107 Sentences With "combinatory" | Random Sentence Generator

The result is the most combinatory device Microsoft's made yet.

It is almost a combinatory mimesis of Howe's and Mackey's poetry.

His words and his charcoal-palette drawings have a combinatory intelligence.

The Surface Book 3303 is the most combinatory device Microsoft's made yet.

The Surface Book 2 is the most combinatory device Microsoft's made yet.

In the new book, as in the earlier one, what is so remarkable is her combinatory genius.

"The Lego system in play is a design language that both stimulates creativity and challenges your combinatory skills," he says.

They get to be with one another, and they are the combinatory Mama for the entirety of the world that will springboard from Sam Porter Bridges saving the world.

The resulting combinatory hues lend a complexity to the work that does not allow the eye to rest easily, reminding us that color, as a product of light, is always in motion.

The ghazal is necessarily a thing of loose form: each sher or couplet should stand as an independent entity, and while the ghazal forms a further whole as well, its structure is associative and combinatory.

Schwarz's combinatory and contradictory practice squeezes the hard nut of reality through a formal filter that transforms a familiar device, the graffiti tag, into a form of pure abstraction wrapped in historically aware quotation marks.

She is at her strongest when she's romping through combinatory, contrary, and contradictory ideas with a vehemence that abandons stylistic consistency and regards formal notions like composition as an afterthought instead of a starting point.

As I sat in the sun with "Untitled" and happily toiled to solve the ad infinitum conundrums it supplied, I kept wanting to fabricate fairy tales out of this vague but grisly mélange of malleable and combinatory superfluity.

These projects indicate the same kind of combinatory impulse: for 2 WTC, weaving together the space of work and the space of neighborhood, and for the Google campus, weaving together the space of work and the space of nature.

LeWitt, who died in 2007 at the age of 78, demonstrated over the course of his career that his combinatory procedures, despite their limited parameters, are capable of yielding configurations that are as richly imaginative as they are seemingly endless.

Purely musical information and commands was a tighter race, as the HomePod's 'Musicologist' feature was much better at delivering musical information (though stumbled a lot on compilations or best of records) and using linking or combinatory commands to drill down through musical choices.

When the arrangement is too obvious in its attempt to shock aesthetic tastes — such as when Bertrand Lavier's post-moderm "Black & Decker" (1998) is placed next to an ancient sword from the Kiribati islands of Micronesia — the combinatory music stops with a dull thud.

At the same time, the imagery and stylistic tropes that Pettibon gleans from historically tawdry sources — modes of expression specializing in abjection, violence, and despair — collide with his multilayered and sometimes lofty inscriptions, amassing a combinatory force that lands a punch to the head again and again.

Premised on a kind of combinatory pragmatism that was all but inescapable at the turn of the 2010s, the band is formula made flesh, an aural manifestation of a few guys kicking around ideas and influences from the inner sanctity of their practice space, not expecting any immediate attention.

The sense you get, upon reaching this room, is that whatever Johns carried away with him from his initial encounter with Munch — alienation, isolation, and existential horror are possible guesses — has been, if not purged, then liberated from the confines of single motifs, generating a newfound combinatory idiom that could take him anywhere and everywhere.

Binary combinatory logic (BCL) is a formulation of combinatory logic using only the symbols 0 and 1.. BCL has applications in the theory of program-size complexity (Kolmogorov complexity).

Axioms P1, P2 and P3, with the deduction rule modus ponens (formalising intuitionistic propositional logic), correspond to combinatory logic base combinators I, K and S with the application operator. Proofs in the Hilbert system then correspond to combinator terms in combinatory logic. See also Curry–Howard correspondence.

The fragment of TL without weak negation and the implication operator is classical logic. TL is thus a logical blend or rather a crossbreed. Peña's plan to investigate the grounds of his logical system as a nonclassical combinatory logic has thus far remained programmatic, but the combinatory account fits his metaphysical approach.

Haskell Brooks Curry (; September 12, 1900 – September 1, 1982) was an American mathematician and logician. Curry is best known for his work in combinatory logic. While the initial concept of combinatory logic was based on a single paper by Moses Schönfinkel,1924\. "Über die Bausteine der mathematischen Logik", Mathematische Annalen 92, pp. 305–316.

To Mock a Mockingbird and Other Logic Puzzles: Including an Amazing Adventure in Combinatory Logic (1985, ) is a book by the mathematician and logician Raymond Smullyan. It contains many nontrivial recreational puzzles of the sort for which Smullyan is well known. It is also a gentle and humorous introduction to combinatory logic and the associated metamathematics, built on an elaborate ornithological metaphor. Combinatory logic, functionally equivalent to the lambda calculus, is a branch of symbolic logic having the expressive power of set theory, and with deep connections to questions of computability and provability.

The existence of these paradoxes meant that the lambda calculus could not be both consistent and complete as a deductive system. Haskell Curry studied of illative (deductive) combinatory logic in 1941. Combinatory logic is closely related to lambda calculus, and the same paradoxes exist in each. Later the lambda calculus was resurrected as a definition of a programming language.

