Results for 'Syntax, categorial grammar, language expressions, dual ontological stauts of language expressions, logic of language'

960 found
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  1. On the Eliminability of Ideal Linguistic Entities.Wybranie-Skardowska Urszula - 1989 - Studia Logica (4):587-615.
    With reference to Polish logical-philosophical tradition two formal theories of language syntax have been sketched and then compared with each other. The first theory is based on the assumption that the basic linguistic stratum is constituted by object-tokens (concrete objects perceived through the senses) and that the types of such objects (ideal objects) are derivative constructs. The other is founded on an opposite philosophical orientation. The two theories are equivalent. The main conclusion is that in syntactic researches it is (...)
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  2. Logic-Language-Ontology.Urszula B. Wybraniec-Skardowska - 2022 - Cham, Switzerland: Springer Nature, Birkhäuser, Studies in Universal Logic series.
    The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of (...) Signs and the Problem of Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)
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  3. Logic and Sense.Urszula Wybraniec-Skardowska - 2016 - Philosophy Study 6 (9).
    In the paper, original formal-logical conception of syntactic and semantic: intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically: in the spirit of some Husserl’s ideas of pure grammar, Leśniewski-Ajukiewicz’s theory syntactic/semantic categories and in accordance with Frege’s ontological canons, Bocheński’s famous motto—syntax mirrors ontology and some ideas of Suszko: language should be a linguistic scheme of ontological reality and (...)
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  4.  54
    Theory of Language Syntax: Categorial Approach.Urszula Wybraniec-Skardowska - 1991 - Dordrecht/Boston/London: Kluwer Academic Publishers.
    This book presents a formal and philosophical analysis of language syntax. It refers to some ideas of E.Husserl and G. Frege, to S. Leśniewski's theory of syntactic categories and K. Ajdukiewicz's conception of formal grammar, also to Ch.S. Pierces's distinction between tokens (concrete linguistic entities) and types (ideal linguistic entities) and to A.A. Markov's theory of algorithms. The central aim of the book is - in the spirit of these ideas - to provide both strict yet comprehensive lectures on (...)
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  5. Logic and Ontology of Language.Urszula Wybraniec-Skardowska - 2019 - In Bartłomiej Skowron, Contemporary Polish Ontology. Berlin: De Gruyter. pp. 109-132.
    The main purpose of the paper is to outline the formal-logical, general theory of language treated as a particular ontological being. The theory itself is called the ontology of language, because it is motivated by the fact that the language plays a special role: it reflects ontology and ontology reflects the world. Language expressions are considered to have a dual ontological status. They are understood as either concretes, that is tokens – material, physical (...)
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  6.  84
    Logic and the Ontology of Language.Urszula Wybraniec-Skardowska - 2019 - In Bartłomiej Skowron, Contemporary Polish Ontology. Berlin: De Gruyter. pp. 109-132.
    The main goal of this paper is to outline a general formal-logical theory of language construed as a particular ontological being. The theory itself will be referred to as an ontology of language, because it is motivated by the fact that language plays a special role: it reflects ontology, and ontology reflects the world. Linguistic expressions will be regarded as having a dual ontological status: they are to be understood as either concreta – i.e. (...)
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  7. Logiczne podstawy ontologii składni języka.Urszula Wybraniec-Skardowska - 1988 - Studia Filozoficzne 271 (6-7):263-284.
    By logical foundations of language syntax ontology we understand here the construction of formalized linguistic theories based on widely conceived mathematical logic and dependent on two trends in language ontology. The formalization includes exclusively the syntactic aspect of logical analysis of language characterized categorially according to Ajdukiewicz's approach [1935, 1960]. Any categorial language L is characterized formally on two levels: on one of them it concerns the language of expression-tokens, on the other one (...)
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  8.  34
    On Universal Grammar and its Formalization.Urszula Wybraniec-Skardowska & Andrzej K. Rogalski - 1998 - The Paideia Archive: Twentieth World Congress of Philosophy 8:153-172.
