Search results for 'Categorial grammar' (try it on Scholar)

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  1.  26
    Raffaella Bernardi (2004). Analyzing the Core of Categorial Grammar. 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 (...)
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  2.  46
    Michael Moortgat (2009). Symmetric Categorial Grammar. 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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  3.  28
    Carlos Areces & Raffaella Bernardi (2004). Analyzing the Core of Categorial Grammar. 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 (...)
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  4.  8
    Erik Aarts & Kees Trautwein (1995). Non‐Associative Lambek Categorial Grammar in Polynomial Time. 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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  5.  2
    Fregean Categorial Grammar (1973). Timothy C. Potts. In Radu J. Bogdan & Ilkka Niiniluoto (eds.), Logic, Language, and Probability. Boston,D. Reidel Pub. Co. 245.
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  6.  32
    Nissim Francez & Mark Steedman (2006). Categorial Grammar and the Semantics of Contextual Prepositional Phrases. 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. Harold D. Levin (1986). Categorial Grammar and the Logical Form of Quantification. Philosophical Review 95 (1):127-129.
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  8.  18
    Erich Rast (2013). On Contextual Domain Restriction in Categorial Grammar. 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. Glyn V. Morrill (1994). Type Logical Grammar Categorial Logic of Signs.
     
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  10.  32
    Reinhard Muskens, Categorial Grammar and Lexical-Functional Grammar.
    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.  1
    Heinrich Wansing (2007). A Note On Negation In Categorial Grammar. 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.  9
    Glyn Morrill (1995). Discontinuity in Categorial Grammar. 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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  13.  17
    Aravind K. Joshi & Seth Kulick (1997). Partial Proof Trees as Building Blocks for a Categorial Grammar. 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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  14.  26
    Lloyd Humberstone (2005). Geach's Categorial Grammar. 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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  15.  38
    Reinhard Muskens, Categorial Grammar and Discourse Representation Theory.
    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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  16.  12
    Yde Venema (1996). Tree Models and (Labeled) Categorial Grammar. 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. Raffaella Bernardi, Reasoning with Categorial Grammar Logic.
    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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  18. Raffaella Bernardi, Categorial Grammar.
    1 Recognition Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Classical Categorial Grammar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 (...)
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  19.  32
    Emmon W. Bach, Discontinous Constituents in Generalized Categorial Grammar.
    [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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  20.  8
    Reinhard Muskens, Separating Syntax and Combinatorics in Categorial Grammar.
    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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  21. Wojciech Buszkowski, Witold Marciszewski & Johan van Benthem (1991). Categorial Grammar. Studia Logica 50 (1):171-172.
     
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  22.  26
    David Dowty, The Dual Analysis of Adjuncts/Complements in Categorial Grammar.
    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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  23.  1
    Wojciech Buszkowski (1982). Compatibility of a Categorial Grammar With an Associated Category System. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 28 (14-18):229-238.
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  24.  11
    Aarne Ranta (1991). Intuitionistic Categorial Grammar. Linguistics and Philosophy 14 (2):203 - 239.
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  25.  3
    Jacek Marciniec (1994). Learning Categorial Grammar by Unification with Negative Constraints. Journal of Applied Non-Classical Logics 4 (2):181-200.
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  26. Johan van Benthem (1990). Categorial Grammar and Type Theory. Journal of Philosophical Logic 19 (2):115-168.
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  27.  13
    Peter Simons (1989). Combinators and Categorial Grammar. Notre Dame Journal of Formal Logic 30 (2):241-261.
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  28.  6
    Johan Benthem (1990). Categorial Grammar and Type Theory. Journal of Philosophical Logic 19 (2):115 - 168.
  29.  1
    Mieszko Tałasiewicz (2014). Categorial Grammar and the Foundations of the Philosophy of Language. In Piotr Stalmaszczyk (ed.), Philosophy of Language and Linguistics: The Legacy of Frege, Russell, and Wittgenstein. De Gruyter 269-294.
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  30.  5
    Timothy C. Potts (1973). Fregean Categorial Grammar. In Radu J. Bogdan & Ilkka Niiniluoto (eds.), Logic, Language, and Probability. Boston,D. Reidel Pub. Co. 245--284.
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  31.  17
    Beom-Mo Kang (1995). On the Treatment of Complex Predicates in Categorial Grammar. Linguistics and Philosophy 18 (1):61 - 81.
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  32.  16
    Jacek Marciniec (1997). Infinite Set Unification with Application to Categorial Grammar. 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.  7
    Jack Hoeksema (1988). Categorial Grammar and the Logical Form of Quantification. International Studies in Philosophy 20 (3):131-132.
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  34. M. J. Cresswell (1985). Review of Levin, H. D.: Categorial grammar and the logical form of quantification. [REVIEW] Theoria 51 (1):55.
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  35.  3
    Hans Karlgren (1978). Categorial Grammar — a Basis for a Natural Language Calculus? Studia Logica 37 (1):65 - 78.
  36.  12
    Witold Marciszewski (1978). On Categorial Grammar and Logical Form. Studia Logica 37 (1):1-5.
  37.  3
    Krystyna Misiuna (1995). Categorial Grammar and Ontological Commitment. In Vito Sinisi & Jan Woleński (eds.), The Heritage of Kazimierz Ajdukiewicz. Rodopi 40--195.
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  38.  1
    Wojciech Buszkowski (1998). On Families of Languages Generated by Categorial Grammar. Poznan Studies in the Philosophy of the Sciences and the Humanities 62:39-48.
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  39.  1
    Urszula Wybraniec-Skardowska (2006). On the Formalization of Classical Categorial Grammar. Poznan Studies in the Philosophy of the Sciences and the Humanities 89:269.
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  40. Pauline Jacobson (1996). The Syntax/Semantics Interface in Categorial Grammar. In Shalom Lappin (ed.), The Handbook of Contemporary Semantic Theory. Blackwell Reference 89--116.
     
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  41. Hans Karlgren (1978). Categorial Grammar — A Basis for a Natural Language Calculus? Studia Logica 37 (1):65-78.
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  42. Natasha Kurtonina (1995). Talking About Explicit Databases in Categorial Grammar. Logic Journal of the Igpl 3 (2-3):357-370.
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  43. Michael Moortgat (2009). Symmetric Categorial Grammar. Journal of Philosophical Logic 38 (6):681-710.
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  44.  13
    Jochen Dörre, Esther König & Dov Gabbay (1996). Fibred Semantics for Feature-Based Grammar Logic. 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.  36
    Makoto Kanazawa (2010). Second-Order Abstract Categorial Grammars as Hyperedge Replacement Grammars. 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 (...)
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  46.  26
    Maciej Kandulski (1995). On Commutative and Nonassociative Syntactic Calculi and Categorial Grammars. 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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  47.  88
    Anna Szabolcsi (1990). Across-the-Board Binding Meets Verb Second. 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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  48.  9
    Makoto Kanazawa (1996). Identification in the Limit of Categorial Grammars. 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) (...)
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  49.  31
    Joachim Lambek (2012). Logic and Grammar. 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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  50.  21
    Christian Retoré & Sylvain Salvati (2010). A Faithful Representation of Non-Associative Lambek Grammars in Abstract Categorial Grammars. Journal of Logic Language and Information 19 (2):185-200.
    This paper solves a natural but still open question: can abstract categorial grammars (ACGs) respresent usual categorial grammars? Despite their name and their claim to be a unifying framework, up to now there was no faithful representation of usual categorial grammars in ACGs. This paper shows that Non-Associative Lambek grammars as well as their derivations can be defined using ACGs of order two. To conclude, the outcome of such a representation are discussed.
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