In lambda calculus two metaoperators are used: application – the same as in combinatory logic, and functional abstraction which binds the only variable in one object.

Moses Ilyich Schönfinkel, also known as Moisei Isai'evich Sheinfinkel' (; 4 September 1889 – 1942), was a Russian logician and mathematician, known for the invention of combinatory logic.

In mathematics, solid partitions are natural generalizations of partitions and plane partitions defined by Percy Alexander MacMahon.P. A. MacMahon, Combinatory Analysis. Cambridge Univ. Press, London and New York, Vol.

"Dancing the doctrine: honji suijaku thought in kagura." In Buddhas and kami in Japan: honji suijaku as a combinatory paradigm, pp. 313–332. and Buddhist schools such as Shingon.Ambros, Barbara. 2008.

Curran's research focuses on natural language processing , making him one of the few Australian computational linguists. Specifically Curran's research has focused on the area of natural language processing known as combinatory categorial grammar parsing. In addition to his contributions to NLP, Curran has produced a paper on the development of search engines to assist in driving problem based learning. Within NLP, he has published papers on combinatory categorial grammar parsing as well as question answering systems.

Richard Statman (born September 6, 1946) is an American computer scientist whose principal research interest is the theory of computation, especially symbolic computation. His research involves lambda calculus, type theory, and combinatory algebra.

Combinatory categorial grammar (CCG) is an efficiently parsable, yet linguistically expressive grammar formalism. It has a transparent interface between surface syntax and underlying semantic representation, including predicate-argument structure, quantification and information structure. The formalism generates constituency-based structures (as opposed to dependency- based ones) and is therefore a type of phrase structure grammar (as opposed to a dependency grammar). CCG relies on combinatory logic, which has the same expressive power as the lambda calculus, but builds its expressions differently.

In the 1930s, Curry's paradox and the related Kleene–Rosser paradox played a major role in showing that formal logic systems based on self-recursive expressions are inconsistent. These include some versions of lambda calculus and combinatory logic. Curry began with the Kleene–Rosser paradox and deduced that the core problem could be expressed in this simpler Curry's paradox. His conclusion may be stated as saying that combinatory logic and lambda calculus cannot be made consistent as deductive languages, while still allowing recursion.

Applicative computing systems, or ACS are the systems of object calculi founded on combinatory logic and lambda calculus.Wolfengagen V.E. Methods and means for computations with objects. Applicative Computational Systems. — M.: JurInfoR Ltd., «Center JurInfoR», 2004.

Although Montague's work is sometimes regarded as syntactically uninteresting, it helped to bolster interest in categorial grammar by associating it with a highly successful formal treatment of natural language semantics. More recent work in categorial grammar has focused on the improvement of syntactic coverage. One formalism which has received considerable attention in recent years is Steedman and Szabolcsi's combinatory categorial grammar which builds on combinatory logic invented by Moses Schönfinkel and Haskell Curry. There are a number of related formalisms of this kind in linguistics, such as type logical grammar and abstract categorial grammar.

Aside from a Turing machine, other equivalent (See: Church–Turing thesis) models of computation are in use. ;Lambda calculus: A computation consists of an initial lambda expression (or two if you want to separate the function and its input) plus a finite sequence of lambda terms, each deduced from the preceding term by one application of Beta reduction. ;Combinatory logic :is a concept which has many similarities to \lambda-calculus, but also important differences exist (e.g. fixed point combinator Y has normal form in combinatory logic but not in \lambda-calculus).

Nikola Obreshkov Prize, the highest Bulgarian award in mathematics, bestowed for his monograph Combinatory Spaces and Recursiveness in Them.A. Soskova, L. Ivanov and I. Georgiev. On Dimiter Skordev by his students. In: Mathematics and Education in Mathematics, 2017.

Although the above definition is formulated in terms of a term algebra, the general concept applies more generally, and can be defined both for combinatory algebras and for lambda calculus proper, specifically, within the framework of explicit substitution.

Christopher Strachey wrote a combinatory love letter algorithm for the Manchester Mark 1 computer in 1952. The poems it generated have been seen as the first piece of digital literature and a queer critique of heteronormative expressions of love.

Joachim Lambek proposed the first noncommutative logic in his 1958 paper Mathematics of Sentence Structure to model the combinatory possibilities of the syntax of natural languages. His calculus has thus become one of the fundamental formalisms of computational linguistics.

P. A. MacMahon. “Combinatory Analysis,” Cambridge Univ. Press, London/New York, 1916; reprinted by Chelsea, New York, 1960. The hook length formula itself was discovered in 1953 by Frame, Robinson, and Thrall as an improvement to the Young–Frobenius formula.

In the study of illative (deductive) combinatory logic, Curry in 1941 recognized the implication of the paradox as implying that, without restrictions, the following properties of a combinatory logic are incompatible: # Combinatorial completeness. This means that an abstraction operator is definable (or primitive) in the system, which is a requirement on the expressive power of the system. # Deductive completeness. This is a requirement on derivability, namely, the principle that in a formal system with material implication and modus ponens, if Y is provable from the hypothesis X, then there is also a proof of X → Y.