    This paper sketches or signals some ideas, results, and proposals connected with the theoretical issues related to the categorial approach to language which originated from the first author and which form the basis for further research by the second author. The main aims are the following: 1) to bring into common use some Polish ideas concerned with classical categorial grammar; 2) to take into consideration a universal and simultaneously formal-logical perspective; 3) to consider Peirce's well-known differentiation of (...)
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  9. Nominalization and Montague grammar: A semantics without types for natural languages.Gennaro Chierchia - 1982 - Linguistics and Philosophy 5 (3):303 - 354.
    We started from the fact that type theory, in the way it was implemented in IL, makes it costly to deal with nominalization processes. We have also argued that the type hierarchy as such doesn't play any real role in a grammar; the classification it provides for different semantic objects is already contained, in some sense, in the categorial structure of the grammar itself. So, on the basis of a theory of properties (Cocchiarella's HST*) we have tried to build (...)
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  10. Symmetric Categorial Grammar.Michael Moortgat - 2009 - Journal of Philosophical Logic 38 (6):681-710.
    The Lambek-Grishin calculus is a symmetric version of categorial grammar obtained by augmenting the standard inventory of type-forming operations (product and residual left and right division) with a dual family: coproduct, left and right difference. Interaction between these two families is provided by distributivity laws. These distributivity laws have pleasant invariance properties: stability of interpretations for the Curry-Howard derivational semantics, and structure-preservation at the syntactic end. The move to symmetry thus offers novel ways of reconciling the demands of (...)
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  11.  15
    Language in Action: Categories, Lambdas and Dynamic Logic.Johan van Benthem - 1995 - MIT Press.
    Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in (...)
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  12.  76
    Logical and philosophical ideas in certain formal approaches to language.Urszula Wybraniec-Skardowska - 1998 - Synthese 116 (2):231-277.
    This paper reminds, puts in order, sketches and also initiates some researches from the field of logic and philosophy of language. It lays emphasis on the logical-linguistic and ontological developmental lines originated with Polish researchers. The author discusses two opposite orientations of the former line in the process of formalization of language, called here nominalistic and Platonistic. The paper mentions the author's result (1989; 1991) concerning theoretical equivalence of two axiomatic approaches to language syntax which (...)
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  13. On Language Adequacy.Urszula Wybraniec-Skardowska - 2015 - Studies in Logic, Grammar and Rhetoric 40 (1):257-292.
    The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and inter-subjective knowledge about these fragments, called here, in brief, language adequacy. This problem is formulated in several aspects, the most being: the compatibility of language syntax with its bi-level semantics: intensional and extensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formal-logical theory T of any categorial language (...)
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  14.  48
    IDL-PMCFG, a Grammar Formalism for Describing Free Word Order Languages.François Hublet - 2022 - Journal of Logic, Language and Information 31 (3):327-388.
    We introduce _Interleave-Disjunction-Lock parallel multiple context-free grammars_ (IDL-PMCFG), a novel grammar formalism designed to describe the syntax of free word order languages that allow for extensive interleaving of grammatical constituents. Though interleaved constituents, and especially the so-called hyperbaton, are common in several ancient (Classical Latin and Greek, Sanskrit...) and modern (Hungarian, Finnish...) languages, these syntactic structures are often difficult to express in existing formalisms. The IDL-PMCFG formalism combines Seki et al.’s parallel multiple context-free grammars (PMCFG) with Nederhof and Satta’s IDL (...)
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  15.  96
    Ontologies and Worlds in Category Theory: Implications for Neural Systems.Michael John Healy & Thomas Preston Caudell - 2006 - Axiomathes 16 (1-2):165-214.
    We propose category theory, the mathematical theory of structure, as a vehicle for defining ontologies in an unambiguous language with analytical and constructive features. Specifically, we apply categorical logic and model theory, based upon viewing an ontology as a sub-category of a category of theories expressed in a formal logic. In addition to providing mathematical rigor, this approach has several advantages. It allows the incremental analysis of ontologies by basing them in an interconnected hierarchy of theories, with (...)
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  16.  34
    Parsing/Theorem-Proving for Logical Grammar CatLog3.Glyn Morrill - 2019 - Journal of Logic, Language and Information 28 (2):183-216.
