given) by virtue of being common knowledge, or by having been discussed previously in the same discourse ("anaphorically recoverable"). Certain theories (such as Roger Schwarzschild's GIVENness Constraint) require all non-focus-marked constituents to be given. Words/information that are not given, or are "textually and situationally non-derivable" are by definition new.

The metric system was originally conceived as a system of measurement that was derivable from unchanging phenomena, but practical limitations necessitated the use of artefacts – the prototype of the metre and prototype of the kilogram – when the metric system was introduced in France in 1799. Although it was designed for long-term stability, the masses of the prototype kilogram and its secondary copies have shown small variations relative to each other over time; they are not thought to be adequate for the increasing accuracy demanded by science, prompting a search for a suitable replacement. The definitions of some units were defined by measurements that are difficult to precisely realise in a laboratory, such as the kelvin, which was defined in terms of the triple point of water. With the 2019 redefinition, the SI became wholly derivable from natural phenomena with most units being based on fundamental physical constants.

The modeling of purely mechanical systems is mainly based on the Lagrangian which is a function of the generalized coordinates and the associated velocities. If all forces are derivable from a potential, then the time behavior of the dynamical systems is completely determined. For simple mechanical systems, the Lagrangian is defined as the difference of the kinetic energy and the potential energy. There exists a similar approach for electrical system.

The Uniform Symbology Algorithm is designed to be human readable, fit into 6 characters, have no symbol clashes and where possible, be derivable from another, freely available code. It will consist of a stock code followed by a single, lower case letter designating the primary listing exchange. The stock code will be derived from the “local code” published by the primary exchange. These will be truncated where necessary.

Markov's rule is the formulation of Markov's principle as a rule. It states that \exists n\;P(n) is derivable as soon as eg eg \exists n\;P(n) is, for P decidable. Formally, :\forall n (P(n)\lor eg P(n)),\ eg eg \exists n\;P(n)\ \vdash\ \exists n\;P(n) Anne S. TroelstraAnne S. Troelstra. Metamathematical Investigation of Intuitionistic Arithmetic and Analysis, Springer Verlag (1973), Theorem 4.2.

The Drell–Yan process is studied both in fixed-target and collider experiments. It provides valuable information about the parton distribution functions (PDFs) which describe the way the momentum of an incoming high-energy nucleon is partitioned among its constituent partons. These PDFs are basic ingredients for calculating essentially all processes at hadron colliders. Although PDFs should be derivable in principle, current ignorance of some aspects of the strong force prevents this.

Teleosemantics, also known as biosemantics, is used to refer to the class of theories of mental content that use a teleological notion of function. Teleosemantics is best understood as a general strategy for underwriting the normative nature of content, rather than any particular theory. What all teleological theories have in common is the idea that semantic norms are ultimately derivable from functional norms. Attempts to naturalize semantics began in the late 1970s.

The obvious exception are implicatures following from the maxim of manner, which explicitly relies on the phrasing. Thus, the following utterances have the same implicature as above: : That fruit cake there looks appetizing. : The dessert you brought is really mouthwatering. Conversational implicatures are calculable: they are supposed to be formally derivable from the literal meaning of the utterance in combination with the cooperative principle and the maxims, as well as contextual information and background knowledge.

Reported in An Etymological Dictionary of the English Language, by Walter W. Skeat (1888) (Downloadable at Archive.org). In An Etymology Dictionary of Modern English by Ernest Weekley (1921) it is reported that Arabic tarashaqun is derivable in turn from Persian talkh chakok, bitter herb (Downloadable at Archive.org). The English name, dandelion, is a corruption of the French dent de lionS. Potter & L. Sargent (1973) Pedigree: essays on the etymology of words from nature.

Axioms in traditional thought were "self-evident truths", but that conception is problematic."The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil." Bertrand Russell (1919), Introduction to Mathematical Philosophy, New York and London, p. 71. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system.

In 1806 Lord Eldon LC sitting in English House of Lords in Lucena v Craufurd (1806) 2 Bos & PNR 269 sought to define an insurable interest, and although that definition is often used, modern commentators regard it as unsatisfactory. Lord Eldon defined it as "a right in property, or a right derivable out of some contract about the property, which in either case may be lost upon some contingency affecting the possession or enjoyment of the party".

In the end, Su Shi was convicted. The failure of the court to notice the extended meanings derivable by comparison of his rhymes with Du Fu's was apparent (to those in the know), and Su Shi and others, such as Wang Shen, having learned a way to avoid censorial persecution while still being able to express themselves to each other would continue to employ and expand upon this rhyme-matching, in conjunction with similarly coded painting.

In Causation in Science, Ben- Menahem offers a novel account of causation, centered on the notion of causal constraint rather than the common notion of causal relation. The book analyses the interrelations between constraints such as determinism, locality, conservation laws, and variation principles. In response to the classic problem of human freedom, Ben-Menahem expounds a concept of lawlessness that permits human action to be subject to causes, without being derivable from, and predictable by, laws of nature.