In 1929 he returned to the Université Saint-Louis, Brussels, and in 1944 he was appointed Professor at the University of Leuven. In 1958 Feys and Haskell B. Curry devised the type inference algorithm for the simply typed lambda calculus (Combinatory Logic).

In mathematics, the MacMahon Master theorem (MMT) is a result in enumerative combinatorics and linear algebra. It was discovered by Percy MacMahon and proved in his monograph Combinatory analysis (1916). It is often used to derive binomial identities, most notably Dixon's identity.

Smullyan's exposition takes the form of an imaginary account of two men going into a forest and discussing the unusual "birds" (combinators) they find there (bird watching was a hobby of one of the founders of combinatory logic, Haskell Curry, and another founder Moses Schönfinkel's name means beautiful bird). Each species of bird in Smullyan's forest stands for a particular kind of combinator appearing in the conventional treatment of combinatory logic. Each bird has a distinctive call, which it emits when it hears the call of another bird. Hence an initial call by certain "birds" gives rise to a cascading sequence of calls by a succession of birds.

Mathematical Systems Theory 27(6): 511–546. demonstrates that Linear Indexed Grammars, Combinatory Categorial Grammars, Tree-adjoining Grammars, and Head Grammars are weakly equivalent formalisms, in that they all define the same string languages. Kuhlmann et al. (2015)Kuhlmann, M., Koller, A., and Satta, G. 2015.

The B, C, K, W system is a variant of combinatory logic that takes as primitive the combinators B, C, K, and W. This system was discovered by Haskell Curry in his doctoral thesis Grundlagen der kombinatorischen Logik, whose results are set out in Curry (1930).

Corrado Böhm (17 January 1923 – 23 October 2017) was a Professor Emeritus at the University of Rome "La Sapienza" and a computer scientist known especially for his contributions to the theory of structured programming, constructive mathematics, combinatory logic, lambda calculus, and the semantics and implementation of functional programming languages.

George Pólya writes in Mathematics and plausible reasoning: : The name "generating function" is due to Laplace. Yet, without giving it a name, Euler used the device of generating functions long before Laplace [..]. He applied this mathematical tool to several problems in Combinatory Analysis and the Theory of Numbers.

Lexicalization and Generative Power in CCG. Computational Linguistics 41(2): 215-247. show that this equivalence, and the ability of CCG to describe {a^n b^n c^n d^n}, rely crucially on the ability to restrict the use of the combinatory rules to certain categories, in ways not explained above.

Vijay-Shanker and Weir (1994)Vijay-Shanker, K. and Weir, David J. 1994. The Equivalence of Four Extensions of Context-Free Grammars. Mathematical Systems Theory 27(6): 511-546. demonstrate that linear indexed grammars, combinatory categorial grammar, tree-adjoining grammars, and head grammars are weakly equivalent formalisms, in that they all define the same string languages.

Vijay-Shanker and Weir (1994)Vijay-Shanker, K. and Weir, David J. 1994. The Equivalence of Four Extensions of Context-Free Grammars. Mathematical Systems Theory 27(6): 511–546. demonstrate that linear indexed grammars, combinatory categorial grammar, tree-adjoining grammars, and head grammars are weakly equivalent formalisms, in that they all define the same string languages.

In mathematics, the Kleene-Rosser paradox is a paradox that shows that certain systems of formal logic are inconsistent, in particular the version of Curry's combinatory logic introduced in 1930, and Church's original lambda calculus, introduced in 1932-1933, both originally intended as systems of formal logic. The paradox was exhibited by Stephen Kleene and J. B. Rosser in 1935.

The Curry-Howard isomorphism between proofs and programs relates to proof theory, especially intuitionistic logic. Formal calculi such as the lambda calculus and combinatory logic are now studied as idealized programming languages. Computer science also contributes to mathematics by developing techniques for the automatic checking or even finding of proofs, such as automated theorem proving and logic programming. Descriptive complexity theory relates logics to computational complexity.

Under a Fulbright fellowship, he collaborated with Robert Feys in Louvain, Belgium. After retiring from Penn State in 1966, Curry accepted a position at the University of Amsterdam. In 1970, after finishing the second volume of his treatise on the combinatory logic, Curry retired from the University of Amsterdam and returned to State College, Pennsylvania. Haskell Curry died on September 1, 1982 in State College, Pennsylvania.

A lexical rule is in a form of syntactic rule used within many theories of natural language syntax. These rules alter the argument structures of lexical items (for example verbs and declensions) in order to alter their combinatory properties. Lexical rules affect in particular specific word classes and morphemes. Moreover, they may have exceptions, do not apply across word boundaries and can only apply to underlying forms.

