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Lambda Grammars and the Syntax-Semantics Interface

In Robert Van Rooij & Martin Stokhof (eds.), Proceedings of the Thirteenth Amsterdam Colloquium. Amsterdam: ILLC. pp. 150-155 (2001)

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  1. 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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  • Pgf: A Portable Run-Time Format for Type-Theoretical Grammars. [REVIEW]Krasimir Angelov, Björn Bringert & Aarne Ranta - 2010 - Journal of Logic, Language and Information 19 (2):201-228.
    Portable Grammar Format (PGF) is a core language for type-theoretical grammars. It is the target language to which grammars written in the high-level formalism Grammatical Framework (GF) are compiled. Low-level and simple, PGF is easy to reason about, so that its language-theoretic properties can be established. It is also easy to write interpreters that perform parsing and generation with PGF grammars, and compilers converting PGF to other formats. This paper gives a concise description of PGF, covering syntax, semantics, and parser (...)
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  • Language, Lambdas, and Logic.Reinhard Muskens - 2003 - In R. Oehrle & J. Kruijff (eds.), Resource Sensitivity, Binding, and Anaphora (Studies in Linguistics and Philosophy 80). Dordrecht: Kluwer Academic Publishers. pp. 23--54.
    The paper develops Lambda Grammars, a form of categorial grammar that, unlike other categorial formalisms, is non-directional. Linguistic signs are represented as sequences of lambda terms and are combined with the help of linear combinators.
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  • A Faithful Representation of Non-Associative Lambek Grammars in Abstract Categorial Grammars.Christian Retoré & Sylvain Salvati - 2010 - 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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  • A Mixed Λ-Calculus.Marie-Renée Fleury & Myriam Quatrini - 2007 - Studia Logica 87 (2-3):269-294.
    The aim of this paper is to define a λ-calculus typed in aMixed (commutative and non-commutative) Intuitionistic Linear Logic. The terms of such a calculus are the labelling of proofs of a linear intuitionistic mixed natural deduction NILL, which is based on the non-commutative linear multiplicative sequent calculus MNL [RuetAbrusci 99]. This linear λ-calculus involves three linear arrows: two directional arrows and a nondirectional one (the usual linear arrow). Moreover, the -terms are provided with seriesparallel orders on free variables. We (...)
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  • On the Effect of the IO-Substitution on the Parikh Image of Semilinear Full AFLs.Pierre Bourreau - 2015 - Journal of Logic, Language and Information 24 (1):1-26.
    Back in the 1980’s, the class of mildly context-sensitive formalisms was introduced so as to capture the syntax of natural languages. While the languages generated by such formalisms are constrained by the constant-growth property, the most well-known and used ones—like tree-adjoining grammars or multiple context-free grammars—generate languages which verify the stronger property of being semilinear. In, the operation of IO-substitution was created so as to exhibit mildly-context sensitive classes of languages which are not semilinear. In the present article, we extend (...)
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  • A Faithful Representation of Non-Associative Lambek Grammars in Abstract Categorial Grammars.Christian Retoré & Sylvain Salvati - 2010 - Journal of Logic, Language and Information 19 (2):185-200.
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