It is a question of definition and the criteria: Beginning with the temperatures, as derivable from Greenland ice core data, it is possible to define an 'Early' or 'Pre-Atlantic' period at around 8040 BC, where the 18O isotope line remains above 33 ppm in the combined curve after Rasmussen et al. (2006),S.O. Rasmussen, B.M. Vinther, H.B. Clausen, and K.K. Andersen. Greenland Ice Core Chronology 2005 (GICC05) Early Holocene section. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2006-119.

Frege, who is considered the founder of analytic philosophy, invented it so as to show all of mathematics was derivable from logic, and make arithmetic rigorous as David Hilbert had done for geometry, the doctrine known as logicism in the foundations of mathematics. The notation Frege used never much caught on. Hugh MacColl published a variant of propositional logic two years prior. The writings of Augustus De Morgan and Charles Sanders Peirce also pioneered classical logic with the logic of relations.

According to Wilhelm Geiger, Sinhala has features that set it apart from other Indo-Aryan languages. Some of the differences can be explained by the substrate influence of the parent stock of the Vedda language. Sinhala has many words that are only found in Sinhala, or shared between Sinhala and Vedda and not etymologically derivable from Middle or Old Indo-Aryan. Common examples are kola for leaf in Sinhala and Vedda, dola for pig in Vedda and offering in Sinhala.

FOL is now a core formalism of mathematical logic, and is presupposed by contemporary treatments of Peano arithmetic and nearly all treatments of axiomatic set theory. The 1928 edition included a clear statement of the Entscheidungsproblem (decision problem) for FOL, and also asked whether that logic was complete (i.e., whether all semantic truths of FOL were theorems derivable from the FOL axioms and rules). The former problem was answered in the negative first by Alonzo Church and independently by Alan Turing in 1936.

It has been claimed that new information in the discourse is accented while given information is not. Generally, the properties of new and given are referred to as a word's discourse status. Definitions of new and given vary. Halliday defines given as "anaphorically" recoverable, while new is defined to be "textually and situationally non- derivable information". To illustrate this point, consider the following discourse in (12) and (13): (12) Why don’t you have some French TOAST? (13) I’ve forgotten how to MAKE French toast.

This requirement was later replicated for life insurance in the Life Assurance Act 1774. Neither statute sought to define an insurable interest, and it was not until the decision of the courts in Lucena v Craufurd(1806) 2 Bos & PNR 269 in 1806 that an insurable interest was first defined as "A right in the property, or a right derivable out of some contract about the property, which in either case may be lost upon some contingency affecting the possession or enjoyment of the party."at 321.

Forces derivable from a potential are also called conservative forces. The work done by a conservative force is :\,W = -\Delta U where \Delta U is the change in the potential energy associated with the force. The negative sign provides the convention that work done against a force field increases potential energy, while work done by the force field decreases potential energy. Common notations for potential energy are PE, U, V, and Ep. Potential energy is the energy by virtue of an object's position relative to other objects.

As in general relativity, equations structurally identical to the Einstein field equations are derivable from a variational principle. A spin tensor can also be supported in a manner similar to Einstein–Cartan–Sciama–Kibble theory. GTG was first proposed by Lasenby, Doran, and Gull in 1998 as a fulfillment of partial results presented in 1993. The theory has not been widely adopted by the rest of the physics community, who have mostly opted for differential geometry approaches like that of the related gauge gravitation theory.

While the quark model is derivable from the theory of quantum chromodynamics, the structure of hadrons is more complicated than this model allows. The full quantum mechanical wave function of any hadron must include virtual quark pairs as well as virtual gluons, and allows for a variety of mixings. There may be hadrons which lie outside the quark model. Among these are the glueballs (which contain only valence gluons), hybrids (which contain valence quarks as well as gluons) and "exotic hadrons" (such as tetraquarks or pentaquarks).

I-62, Page 9 Attached to each platoon was a small evaluation section, consisting of 1-3 evaluatorsI-19b, page 2 who generally operated out of a captured house or tent near the intercept station with their results being passed to the Evaluation platoon of the company. Only the simplest systems were worked on at the NAK level, with the majority of the intercepts being passed to the NAAS, which studied the intercepts using cryptanalysis and well as for tactical intelligence derivable through traffic analysis.

Finally the erstwhile governor of Bombay, Sir Meadows Taylor decided in favour of the mosque authorities. The date of its completion (AD 1802)/(AH 1217) is derivable from the chronogram Jahaz-i- Akhirat, "The ship of the world to come" which contains an allusion to the fact that it was constructed on the tank. A one-story building was therefore erected over the tank and formed the original nucleus of the present Jama Mosque. A top floor was added with the munificence of a prominent konkani merchant Mohammad Ali Roghay in 1814.