The "combinatory" (the word is Quine's) predicate functors, all monadic and peculiar to PFL, are Inv, inv, ∃, +, and p. A term is either an atomic term, or constructed by the following recursive rule. If τ is a term, then Invτ, invτ, ∃τ, +τ, and pτ are terms. A functor with a superscript n, n a natural number > 1, denotes n consecutive applications (iterations) of that functor.

Peggy Cyphers (born 1954) is an American painter, printmaker, professor and art writer, who has shown her work in the U.S. and internationally since 1984. Since Cyphers’ move to New York City over 30 years ago, her inventive and combinatory approaches to the materials of paint, silkscreen and sand have developed into canvases that explore the “Politics of Progress” as it impacts culture and the natural world.

To this end, Kondylis made effective use of his distinction between the "synthetic-harmonising thought- form" and the "analytic-combinatory thought-form" in which the latter set aside the former during the same period as the setting-aside of classical bourgeois liberalism by mass democracy, which for the most part occurred as the re-interpretation and changing of liberalism in accordance with the needs of mass democracy, and not always as an open and programmatic clash between the two. The "synthetic-harmonising thought-form" and the "analytic- combinatory thought-form" distinction is applied by Kondylis to his extensive overview of developments in the arts (including literature, music, architecture, the visual arts, cinema), as well as of developments in philosophy, the sciences and commonplace mind-sets and ways of living, mainly from the second half of the 19th century until the cultural revolution of the 1960s and 1970s.

Barendregt originally introduced the term "functional completeness" in the context of combinatory algebra. Kappa calculus arose out of efforts by Lambek to formulate an appropriate analogue of functional completeness for arbitrary categories (see Hermida and Jacobs, section 1). Hasegawa later developed kappa calculus into a usable (though simple) programming language including arithmetic over natural numbers and primitive recursion. Connections to arrows were later investigated by Power, Thielecke, and others.

The notion of the categorical abstract machine arose in the mid-1980s. It took its place in computer science as a kind of theory of computation for programmers, represented by Cartesian closed category and embedded into the combinatory logic. CAM is a transparent and sound mathematical representation for the languages of functional programming. The machine code can be optimized using the equational form of a theory of computation.

Inspector Craig gets his name from William Craig. His book To Mock a Mockingbird (1985) is a recreational introduction to the subject of combinatory logic. Apart from writing about and teaching logic, Smullyan released a recording of his favorite baroque keyboard and classical piano pieces by composers such as Bach, Scarlatti, and Schubert. Some recordings are available on the Piano Society website, along with the video "Rambles, Reflections, Music and Readings".

The lambda calculus, developed in the 1930s by Alonzo Church, is a formal system of computation built from function application. In 1937 Alan Turing proved that the lambda calculus and Turing machines are equivalent models of computation, showing that the lambda calculus is Turing complete. Lambda calculus forms the basis of all functional programming languages. An equivalent theoretical formulation, combinatory logic, was developed by Moses Schönfinkel and Haskell Curry in the 1920s and 1930s.

For a detailed discussion of Gödel's adoption of Turing's machines as models of computation, see A hypothesis leading to a natural law?: In late 1936 Alan Turing's paper (also proving that the Entscheidungsproblem is unsolvable) was delivered orally, but had not yet appeared in print.. On the other hand, Emil Post's 1936 paper had appeared and was certified independent of Turing's work.cf. Editor's footnote to Post 1936 Finite Combinatory Process. Formulation I. at .

Quote from p. 371: ‘[...] suffice it to say that Alinei clears away all the combinatory work done on Etruscan (for grammar specially) to try to make Uralic inflections fit without ripping the seams. He completely ignores the aforesaid recent findings in phonology (and phoneme/grapheme relationships), returning to the obsolete but convenient theory that the handwriting changed and orthography was not consolidated'. Finno-Ugric experts such as Angela Marcantonio,Marcantonio, Angela (2004).

Vijay-Shanker and Weir (1994) demonstrates that Linear Indexed Grammars, Combinatory Categorial Grammars, Tree-adjoining Grammars, and Head Grammars all define the same class of string languages. Their formal definition of linear indexed grammarsp.517-518 differs from the above. LIGs (and their weakly equivalents) are strictly less expressive (meaning they generate a proper subset) than the languages generated by another family of weakly equivalent formalism, which include: LCFRS, MCTAG, MCFG and minimalist grammars (MGs).

Curry was supervised by David Hilbert and worked closely with Bernays, receiving a Ph.D. in 1930 with a dissertation on combinatory logic. In 1928, before leaving for Göttingen, Curry married Mary Virginia Wheatley. The couple lived in Germany while Curry completed his dissertation, then, in 1929, moved to State College, Pennsylvania where Curry accepted a position at Pennsylvania State College. They had two children, Anne Wright Curry (July 27, 1930) and Robert Wheatley Curry (July 6, 1934).

By the time it entered Japan it was already syncretic, having adapted to and amalgamated with other religions and cultures in India, China, and the Korean Peninsula.Encyclopedia of Shinto, Combinatory Kami, accessed on October 13, 2008. Quotation: "Buddhism was already product of a complex process of adaptation and amalgamation with other belief systems in India, China, and the Korean peninsula." For example, already while in India, it had absorbed Hindu divinities like Brahma (Bonten in Japanese) and Indra (Taishakuten).

