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

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  1. Michael Moortgat (2009). Symmetric Categorial Grammar. Journal of Philosophical Logic 38 (6):681 - 710.score: 240.0
    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. Carlos Areces & Raffaella Bernardi (2004). Analyzing the Core of Categorial Grammar. Journal of Logic, Language and Information 13 (2):121-137.score: 240.0
    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. Raffaella Bernardi (2004). Analyzing the Core of Categorial Grammar. Journal of Logic, Language and Information 13 (2):121-137.score: 240.0
    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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  4. Fregean Categorial Grammar (1973). Timothy C. Potts. In Radu J. Bogdan & Ilkka Niiniluoto (eds.), Logic, Language, and Probability. Boston,D. Reidel Pub. Co.. 245.score: 240.0
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  5. Nissim Francez & Mark Steedman (2006). Categorial Grammar and the Semantics of Contextual Prepositional Phrases. Linguistics and Philosophy 29 (4):381 - 417.score: 216.0
    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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  6. Erik Aarts & Kees Trautwein (1995). Non‐Associative Lambek Categorial Grammar in Polynomial Time. Mathematical Logic Quarterly 41 (4):476-484.score: 210.0
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  7. Erich Rast (2013). On Contextual Domain Restriction in Categorial Grammar. Synthese 190 (12):2085-2115.score: 192.0
    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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  8. Reinhard Muskens, Categorial Grammar and Lexical-Functional Grammar.score: 180.0
    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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  9. Lloyd Humberstone (2005). Geach's Categorial Grammar. Linguistics and Philosophy 28 (3):281 - 317.score: 180.0
    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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  10. Reinhard Muskens, Categorial Grammar and Discourse Representation Theory.score: 180.0
    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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  11. Raffaella Bernardi, Reasoning with Categorial Grammar Logic.score: 180.0
    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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  12. Yde Venema (1996). Tree Models and (Labeled) Categorial Grammar. Journal of Logic, Language and Information 5 (3-4):253-277.score: 180.0
    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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  13. Aravind K. Joshi & Seth Kulick (1997). Partial Proof Trees as Building Blocks for a Categorial Grammar. Linguistics and Philosophy 20 (6):637-667.score: 180.0
    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. Raffaella Bernardi, Categorial Grammar.score: 180.0
    1 Recognition Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Classical Categorial Grammar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 (...)
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  15. Glyn Morrill (1995). Discontinuity in Categorial Grammar. Linguistics and Philosophy 18 (2):175 - 219.score: 180.0
    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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  16. Emmon W. Bach, Discontinous Constituents in Generalized Categorial Grammar.score: 176.0
    [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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  17. Reinhard Muskens, Separating Syntax and Combinatorics in Categorial Grammar.score: 176.0
    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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  18. Makoto Kanazawa (2010). Second-Order Abstract Categorial Grammars as Hyperedge Replacement Grammars. Journal of Logic, Language and Information 19 (2):137-161.score: 156.0
    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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  19. David Dowty, The Dual Analysis of Adjuncts/Complements in Categorial Grammar.score: 152.0
    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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  20. Peter Simons (1989). Combinators and Categorial Grammar. Notre Dame Journal of Formal Logic 30 (2):241-261.score: 150.0
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  21. Jacek Marciniec (1997). Infinite Set Unification with Application to Categorial Grammar. Studia Logica 58 (3):339-355.score: 150.0
    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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  22. Beom-Mo Kang (1995). On the Treatment of Complex Predicates in Categorial Grammar. Linguistics and Philosophy 18 (1):61 - 81.score: 150.0
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  23. Witold Marciszewski (1978). On Categorial Grammar and Logical Form. Studia Logica 37 (1):1-5.score: 150.0
  24. Jack Hoeksema (1988). Categorial Grammar and the Logical Form of Quantification. International Studies in Philosophy 20 (3):131-132.score: 150.0
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  25. Aarne Ranta (1991). Intuitionistic Categorial Grammar. Linguistics and Philosophy 14 (2):203 - 239.score: 150.0
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  26. Krystyna Misiuna (1995). Categorial Grammar and Ontological Commitment. In Vito Sinisi & Jan Woleński (eds.), The Heritage of Kazimierz Ajdukiewicz. Rodopi. 40--195.score: 150.0
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  27. Johan Benthem (1990). Categorial Grammar and Type Theory. Journal of Philosophical Logic 19 (2):115 - 168.score: 150.0
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  28. Hans Karlgren (1978). Categorial Grammar — a Basis for a Natural Language Calculus? Studia Logica 37 (1):65 - 78.score: 150.0
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  29. Jacek Marciniec (1994). Learning Categorial Grammar by Unification with Negative Constraints. Journal of Applied Non-Classical Logics 4 (2):181-200.score: 150.0
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  30. Timothy C. Potts (1973). Fregean Categorial Grammar. In. In Radu J. Bogdan & Ilkka Niiniluoto (eds.), Logic, Language, and Probability. Boston,D. Reidel Pub. Co.. 245--284.score: 150.0
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  31. 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.score: 150.0
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  32. 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.score: 150.0
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  33. Pauline Jacobson (1996). The Syntax/Semantics Interface in Categorial Grammar. In Shalom Lappin (ed.), The Handbook of Contemporary Semantic Theory. Blackwell Reference. 89--116.score: 150.0
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  34. Urszula Wybraniec-Skardowska (2006). On the Formalization of Classical Categorial Grammar. Poznan Studies in the Philosophy of the Sciences and the Humanities 89:269.score: 150.0
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  35. Makoto Kanazawa (1996). Identification in the Limit of Categorial Grammars. Journal of Logic, Language and Information 5 (2):115-155.score: 144.0
    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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  36. 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.score: 144.0
    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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  37. Maciej Kandulski (1995). On Commutative and Nonassociative Syntactic Calculi and Categorial Grammars. Mathematical Logic Quarterly 41 (2):217-235.score: 130.0
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  38. 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.score: 120.0
    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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  39. Sean A. Fulop (2010). Grammar Induction by Unification of Type-Logical Lexicons. Journal of Logic, Language and Information 19 (3):353-381.score: 102.0
    A method is described for inducing a type-logical grammar from a sample of bare sentence trees which are annotated by lambda terms, called term-labelled trees . Any type logic from a permitted class of multimodal logics may be specified for use with the procedure, which induces the lexicon of the grammar including the grammatical categories. A first stage of semantic bootstrapping is performed, which induces a general form lexicon from the sample of term-labelled trees using Fulop’s (J Log (...)
