Results for 'Categorial grammar'

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  1.  72
    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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  2.  65
    Analyzing the Core of Categorial Grammar.Carlos Areces & Raffaella Bernardi - 2004 - Journal of Logic, Language and Information 13 (2):121-137.
    Even though residuation is at the core of Categorial Grammar (Lambek, 1958), it is not always immediate to realize how standard logical systems like Multi-modal Categorial Type Logics (MCTL) (Moortgat, 1997) actually embody this property. In this paper, we focus on the basic system NL (Lambek, 1961) and its extension with unary modalities NL() (Moortgat, 1996), and we spell things out by means of Display Calculi (DC) (Belnap, 1982; Goré, 1998). The use of structural operators in DC (...)
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  3.  14
    Non‐Associative Lambek Categorial Grammar in Polynomial Time.Erik Aarts & Kees Trautwein - 1995 - Mathematical Logic Quarterly 41 (4):476-484.
    We present a new axiomatization of the non-associative Lambek calculus. We prove that it takes polynomial time to reduce any non-associative Lambek categorial grammar to an equivalent context-free grammar. Since it is possible to recognize a sentence generated by a context-free grammar in polynomial time, this proves that a sentence generated by any non-associative Lambek categorial grammar can be recognized in polynomial time.
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  4.  2
    On the Formalization of Classical Categorial Grammar.Urszula Wybraniec-Skardowska - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 89:269.
    This article summarizes the main ideas for formalizing categorial languages genrated by classical categorial grammar originated by K. Ajdukiewicz [1935,1960].This formalization is presented in detail in the author's monographs in Polish "Teorie Języków Syntaktycznie Kategorialnych" ("Theories of Syntactically Categorical Languages"), PWN, Warszawa-Wrocław 1985 and in English "Theory of Language Syntax, Categorial Approach", Kluwer Academic Publishers, Boston-London-Dordrecht 1991.
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  5.  2
    Timothy C. Potts.Fregean Categorial Grammar - 1973 - In Radu J. Bogdan & Ilkka Niiniluoto (eds.), Logic, Language, and Probability. Boston: D. Reidel Pub. Co.. pp. 245.
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  6.  39
    Categorial Grammar and the Semantics of Contextual Prepositional Phrases.Nissim Francez & Mark Steedman - 2006 - Linguistics and Philosophy 29 (4):381 - 417.
    The paper proposes a semantics for contextual (i.e., Temporal and Locative) Prepositional Phrases (CPPs) like during every meeting, in the garden, when Harry met Sally and where I’m calling from. The semantics is embodied in a multi-modal extension of Combinatory Categoral Grammar (CCG). The grammar allows the strictly monotonic compositional derivation of multiple correct interpretations for “stacked” or multiple CPPs, including interpretations whose scope relations are not what would be expected on standard assumptions about surfacesyntactic command and monotonic (...)
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  7.  2
    Categorial Grammar and the Logical Form of Quantification.Harold D. Levin - 1986 - Philosophical Review 95 (1):127-129.
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  8.  37
    On Contextual Domain Restriction in Categorial Grammar.Erich Rast - 2013 - Synthese 190 (12):2085-2115.
    Abstract -/- Quantifier domain restriction (QDR) and two versions of nominal restriction (NR) are implemented as restrictions that depend on a previously introduced interpreter and interpretation time in a two-dimensional semantic framework on the basis of simple type theory and categorial grammar. Against Stanley (2002) it is argued that a suitable version of QDR can deal with superlatives like tallest. However, it is shown that NR is needed to account for utterances when the speaker intends to convey different (...)
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  9. Type Logical Grammar Categorial Logic of Signs.Glyn V. Morrill - 1994
     