When it arrived in Japan, it already had a disposition towards producing the combinatory gods that the Japanese would call . Searching for the origins of a kami in Buddhist scriptures was felt to be nothing out of the ordinary. However, if monks didn't doubt the existence of kami, they certainly saw them as inferior to their buddhas.Bernhard Scheid Hindu gods had already been treated analogously: they had been thought of as un-illuminated and prisoners of saṃsāra.

Schönfinkel attended the Novorossiysk University of Odessa, studying mathematics under Samuil Osipovich Shatunovskii (1859–1929), who worked in geometry and the foundations of mathematics. From 1914 to 1924, Schönfinkel was a member of David Hilbert's group at the University of Göttingen. On 7 December 1920 he delivered a talk to the group where he outlined the concept of combinatory logic. Heinrich Behmann, a member of Hilbert's group, later revised the text and published it in 1924.

Similarly, vowel contrasts (including their prosodic combinatory possibilities) found outside of the stem are significantly neutralized. For details about the morphology of Navajo, see Navajo grammar. Like most Athabascan languages, Navajo is coronal heavy, having many phonological contrasts at coronal places of articulation and less at other places. Also typical of the family, Navajo has a limited number of labial sounds, both in terms of its phonemic inventory and in their occurrence in actual lexical items and displays of consonant harmony.

The lambda calculus was introduced by mathematician Alonzo Church in the 1930s as part of an investigation into the foundations of mathematics.For a full history, see Cardone and Hindley's "History of Lambda- calculus and Combinatory Logic" (2006). The original system was shown to be logically inconsistent in 1935 when Stephen Kleene and J. B. Rosser developed the Kleene–Rosser paradox. Subsequently, in 1936 Church isolated and published just the portion relevant to computation, what is now called the untyped lambda calculus.

Remaining at Harvard, Curry pursued a Ph.D. in mathematics. While he was directed by George David Birkhoff to work on differential equations, his interests continued to shift to logic. In 1927, while an instructor at Princeton University, he discovered the work of Moses Schönfinkel in combinatory logic. Schönfinkel's work had anticipated much of Curry's own research, and as a consequence, he moved to University of Göttingen where he could work with Heinrich Behmann and Paul Bernays, who were familiar with Schönfinkel's work.

Formal Syntax and Semantics of Programming Languages. 1995. p. 144. This replacement mechanism simplifies work in both combinatory logic and lambda calculus and would later be called currying, after Haskell Curry. While Curry attributed the concept to Schönfinkel, it had already been used by FregeWillard Van Orman Quine, introduction to "Bausteine der mathematischen Logik", pp. 305–316. Translated by Stefan Bauer-Mengelberg as "On the building blocks of mathematical logic" in Jean van Heijenoort (1967), A Source Book in Mathematical Logic, 1879–1931.

In computer programming, a parser combinator is a higher-order function that accepts several parsers as input and returns a new parser as its output. In this context, a parser is a function accepting strings as input and returning some structure as output, typically a parse tree or a set of indices representing locations in the string where parsing stopped successfully. Parser combinators enable a recursive descent parsing strategy that facilitates modular piecewise construction and testing. This parsing technique is called combinatory parsing.

His current interests include Probabilistic and Functional Complexity Classes, Combinatory Algebras as a foundation to Theory of Computations, the interconnections of Cryptographic Techniques and Computational Complexity as well as Algorithms for Graph Problems. He has co-organized International Conferences: STOC '87 (and programming committee of STOC '01), ICALP, CiE (Computability in Europe), PLS, ASL (Association for Symbolic Logic) European Summer Meeting, ACAC (Athens Colloquium on Algorithms and Complexity) and NYCAC (New York Colloquium on Algorithms and Complexity). He is the brother of theoretical physicist Cosmas Zachos.

Alonzo Church invented the lambda calculus in the 1930s, originally to provide a new and simpler basis for mathematics.For a full history, see Cardone and Hindley's "History of Lambda-calculus and Combinatory Logic" (2006). However soon after inventing it major logic problems were identified with the definition of the lambda abstraction: The Kleene–Rosser paradox is an implementation of Richard's paradox in the lambda calculus. Haskell Curry found that the key step in this paradox could be used to implement the simpler Curry's paradox.

Also taxifolin inhibited the cellular melanogenesis as effectively as arbutin, one of the most widely used hypopigmenting agents in cosmetics. However, arbutin acts as quercetin extremely mutagenic, carcinogenic and toxic. Taxifolin enhanced also the efficacy of conventional antibiotics like levofloxacin and ceftazidime in vitro, which have potential for combinatory therapy of patients infected with methicillin-resistant Staphylococcus aureus (MRSA). Taxifolin, as well as many other flavonoids, has been found to act as a non-selective antagonist of the opioid receptors, albeit with somewhat weak affinity.