Some of these words are historically derivable from clicks in initial positions (many appear to reflect lexicalized reduplication, for example, and some are due to prefixes), but others are opaque. As in Sandawe, most medial clicks are glottalized, but not all: puche 'a spleen', tanche 'to aim', tacce 'a belt', minca 'to lick one's lips', laqo 'to trip someone', keqhe-na 'slow', penqhenqhe ~ peqeqhe 'to hurry', haqqa-ko 'a stone', shenqe 'to peer over', exekeke 'to listen', naxhi 'to be crowded', khaxxe 'to jump', binxo 'to carry kills under one's belt'.

Probably the oldest, and most famous, list of axioms are the 4 + 1 Euclid's postulates of plane geometry. The axioms are referred to as "4 + 1" because for nearly two millennia the fifth (parallel) postulate ("through a point outside a line there is exactly one parallel") was suspected of being derivable from the first four. Ultimately, the fifth postulate was found to be independent of the first four. Indeed, one can assume that exactly one parallel through a point outside a line exists, or that infinitely many exist.

Specifically in the analysis of layered media, derivation of spatial-domain Green's function necessitates the inversion of analytically-derivable spectral-domain Green's function through Sommerfeld path integral. This integral can not be evaluated analytically and its numerical integration is costly due to its oscillatory and slowly-converging behaviour. For a robust analysis, spatial Green's functions are approximated as complex exponentials with methods such as Prony's method or generalized pencil of function, and the integral is evaluated with Sommerfeld identity. This method is known as discrete complex image method.

The following statements are logically equivalent: #If Lisa is in Denmark, then she is in Europe (a statement of the form d \implies e). #If Lisa is not in Europe, then she is not in Denmark (a statement of the form eg e \implies eg d). Syntactically, (1) and (2) are derivable from each other via the rules of contraposition and double negation. Semantically, (1) and (2) are true in exactly the same models (interpretations, valuations); namely, those in which either Lisa is in Denmark is false or Lisa is in Europe is true.

It goes without saying that the story is apocryphal, but it shows that among the Shiites there were people ready to identify themselves with the Nabateans. Thus it comes as no surprise that especially in the so- called ghulàt movements (extremist Shiites) a lot of material surfaces that is derivable from Mesopotamian sources (cf. Hämeen-Anttila 2001), and the early Shiite strongholds were to a great extent in the area inhabited by Nabateans. "Yaqut also notes, "the identification of Kutha as the original home Shiah Muslims believe to be the Abrahamic roots of Islam.

The Lurish dialects are descended from Middle Persian (Pahlavi). They belong to the Persid or Southern Zagros group, and are lexically similar to modern Persian, differing mainly in phonology. According to the Encyclopædia Iranica, "All Lori dialects closely resemble standard Persian and probably developed from a stage of Persian similar to that represented in Early New Persian texts written in Perso-Arabic script. The sole typical Lori feature not known in early New Persian or derivable from it is the inchoative marker (see below), though even this is found in Judeo- Persian texts".

The previous major change of the metric system occurred in 1960 when the International System of Units (SI) was formally published. At this time the metre was redefined: the definition was changed from the prototype of the metre to a certain number of wavelengths of a spectral line of a krypton-86 radiation, making it derivable from universal natural phenomena.The metre was redefined again in 1983 by fixing the value of the speed of light in vacuum. That definition went unaltered in 2019 and remains in effect today.

In his Meno, Plato raises an important epistemological quandary: How is it that we have certain ideas which are not conclusively derivable from our environments? Noam Chomsky has taken this problem as a philosophical framework for the scientific enquiry into innatism. His linguistic theory, which derives from 18th century classical-liberal thinkers such as Wilhelm von Humboldt, attempts to explain in cognitive terms how we can develop knowledge of systems which are said, by supporters of innatism, to be too rich and complex to be derived from our environment. One such example is our linguistic faculty.

First edition (publ. Geoffrey Bles) Miracles is a book written by C. S. Lewis, originally published in 1947 and revised in 1960. Lewis argues that before one can learn from the study of history whether or not any miracles have ever occurred, one must first settle the philosophical question of whether it is logically possible that miracles can occur in principle. He accuses modern historians and scientific thinkers, particularly secular biblical scholars, of begging the question against miracles, insisting that modern disbelief in miracles is a cultural bias thrust upon the historical record and is not derivable from it.

Tie and Navette tiling (in red on a Penrose background) The three variants of the Penrose tiling are mutually locally derivable. Selecting some subsets from the vertices of a P1 tiling allows to produce other non-periodic tilings. If the corners of one pentagon in P1 are labeled in succession by 1,3,5,2,4 an unambiguous tagging in all the pentagons is established, the order being either clockwise or counterclockwise. Points with the same label define a tiling by Robinson triangles while points with the numbers 3 and 4 on them define the vertices of a Tie-and-Navette tiling.

If only these two original criteria are used to define hypoelasticity, then hyperelasticity would be included as a special case, which prompts some constitutive modelers to append a third criterion that specifically requires a hypoelastic model to not be hyperelastic (i.e., hypoelasticity implies that stress is not derivable from an energy potential). If this third criterion is adopted, it follows that a hypoelastic material might admit nonconservative adiabatic loading paths that start and end with the same deformation gradient but do not start and end at the same internal energy. Note that the second criterion requires only that the function G exists.

