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On Finite Models of the Lambek Calculus
Studia Logica, 2005The main result of the paper is a proof of the finite model property for the Lambek calculus with additive conjunction. This is a modification of \textit{W. Buszkowski}'s results for product-free fragments of the calculus [Math. Log. Q. 48, No. 1, 63--72 (2002; Zbl 0992.03029)]. In the paper under review, restricted cone frames are introduced.
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Language completeness of the Lambek calculus
Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science, 2002Proves that the Lambek calculus (J. Lambek, American Math. Monthly, vol. 65, no. 3, pp. 154-170, 1958), which is essentially a subsystem of noncommutative linear logic, is complete with respect to L-models, i.e. free semigroup models. >
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On the Recognizing Power of the Lambek Calculus with Brackets [PDF]
Journal of Logic, Language and Information, 2018 minor ...
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Classical Non-Associative Lambek Calculus
Studia Logica, 2002We introduce non-associative linear logic, which may be seen as the classical version of the non-associative Lambek calculus. We define its sequent calculus, its theory of proof nets, for which we give a correctness criterion and a sequentialization theorem, and we show proof search in it is polynomial.
de Groote, Philippe, Lamarche, François
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Lambek Calculus for Transformational Grammar
Research on Language and Computation, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A BRIEF SURVEY OF FRAMES FOR THE LAMBEK CALCULUS
Zeitschrift Für Mathematische Logik Und Grundlagen Der Mathematik, 1992AbstractModels for the Lambek calculus of syntactic categories surveyed here are based on frames that are in principle of the same type as Kripke frames for intuitionistic logic. These models are extracted from the literature on models for relevant logics, in particular the ternary relationed models introduced in the early seventies.
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On the Complexity of Nonassociative Lambek Calculus with Unit
Studia Logica, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Lambek calculus enriched with additional connectives
Journal of Logic, Language and Information, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1988
There is a noticeable revival of categorial grammar these days, as a vehicle for linguistic description. The systems used differ somewhat from the original calculus of Ajdukiewicz and Bar-Hillel, however. In particular, there is a component of rules for ‘type change’ of expressions, making for greater flexibility and elegance. One fundamental system of
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There is a noticeable revival of categorial grammar these days, as a vehicle for linguistic description. The systems used differ somewhat from the original calculus of Ajdukiewicz and Bar-Hillel, however. In particular, there is a component of rules for ‘type change’ of expressions, making for greater flexibility and elegance. One fundamental system of
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Lambek Calculus in Natural Deduction
Journal of Logic and Computation, 2007A formulation of Lambek calculus in natural deduction is given. New rules for Lambek's multiplicative, non-commutative conjunction are proposed, rules for Lambek's two implications are standard. Rules for Lambek's conjunction are variants of general elimination rules: a symmetric elimination rule and its specializations, left elimination rule and right
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