In integrated circuit design, dynamic logic (or sometimes clocked logic) is a design methodology in combinatory logic circuits, particularly those implemented in MOS technology. It is distinguished from the so-called static logic by exploiting temporary storage of information in stray and gate capacitances. It was popular in the 1970s and has seen a recent resurgence in the design of high speed digital electronics, particularly computer CPUs. Dynamic logic circuits are usually faster than static counterparts, and require less surface area, but are more difficult to design.

Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F", requiring only a few apparently innocuous logical deduction rules. Since F is arbitrary, any logic having these rules allows one to prove everything. The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic. The paradox is named after the logician Haskell Curry.

GeneDecks is a novel analysis tool to identify similar or partner genes, which provides a similarity metric by highlighting shared descriptors between genes, based on GeneCards’ unique wealth of combinatorial annotations of human genes. # Annotation combinatory: Using GeneDecks, one can get a set of similar genes for a particular gene with a selected combinatorial annotation. The summary table result in ranking the different level of similarity between the identified genes and the probe gene. # Annotation unification: Different data sources often offer annotations with heterogeneous naming system.

Amsterdam: North-Holland Publishing Company, 1952, p. 109. Another treatise was published in 1963 by Aleksandr A. Zinov'ev and othersAleksandr A. Zinov'ev, David Dinsmore Comey and Guido Küng, Philosophical problems of many-valued logic. Dordrecht: D. Reidel, 1963. In 1964, the American philosopher William Alston introduced the term "degree vagueness" to describe vagueness in an idea that results from the absence of a definite cut-off point along an implied scale (in contrast to "combinatory vagueness" caused by a term that has a number of logically independent conditions of application).

In the late 1960s and early 1970s researchers expanded the counter machine model into the register machine, a close cousin to the modern notion of the computer. Other models include combinatory logic and Markov algorithms. Gurevich adds the pointer machine model of Kolmogorov and Uspensky (1953, 1958): "... they just wanted to ... convince themselves that there is no way to extend the notion of computable function."Gurevich 1988:2 All these contributions involve proofs that the models are computationally equivalent to the Turing machine; such models are said to be Turing complete.

The simplest example of an undecidable word problem occurs in combinatory logic: when are two strings of combinators equivalent? Because combinators encode all possible Turing machines, and the equivalence of two Turing machines is undecidable, it follows that the equivalence of two strings of combinators is undecidable. Likewise, one has essentially the same problem in (untyped) lambda calculus: given two distinct lambda expressions, there is no algorithm which can discern whether they are equivalent or not; equivalence is undecidable. For several typed variants of the lambda calculus, equivalence is decidable by comparison of normal forms.

Schönfinkel developed a formal system that avoided the use of bound variables. His system was essentially equivalent to a combinatory logic based upon the combinators B, C, I, K, and S. Schönfinkel was able to show that the system could be reduced to just K and S and outlined a proof that a version of this system had the same power as predicate logic. His paper also showed that functions of two or more arguments could be replaced by functions taking a single argument. (Reprinted lecture notes from 1967.)Kenneth Slonneger and Barry L. Kurtz.

Conversely, combinatory logic and simply typed lambda calculus are not the only models of computation, either. Girard's linear logic was developed from the fine analysis of the use of resources in some models of lambda calculus; is there typed version of Turing's machine that would behave as a proof system? Typed assembly languages are such an instance of "low- level" models of computation that carry types. Because of the possibility of writing non-terminating programs, Turing-complete models of computation (such as languages with arbitrary recursive functions) must be interpreted with care, as naive application of the correspondence leads to an inconsistent logic.

The advocacy of Basic English became his primary activity from 1925 until his death. Basic English is an auxiliary international language of 850 words comprising a system that covers everything necessary for day-to-day purposes. These 850 words, together with its five combinatory rules, were designed to do the work of some 20,000 English words, which appealed to many of the leading communications philosophers and theorists of the time, including Otto Neurath and Willard C. Brinton. To promote Basic English, Ogden in 1927 founded the Orthological Institute, from orthology, the abstract term he proposed for its work (see orthoepeia).

In other words, ZFC cannot be finitely axiomatized. He pioneered a logical approach to natural language semantics which became known as Montague grammar. This approach to language has been especially influential among certain computational linguists—perhaps more so than among more traditional philosophers of language. In particular, Montague's influence lives on in grammar approaches like categorial grammar (such as Unification Categorial Grammar, Left-Associate Grammar, or Combinatory Categorial Grammar), which attempt a derivation of syntactic and semantic representation in tandem and the semantics of quantifiers, scope and discourse (Hans Kamp, a student of Montague, co-developed Discourse Representation Theory).

The origin of Alonzo Church's lambda calculus may have been, "How can you solve an equation, to provide a definition of a function?". This is expressed in this equivalence, This definition is valid if there is one and only one function f that satisfies the equation f\ x = y , but invalid otherwise. This is the core of the problem that Stephen Cole Kleene and then Haskell Curry discovered with combinatory logic and Lambda calculus. The situation may be compared to defining This definition is fine as long as only positive values are allowed for the square root.