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  10.  42
    Categorial Grammar and Lexical-Functional Grammar.Reinhard Muskens - unknown
    This paper introduces λ-grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λ-grammars are multi-dimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λ-terms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more (...)
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  11.  3
    A Note On Negation In Categorial Grammar.Heinrich Wansing - 2007 - Logic Journal of the IGPL 15 (3):271-286.
    A version of strong negation is introduced into Categorial Grammar. The resulting syntactic calculi turn out to be systems of connexive logic.
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  12.  23
    Partial Proof Trees as Building Blocks for a Categorial Grammar.Aravind K. Joshi & Seth Kulick - 1997 - Linguistics and Philosophy 20 (6):637-667.
    We describe a categorial system (PPTS) based on partial proof trees(PPTs) as the building blocks of the system. The PPTs are obtained byunfolding the arguments of the type that would be associated with a lexicalitem in a simple categorial grammar. The PPTs are the basic types in thesystem and a derivation proceeds by combining PPTs together. We describe theconstruction of the finite set of basic PPTs and the operations forcombining them. PPTS can be viewed as a (...) system incorporating someof the key insights of lexicalized tree adjoining grammar, namely the notionof an extended domain of locality and the consequent factoring of recursionfrom the domain of dependencies. PPTS therefore inherits the linguistic andcomputational properties of that system, and so can be viewed as a middleground between a categorial grammar and a phrase structure grammar. We alsodiscuss the relationship between PPTS, natural deduction, and linear logicproof-nets, and argue that natural deduction rather than a proof-net systemis more appropriate for the construction of the PPTs. We also discuss howthe use of PPTs allows us to localize the management of resources, therebyfreeing us from this management as the PPTs are combined. (shrink)
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  13.  13
    Discontinuity in Categorial Grammar.Glyn Morrill - 1995 - Linguistics and Philosophy 18 (2):175 - 219.
    Discontinuity refers to the character of many natural language constructions wherein signs differ markedly in their prosodic and semantic forms. As such it presents interesting demands on monostratal computational formalisms which aspire to descriptive adequacy. Pied piping, in particular, is argued by Pollard (1988) to motivate phrase structure-style feature percolation. In the context of categorial grammar, Bach (1981, 1984), Moortgat (1988, 1990, 1991) and others have sought to provide categorial operators suited to discontinuity. These attempts encounter certain (...)
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  14.  6
    A Geometrical Representation of the Basic Laws of Categorial Grammar.Abrusci V. Michele & Casadio Claudia - 2017 - Studia Logica 105 (3):479-520.
    We present a geometrical analysis of the principles that lay at the basis of Categorial Grammar and of the Lambek Calculus. In Abrusci it is shown that the basic properties known as Residuation laws can be characterized in the framework of Cyclic Multiplicative Linear Logic, a purely non-commutative fragment of Linear Logic. We present a summary of this result and, pursuing this line of investigation, we analyze a well-known set of categorial grammar laws: Monotonicity, Application, Expansion, (...)
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  15.  34
    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 (...)
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  16.  17
    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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  17.  58
    Categorial Grammar and Discourse Representation Theory.Reinhard Muskens - unknown
    In this paper it is shown how simple texts that can be parsed in a Lambek Categorial Grammar can also automatically be provided with a semantics in the form of a Discourse Representation Structure in the sense of Kamp [1981]. The assignment of meanings to texts uses the Curry-Howard-Van Benthem correspondence.
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  18. 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 (...)
     
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  19. Categorial Grammar.Raffaella Bernardi - unknown
    1 Recognition Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Classical Categorial Grammar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 (...)
     
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  20.  47
    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 (...)
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  21.  19
    Separating Syntax and Combinatorics in Categorial Grammar.Reinhard Muskens - manuscript
    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 (...)
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  22. Categorial Grammar.Wojciech Buszkowski, Witold Marciszewski & Johan van Benthem - 1991 - Studia Logica 50 (1):171-172.
     
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  23.  16
    Compatibility of a Categorial Grammar With an Associated Category System.Wojciech Buszkowski - 1982 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 28 (14-18):229-238.
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  24.  19
    Intuitionistic Categorial Grammar.Aarne Ranta - 1991 - Linguistics and Philosophy 14 (2):203 - 239.
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  25.  34
    The Dual Analysis of Adjuncts/Complements in Categorial Grammar.David Dowty - manuscript
    The distinction between COMPLEMENTS and ADJUNCTS has a long tradition in grammatical theory, and it is also included in some way or other in most current formal linguistic theories. But it is a highly vexed distinction for several reasons, one of which is that no diagnostic criteria have emerged that will reliably distinguish adjuncts from complements in all cases — too many examples seem to fall into the crack between the two categories, no matter how theorists wrestle with them.
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  26.  19
    Categorial Grammar — A Basis for a Natural Language Calculus?Hans Karlgren - 1978 - Studia Logica 37 (1):65-78.
  27.  1
    Categorial Grammar and Type Theory.Johan van Benthem - 1990 - Journal of Philosophical Logic 19 (2):115-168.
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  28.  5
    Learning Categorial Grammar by Unification with Negative Constraints.Jacek Marciniec - 1994 - Journal of Applied Non-Classical Logics 4 (2):181-200.
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  29.  17
    Categorial Grammar and Type Theory.Johan Benthem - 1990 - Journal of Philosophical Logic 19 (2):115 - 168.
  30.  14
    Combinators and Categorial Grammar.Peter Simons - 1989 - Notre Dame Journal of Formal Logic 30 (2):241-261.
  31.  28
    On the Treatment of Complex Predicates in Categorial Grammar.Beom-Mo Kang - 1995 - Linguistics and Philosophy 18 (1):61 - 81.
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  32.  29
    Infinite Set Unification with Application to Categorial Grammar.Jacek Marciniec - 1997 - Studia Logica 58 (3):339-355.
    In this paper the notion of unifier is extended to the infinite set case. The proof of existence of the most general unifier of any infinite, unifiable set of types (terms) is presented. Learning procedure, based on infinite set unification, is described.
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  33. Review of Levin, H. D.: Categorial grammar and the logical form of quantification. [REVIEW]M. J. Cresswell - 1985 - Theoria 51 (1):55.
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  34.  17
    On Categorial Grammar and Logical Form.Witold Marciszewski - 1978 - Studia Logica 37 (1):1-5.
  35.  8
    Categorial Grammar and the Logical Form of Quantification.Jack Hoeksema - 1988 - International Studies in Philosophy 20 (3):131-132.
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  36.  5
    Fregean Categorial Grammar.Timothy C. Potts - 1973 - In Radu J. Bogdan & Ilkka Niiniluoto (eds.), Logic, Language, and Probability. Boston: D. Reidel Pub. Co.. pp. 245--284.
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  37.  3
    Categorial Grammar and Ontological Commitment.Krystyna Misiuna - 1995 - In Vito Sinisi & Jan Woleński (eds.), The Heritage of Kazimierz Ajdukiewicz. Rodopi. pp. 40--195.
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  38.  2
    On Families of Languages Generated by Categorial Grammar.Wojciech Buszkowski - 1998 - Poznan Studies in the Philosophy of the Sciences and the Humanities 62:39-48.
  39.  1
    Talking About Explicit Databases in Categorial Grammar.Natasha Kurtonina - 1995 - Logic Journal of the IGPL 3 (2-3):357-370.
  40.  1
    Categorial Grammar and the Foundations of the Philosophy of Language.Mieszko Tałasiewicz - 2014 - In Piotr Stalmaszczyk (ed.), Philosophy of Language and Linguistics: The Legacy of Frege, Russell, and Wittgenstein. De Gruyter. pp. 269-294.
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  41. The Syntax/Semantics Interface in Categorial Grammar.Pauline Jacobson - 1996 - In Shalom Lappin (ed.), The Handbook of Contemporary Semantic Theory. Blackwell Reference. pp. 89--116.
     