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  40. Wojciech Buszkowski & Gerald Penn (1990). Categorial Grammars Determined From Linguistic Data by Unification. Studia Logica 49 (4):431 - 454.score: 100.0
    We provide an algorithm for determining a categorial grammar from linguistic data that essentially uses unification of type-schemes assigned to atoms. The algorithm presented here extends an earlier one restricted to rigid categorial grammars, introduced in [4] and [5], by admitting non-rigid outputs. The key innovation is the notion of an optimal unifier, a natural generalization of that of a most general unifier.
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  41. Joachim Lambek (2012). Logic and Grammar. Studia Logica 100 (4):667-681.score: 96.0
    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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  42. Philippe de Groote & Sylvain Pogodalla (2004). On the Expressive Power of Abstract Categorial Grammars: Representing Context-Free Formalisms. [REVIEW] Journal of Logic, Language and Information 13 (4):421-438.score: 96.0
    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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  43. Carl Pollard (forthcoming). Agnostic Hyperintensional Semantics. Synthese:1-28.score: 90.0
    A hyperintensional semantics for natural language is proposed which is agnostic about the question of whether propositions are sets of worlds or worlds are (maximal consistent) sets of propositions. Montague’s theory of intensional senses is replaced by a weaker theory, written in standard classical higher-order logic, of fine-grained senses which are in a many-to-one correspondence with intensions; Montague’s theory can then be recovered from the proposed theory by identifying the type of propositions with the type of sets of worlds and (...)
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  44. Lawrence S. Moss (2012). The Soundness of Internalized Polarity Marking. Studia Logica 100 (4):683-704.score: 90.0
    This paper provides a foundation for the polarity marking technique introduced by David Dowty [3] in connection with monotonicity reasoning in natural language and in linguistic analyses of negative polarity items based on categorial grammar. Dowty's work is an alternative to the better-known algorithmic approach first proposed by Johan van Benthem [11], and elaborated by Víctor Sánchez Valencia [10]. Dowty's system internalized the monotonicity/polarity markings by generating strings using a categorial grammar whose categories already contain the (...)
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  45. Glyn Morrill, Oriol Valentín & Mario Fadda (2011). The Displacement Calculus. Journal of Logic, Language and Information 20 (1):1-48.score: 90.0
    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 of (...)
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  46. Jean-Pierre Desclés, Anca Christine Pascu & Hee-Jin Ro (2014). Aspecto-Temporal Meanings Analysed by Combinatory Logic. Journal of Logic, Language and Information 23 (3):253-274.score: 86.0
    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 (GRACE) (Desclés and Ro in Math Sci Hum 194:39–70, 2011), using the applicative formalism, functional types of categorial grammars and combinatory logic (CL) (Curry and Feys in Combinatory Logic. North-Holland Publishing, (...)
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  47. Sylvain Salvati (2010). On the Membership Problem for Non-Linear Abstract Categorial Grammars. Journal of Logic, Language and Information 19 (2):163-183.score: 76.0
    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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  48. Reinhard Muskens (2010). New Directions in Type-Theoretic Grammars. Journal of Logic, Language and Information 19 (2):129-136.score: 72.0
    This paper argues for the idea that in describing language we should follow Haskell Curry in distinguishing between the structure of an expression and its appearance or manifestation . It is explained how making this distinction obviates the need for directed types in type-theoretic grammars and a simple grammatical formalism is sketched in which representations at all levels are lambda terms. The lambda term representing the abstract structure of an expression is homomorphically translated to a lambda term representing its manifestation, (...)
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  49. Wojciech Buszkowski (1988). Gaifman's Theorem on Categorial Grammars Revisited. Studia Logica 47 (1):23 - 33.score: 72.0
    The equivalence of (classical) categorial grammars and context-free grammars, proved by Gaifman [4], is a very basic result of the theory of formal grammars (an essentially equivalent result is known as the Greibach normal form theorem [1], [14]). We analyse the contents of Gaifman's theorem within the framework of structure and type transformations. We give a new proof of this theorem which relies on the algebra of phrase structures and exhibit a possibility to justify the key construction used in (...)
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  50. Wojciech Zielonka (1978). A Direct Proof of the Equivalence of Free Categorial Grammars and Simple Phrase Structure Grammars. Studia Logica 37 (1):41 - 57.score: 72.0
    In [2], Bar-Hillel, Gaifman, and Shamir prove that the simple phrase structure grammars (SPGs) defined by Chomsky are equivalent in a certain sense to Bar-Hillel's bidirectional categorial grammars (BCGs). On the other hand, Cohen [3] proves the equivalence of the latter ones to what the calls free categorial grammars (FCGs). They are closely related to Lambek's syntactic calculus which, in turn, is based on the idea due to Ajdukiewicz [1]. For the reasons which will be discussed in the (...)
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