    \ is a 7000 line Prolog parser/theorem-prover for logical categorial grammar. In such logical categorial grammar syntax is universal and grammar is reduced to logic: an expression is grammatical if and only if an associated logical statement is a theorem of a fixed calculus. Since the syntactic component is invariant, being the logic of the calculus, logical categorial grammar is purely lexicalist and a particular language model is defined by just a lexical dictionary. The (...)
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  17. On the type-token relationships.Urszula Wybraniec-Skardowska - 1986 - Bulletin of the Section of Logic 15 (4):164-168.
    The two-fold ontological character of linguistic objects revealed due to the distinction between “type” and “token” introduced by Ch. S. Peirce can be a base of the two-fold, both theoretical and axiomatic, approach to the language. Referring to some ideas included in A. A. Markov’s work [1954] (in Russian) on Theory of Algorithms and in some earlier papers of the author, the problem of formalization of the concrete and abstract words theories raised by J. Słupecki was solved. The (...)
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  18. Separating syntax and combinatorics in categorial grammar.Reinhard Muskens - 2007 - Research on Language and Computation 5 (3):267-285.
    The ‘syntax’ and ‘combinatorics’ of my title are what Curry (1961) referred to as phenogrammatics and tectogrammatics respectively. Tectogrammatics is concerned with the abstract combinatorial structure of the grammar and directly informs semantics, while phenogrammatics deals with concrete operations on syntactic data structures such as trees or strings. In a series of previous papers (Muskens, 2001a; Muskens, 2001b; Muskens, 2003) I have argued for an architecture of the grammar in which finite sequences of lambda terms are the basic data structures, (...)
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  19. Dwojaka natura ontologiczna znaków językowych i problem ich wzajemnych relacji.Urszula Wybraniec-Skardowska - 2021 - Ruch Filozoficzny 77 (1):7-24.
    The subject matter of this work covers the issues or problems listed below: * The problem of the ontological status of language signs and a more general philosophical problem connected with it: * What is language as a system of signs, which – on the one hand – serves to: 1) represent our knowledge about the reality which is being recognized, and, on the other one to: 2) a. explore and better cognize or discover it, b. describe (...)
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  20.  72
    Second-order abstract categorial grammars as hyperedge replacement grammars.Makoto Kanazawa - 2010 - Journal of Logic, Language and Information 19 (2):137-161.
    Second-order abstract categorial grammars (de Groote in Association for computational linguistics, 39th annual meeting and 10th conference of the European chapter, proceedings of the conference, pp. 148–155, 2001) and hyperedge replacement grammars (Bauderon and Courcelle in Math Syst Theory 20:83–127, 1987; Habel and Kreowski in STACS 87: 4th Annual symposium on theoretical aspects of computer science. Lecture notes in computer science, vol 247, Springer, Berlin, pp 207–219, 1987) are two natural ways of generalizing “context-free” grammar formalisms for string and (...)
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  21.  45
    Names and Quantifiers: Bringing Them Together in Classical Logic.Jacek Paśniczek - 2023 - Journal of Logic, Language and Information 32 (3):473-487.
    Putting individual constants and quantifiers into the same syntactic category within first-order language promises to have far-reaching consequences: a syntax of this kind can reveal the potential of any such language, allowing us to realize that a vast class of noun phrases, including non-denoting terms, can be accommodated in the new syntax as expressions suited to being subjects of sentences. In the light of this, a formal system that is an extension of classical first-order logic is developed (...)
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  22.  27
    Sunyata and Otherness: Applying Mutually Transformative Categories from Buddhist-Christian Dialogue in Christology.Susie Paulik Babka - 2015 - Buddhist-Christian Studies 35:73-90.
    In lieu of an abstract, here is a brief excerpt of the content:Sunyata and Otherness:Applying Mutually Transformative Categories from Buddhist-Christian Dialogue in ChristologySusie Paulik Babka“The universe is expanding,” the physicists tell us. “But doesn’t an expansion of something mean the presupposition of boundaries?” my naïve mind inquires, thinking too much in terms of discrete substances. Can “something” expand “into” nothing, “into” emptiness? Shot through with “dark energy” (the name an intellectual signifier allowing physicists to speak of the ineffable), the immensity (...)