Z-relation on two pitch sets analyzable as or derivable from Z17 , with intervals between pitch classes labeled for ease of comparison between the two sets and their common interval vector, 212320. Set 3-1 has three possible rotations/inversions, the normal form of which is the smallest pie or most compact form Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music . Other theorists, such as Allen Forte, further developed the theory for analyzing atonal music , drawing on the twelve-tone theory of Milton Babbitt.

That is, it implies the axiom of global choice.John Harrison, "The Bourbaki View" eprint. Hilbert realized this when introducing epsilon calculus."Here, moreover, we come upon a very remarkable circumstance, namely, that all of these transfinite axioms are derivable from a single axiom, one that also contains the core of one of the most attacked axioms in the literature of mathematics, namely, the axiom of choice: A(a)\to A(\varepsilon(A)), where \varepsilon is the transfinite logical choice function." Hilbert (1925), “On the Infinite”, excerpted in Jean van Heijenoort, From Frege to Gödel, p. 382.

Focus is a grammatical category or attribute that determines indicating that part of an utterance contributes new, non-derivable, or contrastive information. Some theories (in line with work by Mats Rooth) link focus to the presence of alternatives (see Focus: Alternative Semantics). An alternatives theory of focus would account for the stress pattern in the example from the previous section (When did Jane sell the book? She sold the book YESTERDAY), saying that YESTERDAY receives focus because it could be substituted with alternative time periods (TODAY or LAST WEEK) and still serve to answer the question the first speaker asked.

Nowadays the material is available freely on the Internet.elämänkatsomustieto As a thinker, Hartikainen supports atheism and ontological materialism. He favours the words 'reality research', 'realityconception' (conception of reality) and 'lifeconception' as better alternatives for words 'science', 'world view' and 'philosophy of life' (life stance). He supports Finnish physicist Kari Enqvist's view, that emergence means 'coarsening' and the losing of information relating to the description of reality (examples: statistical thermodynamics, classical electrodynamics, thinking of an animal etc.) Hartikainen is a modern logical empiricist and he recommends not using words "a priori truth" and saying "correct by definition" or "derivable from axioms" instead.

However, to accommodate a security problem with Microsoft's Internet Explorer, they decided that they would soon refuse to register DOI suffixes that contain the colon character. The SICI is a recognized international standard and is in wide use by publishers and the bibliographic community, primarily as an aid to finding existing articles or issues. JSTOR adopted SICIs in 2001 as its primary article-level identifier and the core of its stable and citation-derivable URLs. SICI was selected over simpler alternatives because of its ability to encompass the many varieties of journal metadata found in JSTOR's archive.

Any ratio between physical constants of the same dimensions results in a dimensionless physical constant, for example, the proton-to- electron mass ratio. Any relation between physical quantities can be expressed as a relation between dimensionless ratios via a process known as nondimensionalisation. The term of "fundamental physical constant" is reserved for physical quantities which, according to the current state of knowledge, are regarded as immutable and as non-derivable from more fundamental principles. Notable examples are the speed of light c, and the gravitational constant G. The fine-structure constant α is the best known dimensionless fundamental physical constant.

For one such construction the size of the constructed grammar is O(4) in the general case and O(3) if no derivation of the original grammar consists of a single nonterminal symbol, where is the size of the original grammar. This conversion can be used to prove that every context-free language can be accepted by a real-time (non-deterministic) pushdown automaton, i.e., the automaton reads a letter from its input every step. Given a grammar in GNF and a derivable string in the grammar with length , any top- down parser will halt at depth .

Mathematically, quasicrystals have been shown to be derivable from a general method that treats them as projections of a higher-dimensional lattice. Just as circles, ellipses, and hyperbolic curves in the plane can be obtained as sections from a three-dimensional double cone, so too various (aperiodic or periodic) arrangements in two and three dimensions can be obtained from postulated hyperlattices with four or more dimensions. Icosahedral quasicrystals in three dimensions were projected from a six- dimensional hypercubic lattice by Peter Kramer and Roberto Neri in 1984. The tiling is formed by two tiles with rhombohedral shape.

The only physical property directly derivable to that of the central star, which follows from the amount of occultation of stellar light during a transit. This ratio was measured to be 0.021, giving a planetary radius of 1.11±0.14 times that of Earth. The planet is about 11% larger in radius than Earth (between 4.5% smaller and 26.5% larger), giving a volume about 1.37 times that of Earth (between 0.87 and 2.03 times as large). A very wide range of possible masses can be calculated by combining the radius with densities derived from the possible types of matter from which planets can be made.