Dynamic Syntax (DS) is a grammar formalism and linguistic theory whose overall aim is to explain the real-time twin processes of language understanding and production. Under the DS approach, syntactic knowledge is understood as the ability to incrementally analyse the structure and content of spoken and written language in context and in real-time. While it posits representations similar to those used in Combinatory Categorial Grammars (CCG), it builds those representations left-to-right going word-by-word. Thus it differs from other syntactic models which generally abstract way from features of everyday conversation such as interruption, backtracking, and self-correction.

Combinatory logic was developed with great ambitions: understanding the nature of paradoxes, making foundations of mathematics more economic (conceptually), eliminating the notion of variables (thus clarifying their role in mathematics). ;μ-recursive functions: a computation consists of a mu-recursive function, i.e. its defining sequence, any input value(s) and a sequence of recursive functions appearing in the defining sequence with inputs and outputs. Thus, if in the defining sequence of a recursive function f(x) the functions g(x) and h(x,y) appear, then terms of the form 'g(5)=7' or 'h(3,2)=10' might appear.

In his 1936 paper "Finite Combinatory Processes--Formulation 1", Emil Post described a model of which he conjectured is "logically equivalent to recursiveness". Post's model of a computation differs from the Turing-machine model in a further "atomization" of the acts a human "computer" would perform during a computation. Post's model employs a "symbol space" consisting of a "two-way infinite sequence of spaces or boxes", each box capable of being in either of two possible conditions, namely "marked" (as by a single vertical stroke) and "unmarked" (empty). Initially, finitely-many of the boxes are marked, the rest being unmarked.

The proposal that Liberman does is to investigate the processes from a semiotic and linguistic perspective. He proposed to consider psychoanalysis as an empirical science, and sustained that it exist two possible researches: during session, in the patient, and out of it, in the patient, the therapist or the bond between them. He added that it is convenient to think each patient not as a separate unit but in connection with the therapist. He postulated also that the empirical basis of the psychoanalytic research is the exchanges between the patient and therapist, each of them with a combinatory of expressive styles, which cover the verbal and non-verbal terrain.

Much work to functionally study bioelectric signaling has made use of applied (exogenous) electric currents and fields via DC and AC voltage-delivering apparatus integrated with agarose salt bridges. These devices can generate countless combinations of voltage magnitude and direction, pulses, and frequencies. Currently, lab-on-a-chip mediated application of electric fields is gaining ground in the field with the possibility to allow high-throughput screening assays of the large combinatory outputs. Figure 6 - Tools for manipulating non-neural bioelectricity include pharmacological and genetic reagents to alter cell connectivity (control gap junctions), cell Vmem (control ion channels/pumps), and bioelectrically-guided 2nd messengers (control neurotransmitters and other small molecules).

A model of computation is a formal description of a particular type of computational process. The description often takes the form of an abstract machine that is meant to perform the task at hand. General models of computation equivalent to a Turing machine (see Church–Turing thesis) include: ;Lambda calculus: A computation consists of an initial lambda expression (or two if you want to separate the function and its input) plus a finite sequence of lambda terms, each deduced from the preceding term by one application of beta reduction. ;Combinatory logic :A concept which has many similarities to \lambda-calculus, but also important differences exist (e.g.

These combinatory structures can be understood, he argues, with the help of an overall sign typology consisting of anaphones (sonic, tactile, kinetic, social), style flags (style determinants, genre synecdoches, etc.) and episodic markers.See chapter 13 in Philip Tagg, Music’s Meanings, 2013. The semiotic theory is basically Peircean but it draws also on Umberto Eco's theories of connotation.See chapter 5 in Philip Tagg, Music’s Meanings, 2013, esp. pp. 158–171. The actual analysis method is based on both metamusical information about the analysis object (reception tests, opinions, ethnographic observation, etc.) to arrive at paramusical fields of connotation (PMFCs),See chapter 6 in Philip Tagg, Music’s Meanings, 2013.

During the period of migration of barbarian tribes and the transformation of the Roman empire the architectural mnemonic fell into disuse. However the use of tables, charts and signs appears to have continued and developed independently. Mary Carruthers has made it clear that a trained memory occupied a central place in late antique and medieval pedagogy, and has documented some of the ways in which the development of medieval memorial arts was intimately intertwined with the emergence of the book as we understand it today. Examples of the development of the potential inherent in the graphical mnemonic include the lists and combinatory wheels of the Majorcan Ramon Llull.

Amongst the styles of the therapist and the patient it could be given complementarities that improve the clinic work or missed encounters that disturb it. He described each patient as a combinatory of styles, with one of them dominant. Thus, he sustained that in the obsessive patient it predominates a narrative style, in the patient with anxiety hysteria, the dramatic with suspense style, in the patient with conversion hysteria, the dramatic with aesthetic impact style, in the transgressor patient, the epic style, in the depressive patient, the lyrical style and in the schizoid patient, the reflexive style. In each case it is possible to observe variations that accentuate or attenuate the stylistic pathological features.