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  23. On the axiomatic systems of syntactically-categorial languages.Urszula Wybraniec-Skardowska - 1984 - Bulletin of the Section of Logic 13 (4):241-249.
    The paper contains an overview of the most important results presented in the monograph of the author "Teorie Językow Syntaktycznie-Kategorialnych" ("Theories of Syntactically-Categorial Languages" (in Polish), PWN, Warszawa-Wrocław 1985. In the monograph four axiomatic systems of syntactically-categorial languages are presented. The first two refer to languages of expression-tokens. The others also takes into consideration languages of expression-types. Generally, syntactically-categorial languages are languages built in accordance with principles of the theory of syntactic categories introduced by S. Leśniewski [1929,1930]; (...)
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  24.  62
    On the expressive power of abstract categorial grammars: Representing context-free formalisms. [REVIEW]Philippe de Groote & Sylvain Pogodalla - 2004 - Journal of Logic, Language and Information 13 (4):421-438.
    We show how to encode context-free string grammars, linear context-free tree grammars, and linear context-free rewriting systems as Abstract Categorial Grammars. These three encodings share the same constructs, the only difference being the interpretation of the composition of the production rules. It is interpreted as a first-order operation in the case of context-free string grammars, as a second-order operation in the case of linear context-free tree grammars, and as a third-order operation in the case of linear context-free rewriting systems. (...)
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  25. The meaning of category theory for 21st century philosophy.Alberto Peruzzi - 2006 - Axiomathes 16 (4):424-459.
    Among the main concerns of 20th century philosophy was that of the foundations of mathematics. But usually not recognized is the relevance of the choice of a foundational approach to the other main problems of 20th century philosophy, i.e., the logical structure of language, the nature of scientific theories, and the architecture of the mind. The tools used to deal with the difficulties inherent in such problems have largely relied on set theory and its “received view”. There are specific (...)
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  26.  47
    Language in action.Johan Benthem - 1991 - Journal of Philosophical Logic 20 (3):225 - 263.
    A number of general points behind the story of this paper may be worth setting out separately, now that we have come to the end.There is perhaps one obvious omission to be addressed right away. Although the word “information” has occurred throughout this paper, it must have struck the reader that we have had nothing to say on what information is. In this respect, our theories may be like those in physics: which do not explain what “energy” is (a notion (...)
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  27.  23
    Aspecto-Temporal Meanings Analysed by Combinatory Logic.Jean-Pierre Desclés, Anca Christine Pascu & Hee-Jin Ro - 2014 - Journal of Logic, Language and Information 23 (3):253-274.
    What is the meaning of language expressions and how to compute or calculate it? In this paper, we give an answer to this question by analysing the meanings of aspects and tenses in natural languages inside the formal model of an grammar of applicative, cognitive and enunciative operations , using the applicative formalism, functional types of categorial grammars and combinatory logic . In the enunciative theory and following , an utterance can be decomposed into two components: a (...)
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  28. Logical categories, signs, and elucidation in Frege.Wim Vanrie - 2021 - Dissertation, University of Ghent
    Frege's conception of the logical categories has vexed commentators for decades. In this dissertation, I argue that it revolves around two forms of internality. The first is the internality of its use in the expression of judgment to the sign. A proper understanding of that internality reveals how Frege's philosophical logic cannot be fit into the framework given by the contemporary syntax/semantics distinction. The second is the internality that obtains between the way in which Begriffsschrift signs stratify into different (...)
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  29. Reasoning with categorial grammar logic.Raffaella Bernardi - unknown
    The article presents the first results we have obtained studying natural reasoning from a proof-theoretic perspective. In particular we focus our attention on monotonic reasoning. Our system consists of two parts: (i) A Formal Grammar – a multimodal version of classical Categorial Grammar – which while syntactically analysing linguistic expressions given as input, computes semantic information (In particular information about the monotonicity properties of the components of the input string are displayed.); (ii) A simple Natural Logic which derives (...)