In infinitary logic, degrees of provability of propositions can be expressed in terms of infinite-valued logic that can be described via evaluated formulas, written as ordered pairs each consisting of a truth degree symbol and a formula. In mathematics, number-free semantics can express facts about classical mathematical notions and make them derivable by logical deductions in infinite-valued logic. T-norm fuzzy logics can be applied to eliminate references to real numbers from definitions and theorems, in order to simplify certain mathematical concepts and facilitate certain generalizations. A framework employed for number-free formalization of mathematical concepts is known as fuzzy class theory.

Although there is generally no one-to-one correspondence between illuminants and white points, in the case of the CIE D-series standard illuminants, the spectral power distributions are mathematically derivable from the chromaticity coordinates of the corresponding white points. Knowing the illuminant's spectral power distribution, the reflectance spectrum of the specified white object (often taken as unity), and the numerical definition of the observer allows the coordinates of the white point in any color space to be defined. For example, one of the simplest illuminants is the "E" or "Equal Energy" spectrum. Its spectral power distribution is flat, giving the same power per unit wavelength at any wavelength.

The process of diaphonic identification occurs when pidgins are fashioned; although lexical and morphosyntactic patterns are shared, speakers often use the phonological systems of their native language, meaning they must learn to recognize such diaphonic correspondences in the speech of others to facilitate the mutual intelligibility of a working pidgin.. The author notes (p.48) a parallel process with culturally defined gestures and offers the term gestural diamorph for this phenomenon. proposes that rule differences can be used to determine the distance a particular utterance has between a post-creole continuum's acrolectal and basolectal forms. points out that mesolectal varieties often have features not derivable from such rules.

They must be derivable without error from axioms and already-proven statements. HoTT adds the univalence axiom, which relates the equality of logical-mathematical propositions to homotopy theory. An equation such as “a=b” is a mathematical proposition in which two different symbols have the same value. In homotopy type theory, this is taken to mean that the two shapes which represent the values of the symbols are topologically equivalent. These topological equivalence relationships, ETH Zürich Institute for Theoretical Studies director Giovanni Felder argues, can be better formulated in homotopy theory because it is more comprehensive: Homotopy theory explains not only why “a equals b” but also how to derive this.

In the philosophy of mathematics, he is best known for his book Frege's Conception of Numbers as Objects (1983), where he argues that Frege's logicist project could be revived by removing the axiom schema of unrestricted comprehension (sometimes referred to as Basic Law V) from the formal system. Arithmetic is then derivable in second-order logic from Hume's principle. He gives informal arguments that (i) Hume's principle plus second-order logic is consistent, and (ii) from it one can produce the Dedekind–Peano axioms. Both results were proven informally by Gottlob Frege (Frege's Theorem), and would later be more rigorously proven by George Boolos and Richard Heck.

The speed-adaption mechanism is a mechanism used to determine the required torque from the joints at different moving speeds. During the stance phase it has been seen that quasistiffness, which is the derivative of the torque angle relationship with respect the angle, changes constantly as a function of walking speed. This means that over the stance phase, depending on the speed the subject is moving, there is a derivable torque angle relationship that can be used to control a lower limb prosthesis. During the swing phase joint torque increases proportionally to walking speed and the duration of the swing phase decreases proportionally to the stride time.

Even in the presence of an orientation, there is in general no meaningful way to integrate -forms over subsets for because there is no consistent way to use the ambient orientation to orient -dimensional subsets. Geometrically, a -dimensional subset can be turned around in place, yielding the same subset with the opposite orientation; for example, the horizontal axis in a plane can be rotated by 180 degrees. Compare the Gram determinant of a set of vectors in an -dimensional space, which, unlike the determinant of vectors, is always positive, corresponding to a squared number. An orientation of a -submanifold is therefore extra data not derivable from the ambient manifold.

Boolos’s name for Zermelo set theory minus extensionality was Z-. Boolos derived in S all axioms of Z- except the axiom of choice.Boolos (1998: 95–96; 103–04). The purpose of this exercise was to show how most of conventional set theory can be derived from the iterative conception of set, assumed embodied in S. Extensionality does not follow from the iterative conception, and so is not a theorem of S. However, S + Extensionality is free of contradiction if S is free of contradiction. Boolos then altered Spec to obtain a variant of S he called S+, such that the axiom schema of replacement is derivable in S+ + Extensionality.

The toponyms of Turkey result from the legacy left by several linguistic heritages: the Turkish language (spoken as first language by the majority of the population), the Greek language, the Armenian language, the Kurdish language, the Laz language as well as several other languages once spoken widely in Turkey. Turkey's place names range from those of unknown or unrecognizable origins to more clearly derivable onomastics. Many places have had their names changed throughout history as new language groups dominated the landbridge that present day Turkey is. A systematic turkification of place names was carried out when the worldwide wave of nationalism reached Turkey during the 20.

In the area of measurement, BIPM has identified nine metrology areas, which are acoustics, electricity and magnetism, length, mass and related quantities, photometry and radiometry, ionizing radiation, time and frequency, thermometry, and chemistry. As of May 2019 no physical objects define the base units.Decision CIPM/105-13 (October 2016) The motivation in the change of the base units is to make the entire system derivable from physical constants, which required the removal of the prototype kilogram as it is the last artefact the unit definitions depend on. Scientific metrology plays an important role in this redefinition of the units as precise measurements of the physical constants is required to have accurate definitions of the base units.