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  42. Categorial Grammar and the Logical Form of Quantification.Harold D. Levin - 1986 - Studia Logica 45 (4):429-430.
     
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  43. Lamber Joachim. The Mathematics of Sentence Structure. American Mathematical Monthly, Vol. 65 No. 3 , Pp. 154–170.Lambek Joachim. Contributions to a Mathematical Analysis of the English Verb-Phrase. Journal of the Canadian Linguistic Association, Vol. 5 , Pp. 83–89.Lambek Joachim. On the Calculus of Syntactic Types. Structure of Language and its Mathematical Aspects, Proceedings of Symposia in Applied Mathematics, Vol. 12, American Mathematical Society, Providence 1961, Pp. 166–178.Court L. M., Lambek J., Hiż H.. Comments. Structure of Language and its Mathematical Aspects, Proceedings of Symposia in Applied Mathematics, Vol. 12, American Mathematical Society, Providence 1961, Pp. 264–265.Cohen Joel M.. The Equivalence of Two Concepts of Categorial Grammar. Information and Control, Vol. 10 , Pp. 475–484. [REVIEW]Eliahu Shamir - 1969 - Journal of Symbolic Logic 33 (4):627-628.
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  44.  16
    Fibred Semantics for Feature-Based Grammar Logic.Jochen Dörre, Esther König & Dov Gabbay - 1996 - Journal of Logic, Language and Information 5 (3-4):387-422.
    This paper gives a simple method for providing categorial brands of feature-based unification grammars with a model-theoretic semantics. The key idea is to apply the paradigm of fibred semantics (or layered logics, see Gabbay (1990)) in order to combine the two components of a feature-based grammar logic. We demonstrate the method for the augmentation of Lambek categorial grammar with Kasper/Rounds-style feature logic. These are combined by replacing (or annotating) atomic formulas of the first logic, i.e. the (...)
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  45. 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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  46.  38
    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 (...)
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  47.  15
    Identification in the Limit of Categorial Grammars.Makoto Kanazawa - 1996 - Journal of Logic, Language and Information 5 (2):115-155.
    It is proved that for any k, the class of classical categorial grammars that assign at most k types to each symbol in the alphabet is learnable, in the Gold (1967) sense of identification in the limit from positive data. The proof crucially relies on the fact that the concept known as finite elasticity in the inductive inference literature is preserved under the inverse image of a finite-valued relation. The learning algorithm presented here incorporates Buszkowski and Penn's (1990) algorithm (...)
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  48. Across-the-Board Binding Meets Verb Second.Anna Szabolcsi - 1990 - In M. Nespor & J. Mascaro (eds.), Grammar in progress. Foris.
    Right-node raising of anaphors and bound pronouns out of coordinations, as in "Every student likes, and every professor hates, himself / his neighbors" is judged more acceptable in German and Dutch than in English. Using combinatory categorial grammar, this paper ties the cross-linguistic difference to the fact that German and Dutch are V-2 languages, and V-2 necessitates a lifted category for verbs that automatically caters to the right-node raised duplicator. The same lifted category is optionally available in English, (...)
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  49.  31
    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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  50.  34
    Logic and Grammar.Joachim Lambek - 2012 - Studia Logica 100 (4):667-681.
    Grammar can be formulated as a kind of substructural propositional logic. In support of this claim, we survey bare Gentzen style deductive systems and two kinds of non-commutative linear logic: intuitionistic and compact bilinear logic. We also glance at their categorical refinements.
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