     
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  30.  88
    Discontinous Constituents in Generalized Categorial Grammar.Emmon W. Bach - unknown
    [1]. Recently renewed interest in non transformational approaches to syntax [2] suggests that it might be well to take another look at categorial grammars, since they seem to have been neglected largely because they had been shown to be equivalent to context free phrase structure grammars in weak generative capacity and it was believed that such grammars were incapable of describing natural languages in a natural way. It is my purpose here to sketch a theory of grammar which represents (...)
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  31.  24
    Modeling Structure‐Building in the Brain With CCG Parsing and Large Language Models.Miloš Stanojević, Jonathan R. Brennan, Donald Dunagan, Mark Steedman & John T. Hale - 2023 - Cognitive Science 47 (7):e13312.
    To model behavioral and neural correlates of language comprehension in naturalistic environments, researchers have turned to broad‐coverage tools from natural‐language processing and machine learning. Where syntactic structure is explicitly modeled, prior work has relied predominantly on context‐free grammars (CFGs), yet such formalisms are not sufficiently expressive for human languages. Combinatory categorial grammars (CCGs) are sufficiently expressive directly compositional models of grammar with flexible constituency that affords incremental interpretation. In this work, we evaluate whether a more expressive CCG (...)
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  32.  8
    Logic: Mathematics, Language, Computer Science, and Philosophy.H. C. M. De Swart - 1993 - Peter Lang.
    Depending on what one means by the main connective of logic, the -if..., then... -, several systems of logic result: classic and modal logics, intuitionistic logic or relevance logic. This book presents the underlying ideas, the syntax and the semantics of these logics. Soundness and completeness are shown constructively and in a uniform way. Attention is paid to the interdisciplinary role of logic: its embedding in the foundations of mathematics and its intimate connection with philosophy, (...)
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  33.  33
    Language and ontology.Jack Kaminsky - 1969 - Carbondale,: Southern Illinois University Press.
    The acceptance of the concept of necessary linguistic cate­gories has given renewed prominence to the subject of ontology in contemporary discussions of language and logic. Jack Kaminsky, Professor of Philosophy at the State University of New York at Binghamton, here contributes an important expo­sition of this school of thought. He examines the views of many philosophers who either admit or deny that ontological com­mitments are necessary, and he raises broad questions and shows why there is a compelling (...)
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  34.  60
    The Displacement Calculus.Glyn Morrill, Oriol Valentín & Mario Fadda - 2011 - Journal of Logic, Language and Information 20 (1):1-48.
    If all dependent expressions were adjacent some variety of immediate constituent analysis would suffice for grammar, but syntactic and semantic mismatches are characteristic of natural language; indeed this is a, or the, central problem in grammar. Logical categorial grammar reduces grammar to logic: an expression is well-formed if and only if an associated sequent is a theorem of a categorial logic. The paradigmatic categorial logic is the Lambek calculus, but being a logic (...)
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  35.  64
    On Commutative and Nonassociative Syntactic Calculi and Categorial Grammars.Maciej Kandulski - 1995 - Mathematical Logic Quarterly 41 (2):217-235.
    Two axiomatizations of the nonassociative and commutative Lambek syntactic calculus are given and their equivalence is proved. The first axiomatization employs Permutation as the only structural rule, the second one, with no Permutation rule, employs only unidirectional types. It is also shown that in the case of the Ajdukiewicz calculus an analogous equivalence is valid only in the case of a restricted set of formulas. Unidirectional axiomatizations are employed in order to establish the generative power of categorial grammars based (...)
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  36.  91
    Geach’s Categorial Grammar.Lloyd Humberstone - 2004 - Linguistics and Philosophy 28 (3):281 - 317.
    Geach’s rich paper ‘A Program for Syntax’ introduced many ideas into the arena of categorial grammar, not all of which have been given the attention they warrant in the thirty years since its first publication. Rather surprisingly, one of our findings (Section 3 below) is that the paper not only does not contain a statement of what has widely come to be known as “Geach’s Rule”, but in fact presents considerations which are inimical to the adoption of the rule (...)