The diagram is believed to be derivable from the flower of life. Scholars believe that the concept of a tree of life with different spheres encompassing aspects of reality traces its origins back to Assyria in the 9th century BC. The Assyrians also assigned values and specific numbers to their deities similar to those used by the later Jewish Kabbalah. The beginnings of the Jewish Kabbalah are traced back by scholars to the Medieval Age, originating in the Book of Bahir and the Book of Zohar. However, the first historical instance of the modern diagram appeared centuries later in the cover of the Latin translation of Gates of Light in the year 1516.

As a theorist, Homans' overall intellectual ambition was to create a more unified social science on a firm theoretical basis. His approach to theory developed in two phases, usually interpreted by commentators as inductive and deductive. Although this is a bit of an oversimplification, it provides a framework for outlining his theoretical contributions. In its mature (1974) form, Homans' theory rests upon two metatheoretical claims: (1) the basic principles of social science must be true of individuals as members of the human species, not as members of particular groups or cultures; and (2) any other generalizations or facts about human social life will be derivable from these principles (and suitable initial conditions).

In January 1839 The Colonist ran an editorial announcing the school would re-open on 10 January when McEachern, through some unspecified "recent arrangements" that he had made, would be able to accommodate a larger number of boarders than hitherto: Under the domestic management of Mrs. McE, together with the substantial comforts derivable from the farm, with its dairy and excellent garden, we should think that the Summerhill Academy ought to be one of the most eligible establishments for the education of youth in the southern districts of the colony.The Colonist 8 September 1838.2 January 1839.The Sydney Herald, 21 November 1838 Two months later the property was again on the market.

Spaced responding and choice: A preliminary analysis. Journal of the Experimental Analysis of Behavior, 11, 669-682. and was generalized by (Baum, 1974)Baum, W. M. (1974) On two types of deviation from the matching law: bias and undermatching. J. Exp. Anal. Behav. 22(1), 231-242.. It has been found to fit a wide variety of matching data. The power law was shown by Mackay (1963) MacKay, D. M. Psychophysics of perceived intensity:A theoretical basis for Fechner's and Stevens' laws. Science, 1963, 139, 1213-1216. to be derivable from input and output logarithmic function and psychophysical and other behavioral data fitting this model were described by Staddon (1975). Staddon, J. E. R. (1978).

Analytic truth defined as a true statement derivable from a tautology by putting synonyms for synonyms is near Kant's account of analytic truth as a truth whose negation is a contradiction. Analytic truth defined as a truth confirmed no matter what however, is closer to one of the traditional accounts of a priori. While the first four sections of Quine's paper concern analyticity, the last two concern apriority. Putnam considers the argument in the two last sections as independent of the first four, and at the same time as Putnam criticizes Quine, he also emphasizes his historical importance as the first top rank philosopher to both reject the notion of apriority and sketch a methodology without it.

Helmholtz says "Yellow and indigo blue" are complements. Grassmann reconstructs Newton's category boundaries in terms of wavelengths and says "This indigo therefore falls within the limits of color between which, according to Helmholtz, the complementary colors of yellow lie." Newton's own color circle has yellow directly opposite the boundary between indigo and violet. These results, that the complement of yellow is a wavelength shorter than 450 nm, are derivable from the modern CIE 1931 system of colorimetry if it is assumed that the yellow is about 580 nm or shorter wavelength, and the specified white is the color of a blackbody radiator of temperature 2800 K or lower (that is, the white of an ordinary incandescent light bulb).

Parabolic (1) and hyperbolic (3) orbits are escape orbits, whereas elliptical and circular orbits (2) are captive. gravitational potential well of the central mass's field of potential energy shown in black and the height of the kinetic energy of the moving body shown in red extending above that, correlating to changes in speed as distance changes according to Kepler's laws. Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections (this assumes that the force of gravity propagates instantaneously). Newton showed that, for a pair of bodies, the orbits' sizes are in inverse proportion to their masses, and that those bodies orbit their common center of mass.

In 1934, Popper published Zur Kritik der Ungenauigkeitsrelationen (Critique of the Uncertainty Relations) in Naturwissenschaften, and in the same year Logik der Forschung (translated and updated by the author as The Logic of Scientific Discovery in 1959), outlining his arguments for the statistical interpretation. In 1982, he further developed his theory in Quantum theory and the schism in Physics, writing: > [Heisenberg's] formulae are, beyond all doubt, derivable statistical > formulae of the quantum theory. But they have been habitually misinterpreted > by those quantum theorists who said that these formulae can be interpreted > as determining some upper limit to the precision of our measurements. > [original emphasis]Popper, K. Quantum theory and the schism in Physics, > Unwin Hyman Ltd, 1982, pp. 53–54.