PLN begins with a term logic foundation, and then adds on elements of probabilistic and combinatory logic, as well as some aspects of predicate logic and autoepistemic logic, to form a complete inference system, tailored for easy integration with software components embodying other (not explicitly logical) aspects of intelligence. PLN represents truth values as intervals, but with different semantics than in Imprecise Probability Theory. In addition to the interpretation of truth in a probabilistic fashion, a truth value in PLN also has an associated amount of certainty. This generalizes the notion of truth values used in autoepistemic logic, where truth values are either known or unknown, and when known, are either true or false.

He wrote with Jorge Gil Música y Teoría de Grupos Finitos, 3 Variables Booleanas, with an English abstract (IIE UNAM, Mexico 1984). He has postulated a General Theory of Intervallic Classes, applicable to macro and microintervallic scales of duration and of pitch. He has developed together with M. Díaz and Víctor Adán the computer music program MUSIIC to generate the combinatory potential of music scales based on the division of the octave. In the field of the continuum Estrada has developed new methods of multidimensional graphic representation of different components of sound (pitch, dynamics, colour), rhythm (pulse, attack, vibrato) and three- dimensional physical space. His first research on the continuum field was published in 1998 in Darmstadt : Ouvrir l’horizon du son: le continuum.

In 1922, Indian physicist C. V. Raman published his work on the "Molecular Diffraction of Light", the first of a series of investigations with his collaborators that ultimately led to his discovery (on 28 February 1928) of the radiation effect that bears his name. The Raman effect was first reported by Raman and his coworker K. S. Krishnan, and independently by Grigory Landsberg and Leonid Mandelstam, in Moscow on 21 February 1928 (one week earlier than Raman and Krishnan). In the former Soviet Union, Raman's contribution was always disputed; thus in Russian scientific literature the effect is usually referred to as "combination scattering" or "combinatory scattering". Raman received the Nobel Prize in 1930 for his work on the scattering of light.

And the verb waited/wait subcategorizes for two arguments as well, although the second of these is an optional prepositional argument associated with the preposition for. In this regard, we see that the subcategorization frame of verbs can contain specific words. Subcategorization frames are sometimes schematized in the following manner: ::work [NP __ ] ::eat [NP __ (NP)] ::wait [NP __ (for NP)] These examples demonstrate that subcategorization frames are specifications of the number and types of arguments of a word (usually a verb), and they are believed to be listed as lexical information (that is, they are thought of as part of a speaker's knowledge of the word in the vocabulary of the language). Dozens of distinct subcategorization frames are needed to accommodate the full combinatory potential of the verbs of any given language.

In computer programming, two notions of parameter are commonly used, and are referred to as parameters and arguments—or more formally as a formal parameter and an actual parameter. For example, in the definition of a function such as : y = f(x) = x + 2, x is the formal parameter (the parameter) of the defined function. When the function is evaluated for a given value, as in :f(3): or, y = f(3) = 3 + 2 = 5, 3 is the actual parameter (the argument) for evaluation by the defined function; it is a given value (actual value) that is substituted for the formal parameter of the defined function. (In casual usage the terms parameter and argument might inadvertently be interchanged, and thereby used incorrectly.) These concepts are discussed in a more precise way in functional programming and its foundational disciplines, lambda calculus and combinatory logic.

The beginnings of the Curry–Howard correspondence lie in several observations: # In 1934 Curry observes that the types of the combinators could be seen as axiom-schemes for intuitionistic implicational logic. # In 1958 he observes that a certain kind of proof system, referred to as Hilbert-style deduction systems, coincides on some fragment to the typed fragment of a standard model of computation known as combinatory logic. # In 1969 Howard observes that another, more "high- level" proof system, referred to as natural deduction, can be directly interpreted in its intuitionistic version as a typed variant of the model of computation known as lambda calculus. In other words, the Curry–Howard correspondence is the observation that two families of seemingly unrelated formalisms—namely, the proof systems on one hand, and the models of computation on the other—are in fact the same kind of mathematical objects.

Duchenne's experiments for the aesthetic section of the Mechanism included the use of performance and narratives which may well have been influenced by gestures and poses found in the pantomime of the period. He believed that only by electroshock and in the setting of elaborately constructed theatre pieces featuring gestures and accessory symbols could he faithfully depict the complex combinatory expressions resulting from conflicting emotions and ambivalent sentiments. These melodramatic tableaux include a nun in "extremely sorrowful prayer" experiencing "saintly transports of virginal purity"; a mother feeling both pain and joy while leaning over a child's crib; a bare-shouldered coquette looking at once offended, haughty and mocking; and three scenes from Lady Macbeth expressing the "aggressive and wicked passions of hatred, of jealousy, of cruel instincts," modulated to varying degrees of contrary feelings of filial piety.Duchenne, Mecanisme, part 3, 169-74; Cuthbertson trans.