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  37. Explaining crossover and superiority as left-to-right evaluation.Chung-Chieh Shan & Chris Barker - 2005 - Linguistics and Philosophy 29 (1):91 - 134.
    We present a general theory of scope and binding in which both crossover and superiority violations are ruled out by one key assumption: that natural language expressions are normally evaluated (processed) from left to right. Our theory is an extension of Shan’s (2002) account of multiple-wh questions, combining continuations (Barker, 2002) and dynamic type-shifting. Like other continuation-based analyses, but unlike most other treatments of crossover or superiority, our analysis is directly compositional (in the sense of, e.g., Jacobson, 1999). In (...)
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  38.  10
    Ocherki ėvoli︠u︡t︠s︡ionno-sinteticheskoĭ teorii i︠a︡zyka =.A. D. Koshelev - 2017 - Moskva: Izdatelʹskiĭ Dom I︠A︡SK.
    The monograph shows that in the last 50 years theoretical linguistics remains a compendium of mutually contradicting doctrines on multiple levels: the level of general theories of language, the level of its main constituents (the lexicon, syntax, and the lexical-syntactic interface that connects them), and the lower levels of specific linguistic problems (such as lexical polysemy, grammatical meanings, etc.). The contradictions of contemporary linguistic theories are indicative of a deep crisis. Evolutionary-synthetic theory of language is aimed at overcoming (...)
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  39.  8
    Polymorphic Quantifiers and Underspecification in Natural Language.Chris Fox & Shalom Lappin - 2005 - In S. Artemov, H. Barringer, A. Garcez, L. Lamb & J. Woods, We Will Show Them: Essays in Honour of Dov Gabbay. London: College Publications.
    It is reasonably well-understood that natural language displays polymorphic behaviour in both its syntax and semantics, where various constructions can operate on a range of syntactic categories, or semantic types. In mathematics, logic and computer science it is appreciated that there are various ways in which such type-general behaviours can be formulated. It is also known that natural languages are highly ambiguous with respect to scoping artifacts, as evident with quantifiers, negation and certain modifier expressions. To deal with (...)
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  40.  46
    Toward using bio-ontologies in the Semantic Web: trade-offs between ontology languages.Mariano Rodr´Iguez - unknown
    Ontology languages for the Semantic Web have their strengths and weaknesses, in particular in the light of deploying them for biological and medical information systems. We survey and compare the Description Logics-based OWL languages, and the DL-Lite and DLR families of languages. Language choices that an ontology developer has to make are, among others, expressivity with n-ary relations (where n > 2) and more role properties versus ontology usage for data-intensive tasks. Guidelines are suggested to facilitate choosing the (...) best fitted for a task. (shrink)
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  41.  19
    On the Expressive Power of Abstract Categorial Grammars: Representing Context-Free Formalisms.Philippe Groote & Sylvain Pogodalla - 2004 - Journal of Logic, Language and Information 13 (4):421-438.
    We show how to encode context-free string grammars, linear context-free tree grammars, and linear context-free rewriting systems as Abstract Categorial Grammars. These three encodings share the same constructs, the only difference being the interpretation of the composition of the production rules. It is interpreted as a first-order operation in the case of context-free string grammars, as a second-order operation in the case of linear context-free tree grammars, and as a third-order operation in the case of linear context-free rewriting systems. (...)
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  42.  27
    Commutative Lambek Grammars.Tikhon Pshenitsyn - 2023 - Journal of Logic, Language and Information 32 (5):887-936.
    Lambek categorial grammars is a class of formal grammars based on the Lambek calculus. Pentus proved in 1993 that they generate exactly the class of context-free languages without the empty word. In this paper, we study categorial grammars based on the Lambek calculus with the permutation rule LP. Of particular interest is the product-free fragment of LP called the Lambek-van Benthem calculus LBC. Buszkowski in his 1984 paper conjectured that grammars based on the Lambek-van Benthem calculus (LBC-grammars for (...)
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  43.  60
    Tree models and (labeled) categorial grammar.Yde Venema - 1996 - Journal of Logic, Language and Information 5 (3-4):253-277.