OWL DL is designed to provide the maximum expressiveness possible while retaining computational completeness (either φ or ¬φ holds), decidability (there is an effective procedure to determine whether φ is derivable or not), and the availability of practical reasoning algorithms. OWL DL includes all OWL language constructs, but they can be used only under certain restrictions (for example, number restrictions may not be placed upon properties which are declared to be transitive; and while a class may be a subclass of many classes, a class cannot be an instance of another class). OWL DL is so named due to its correspondence with description logic, a field of research that has studied the logics that form the formal foundation of OWL.

It is the energy of configuration of a given system of conservative forces (that is why it is called potential) and only has meaning with respect to a defined set of references (or data). Expressions for all other thermodynamic energy potentials are derivable via Legendre transforms from an expression for . In thermodynamics, external forces, such as gravity, are typically disregarded when formulating expressions for potentials. For example, while all the working fluid in a steam engine may have higher energy due to gravity while sitting on top of Mount Everest than it would at the bottom of the Mariana Trench, the gravitational potential energy term in the formula for the internal energy would usually be ignored because changes in gravitational potential within the engine during operation would be negligible.

PaX does not change the load order of libraries. This means if an attacker knows the address of one library, he can derive the locations of all other libraries; however, it is notable that there are more serious problems if the attacker can derive the location of a library in the first place, and extra randomization will not likely help that. Further, typical attacks only require finding one library or function; other interesting elements such as the heap and stack are separately randomized and are not derivable from the mmap() base. When ET_DYN executables—that is, executables compiled with position independent code in the same way as shared libraries—are loaded, their base is also randomly chosen, as they are mmap()ed into RAM just like regular shared objects.

This proof is taken from Chapter 10, section 4, 5 of Mathematical Logic by H.-D. Ebbinghaus. As in the most common proof of Gödel's First Incompleteness Theorem through using the undecidability of the halting problem, for each Turing machine M there is a corresponding arithmetical sentence \phi_M, effectively derivable from M, such that it is true if and only if M halts on the empty tape. Intuitively, \phi_M asserts "there exists a natural number that is the Gödel code for the computation record of M on the empty tape that ends with halting". If the machine M does halt in finite steps, then the complete computation record is also finite, then there is a finite initial segment of the natural numbers such that the arithmetical sentence \phi_M is also true on this initial segment.

Database theory encapsulates a broad range of topics related to the study and research of the theoretical realm of databases and database management systems. Theoretical aspects of data management include, among other areas, the foundations of query languages, computational complexity and expressive power of queries, finite model theory, database design theory, dependency theory, foundations of concurrency control and database recovery, deductive databases, temporal and spatial databases, real-time databases, managing uncertain data and probabilistic databases, and Web data. Most research work has traditionally been based on the relational model, since this model is usually considered the simplest and most foundational model of interest. Corresponding results for other data models, such as object-oriented or semi- structured models, or, more recently, graph data models and XML, are often derivable from those for the relational model.

The SDT view is that social constructions employing ideology and social narratives may be used as effective justifications regardless whether they are epistemologically true or false, or whether they legitimize inequality or equality. From the Marxian economic determinist perspective, race, ethnic and gender conflict are sociological epiphenomena derivable from the primary economic class conflict. Unlike Marxian sociologists, SDT along with Mosca, Michels, and Pareto together reject reduction solely to economic causes, and are skeptical of the hoped for class revolution. Pareto’s analysis was that “victory” in the class struggle will merely usher in a new set of socially dominant elites. Departing from elite theory’s near exclusive focus on social structures manipulated by rational actors, SDT follows Pareto’s new direction towards examining collective psychological forces, asserting that human behavior is not primarily driven by either reason or logic.

Some varieties of emergentism are not specifically concerned with the mind–body problem, and instead suggest a hierarchical or layered view of the whole of nature, with the layers arranged in terms of increasing complexity with each requiring its own special science. Typically physics (mathematical physics, particle physics, and classical physics) is basic, with chemistry built on top of it, then biology, psychology, and social sciences. Reductionists respond that the arrangement of the sciences is a matter of convenience, and that chemistry is derivable from physics (and so forth) in principle, an argument which gained force after the establishment of a quantum-mechanical basis for chemistry.Crane, T. The Significance of Emergence Other varieties see mind or consciousness as specifically and anomalously requiring emergentist explanation, and therefore constitute a family of positions in the philosophy of mind.

In Speech Acts, John Searle argues that from the difficulties encountered in trying to explicate analyticity by appeal to specific criteria, it does not follow that the notion itself is void. Considering the way which we would test any proposed list of criteria, which is by comparing their extension to the set of analytic statements, it would follow that any explication of what analyticity means presupposes that we already have at our disposal a working notion of analyticity. In "'Two Dogmas' Revisited", Hilary Putnam argues that Quine is attacking two different notions: Analytic truth defined as a true statement derivable from a tautology by putting synonyms for synonyms is near Kant's account of analytic truth as a truth whose negation is a contradiction. Analytic truth defined as a truth confirmed no matter what, however, is closer to one of the traditional accounts of a priori.

As a form of epistemological idealism, rationalism interprets existence as cognizable and rational, that all things are composed of strings of reasoning, requiring an associated idea of the thing, and all phenomena (including consciousness) are the result of an understanding of the imprint from the noumenal world in which lies beyond the thing-in-itself. In scholasticism, existence of a thing is not derived from its essence but is determined by the creative volition of God, the dichotomy of existence and essence demonstrates that the dualism of the created universe is only resolvable through God. Empiricism recognizes existence of singular facts, which are not derivable and which are observable through empirical experience. The exact definition of existence is one of the most important and fundamental topics of ontology, the philosophical study of the nature of being, existence, or reality in general, as well as of the basic categories of being and their relations.

Pointing at stationary targets such as buttons, windows, images, menu items, and controls on computer displays is commonplace and has a well- established modeling tool for analysis - Fitt's law (Fitts, 1954) - which states that the time to make an aimed movement (MT) is a linear function of the index of difficulty of the movement: MT = a + bID. The index of difficulty (ID) for any given movement is a function of the ratio of distance to the target (D) and width of the target (W): ID = log2(2D/W) - a relationship derivable from information theory. Fitt's law is actually responsible for the ubiquity of the computer mouse, due to the research of Card, English, and Burr (1978). Extensions of Fitt's law also apply to pointing at spatially moving targets, via the steering law, originally discovered by C.G. Drury in 1971 and later on rediscovered in the context of human-computer interaction by Accott & Zhai (1997, 1999).

03 referred the following questions to the Enlarged Board of Appeal (considered under case number G 1/06): :"(1) In the case of a sequence of applications consisting of a root (originating) application followed by divisional applications, each divided from its predecessor, is it a necessary and sufficient condition for a divisional application of that sequence to comply with Article 76(1) EPC, second sentence, that anything disclosed in that divisional application be directly, unambiguously and separately derivable from what is disclosed in each of the preceding applications as filed? :(2) If the above condition is not sufficient, does said sentence impose the additional requirement ::(a) that the subject-matter of the claims of said divisional be nested within the subject-matter of the claims of its divisional predecessors? or ::(b) that all the divisional predecessors of said divisional comply with Article 76(1) EPC?" G 1/05, Summary of Facts and Submissions II.

Specifically, Jablonski's assertions suggest that the adjective "woolly" in reference to Afro-hair is a misnomer in connoting the high heat insulation derivable from the true wool of sheep. Instead, the relatively sparse density of Afro-hair, combined with its springy coils actually results in an airy, almost sponge-like structure that in turn, Jablonski argues, more likely facilitates an increase in the circulation of cool air onto the scalp. Further, wet Afro-hair does not stick to the neck and scalp unless totally drenched and instead tends to retain its basic springy puffiness because it less easily responds to moisture and sweat than straight hair does. In this sense, the trait may enhance comfort levels in intense equatorial climates more than straight hair (which, on the other hand, tends to naturally fall over the ears and neck to a degree that provides slightly enhanced comfort levels in cold climates relative to tightly coiled hair).

Today, the bulk of extant mathematics is believed to be derivable logically from a small number of extralogical axioms, such as the axioms of Zermelo–Fraenkel set theory (or its extension ZFC), from which no inconsistencies have as yet been derived. Thus, elements of the logicist programmes have proved viable, but in the process theories of classes, sets and mappings, and higher-order logics other than with Henkin semantics, have come to be regarded as extralogical in nature, in part under the influence of Quine's later thought. Kurt Gödel's incompleteness theorems show that no formal system from which the Peano axioms for the natural numbers may be derived — such as Russell's systems in PM — can decide all the well-formed sentences of that system."On the philosophical relevance of Gödel's incompleteness theorems" This result damaged Hilbert's programme for foundations of mathematics whereby 'infinitary' theories — such as that of PM — were to be proved consistent from finitary theories, with the aim that those uneasy about 'infinitary methods' could be reassurred that their use should provably not result in the derivation of a contradiction.

American Christian radio host Harold Camping stated that the Rapture and Judgment Day would take place on May 21, 2011, and that the end of the world would take place five months later on October 21, 2011, based on adding the 153 fish of John 20 to May 21. The Rapture, as indicated in 1 Thessalonians 4:17 (harpagēsometha = we shall be raptured / taken up, "rapture" derivable from the Latin translation rapiemur) is the taking up of believers to a meeting in the air with the Lord Jesus, but for Camping the rapture was also associated with the End of the World. Camping, who was then president of the Family Radio Christian network, claimed the Bible as his source and said May 21 would be the date of the Rapture and the day of judgment "beyond the shadow of a doubt". Camping suggested that it would occur at 6 pm local time, with the Rapture sweeping the globe time zone by time zone, while some of his supporters claimed that around 200 million people (approximately 3% of the world's population) would be 'raptured'. Camping had previously claimed that the Rapture would occur in September 1994.