    This paper studies the relation between some extensions of the non-associative Lambek Calculus NL and their interpretation in tree models (free groupoids). We give various examples of sequents that are valid in tree models, but not derivable in NL. We argue why tree models may not be axiomatizable if we add finitely many derivation rules to NL, and proceed to consider labeled calculi instead.We define two labeled categorial calculi, and prove soundness and completeness for interpretations that are almost the (...)
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  44.  20
    Concepts and Categories: A Data Science Approach to Semiotics.André Włodarczyk - 2022 - Studies in Logic, Grammar and Rhetoric 67 (1):169-200.
    Compared to existing classical approaches to semiotics which are dyadic (signifier/signified, F. de Saussure) and triadic (symbol/concept/object, Ch. S. Peirce), this theory can be characterized as tetradic ([sign/semion]//[object/noema]) and is the result of either doubling the dyadic approach along the semiotic/ordinary dimension or splitting the ‘concept’ of the triadic one into two (semiotic/ordinary). Other important features of this approach are (a) the distinction made between concepts (only functional pairs of extent and intent) and categories (as representations of expressions) and (b) (...)
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  45. A Language for Ontological Nihilism.Catharine Diehl - 2018 - Ergo: An Open Access Journal of Philosophy 5:971-996.
    According to ontological nihilism there are, fundamentally, no individuals. Both natural languages and standard predicate logic, however, appear to be committed to a picture of the world as containing individual objects. This leads to what I call the \emph{expressibility challenge} for ontological nihilism: what language can the ontological nihilist use to express her account of how matters fundamentally stand? One promising suggestion is for the nihilist to use a form of \emph{predicate functorese}, a language (...)
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  46.  51
    On the membership problem for non-linear abstract categorial grammars.Sylvain Salvati - 2010 - Journal of Logic, Language and Information 19 (2):163-183.
    In this paper we show that the membership problem for second order non-linear Abstract Categorial Grammars is decidable. A consequence of that result is that Montague-like semantics yield to a decidable text generation problem. Furthermore the proof we propose is based on a new tool, Higher Order Intersection Signatures, which grasps statically dynamic properties of λ-terms and presents an interest in its own.
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    Extending Lambek grammars to basic categorial grammars.Wojciech Buszkowski - 1996 - Journal of Logic, Language and Information 5 (3-4):279-295.
    Pentus (1992) proves the equivalence of LCG's and CFG's, and CFG's are equivalent to BCG's by the Gaifman theorem (Bar-Hillel et al., 1960). This paper provides a procedure to extend any LCG to an equivalent BCG by affixing new types to the lexicon; a procedure of that kind was proposed as early, as Cohen (1967), but it was deficient (Buszkowski, 1985). We use a modification of Pentus' proof and a new proof of the Gaifman theorem on the basis of the (...)
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  48. Ontological categories in GOL.Barbara Heller & Heinrich Herre - 2004 - Axiomathes 14 (1):57-76.
    General Ontological Language (GOL) is a formal framework for representing and building ontologies. The purpose of GOL is to provide a system of top-level ontologies which can be used as a basis for building domain-specific ontologies. The present paper gives an overview about the basic categories of the GOL-ontology. GOL is part of the work of the research group Ontologies in Medicine (Onto-Med) at the University of Leipzig which is based on the collaborative work of the Institute of (...)
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  49.  53
    Free Logics.Karel Lambert - 2001 - In Lou Goble, The Blackwell Guide to Philosophical Logic. Malden, Mass.: Wiley-Blackwell. pp. 258–279.
    The expression ‘free logic,’ coined by the author in 1960, is an abbreviation for ‘logic free of existence assumptions with respect to its terms, singular and general, but whose quantifiers are treated exactly as in standard quantifier logic.’ In more traditional language, such logics do not presume that either singular or general terms — the two distinct categories of terms emphasized in modern logical grammar — have existential import. A singular term ‘t’ has existential import just (...)
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  50. Quantifiers in Language and Logic.Stanley Peters & Dag Westerståhl - 2006 - Oxford, England: Clarendon Press.
    Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role.
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