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Extending the Lambek Calculus with Classical Negation
Studia Logica, 2021Let \textbf{NL} be the non-associative Lambek calculus and S (our symbol) be the ternary relational semantics for \textbf{NL} as defined in [\textit{K. Došen}, Z. Math. Logik Grundlagen Math. 38, No. 2, 179--187 (1992; Zbl 0793.03025)]. Moreover, let negation be classically interpreted when ``a world satisfies the negation of a formula if and only if ...
Michael Kaminski, Kaminski Michael
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Classical Non-Associative Lambek Calculus
Studia Logica, 2002 We 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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The Lambek calculus enriched with additional connectives
Journal of Logic, Language and Information, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Makoto Kanazawa
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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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Lambek Calculus Proofs and Tree Automata
, 2001 We investigate natural deduction proofs of the Lambek calculus from the point of view of tree automata. The main result is that the set of proofs of the Lambek calculus cannot be accepted by a finite tree automaton. The proof is extended to cover the proofs used by grammars based on the Lambek calculus, which typically use only a subset of the set of ...
Hans-joerg Tiede
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Lambek Calculus and its relational semantics: Completeness and incompleteness
Journal of Logic, Language and Information, 1994 The problem of whether Lambek Calculus is complete with respect to (w.r.t.) relational semantics, has been raised several times, cf. van Benthem (1989a) and van Benthem (1991). In this paper, we show that the answer is in the affirmative. More precisely,
Hajnal Andreka +2 more
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Lambek Calculus with Conjugates
Studia Logica, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Igor Sedlár, Andrew Tedder
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On the Selective Lambek Calculus
2005An intermediate logical system in comparison with the non-associative (NL) and the associative Lambek Calculus(L) is obtained by extending their language by means of a so-called “combining permission”, which is used to regulate the introduction of a product formula in the scope of a derivation and to impose a control on applications of the association ...
Marcelo da Silva Corrêa +1 more
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Proof Nets for Lambek Calculus
Journal of Logic and Computation, 1992The representation of a proof as you find it in textbooks is just a linear sequence of derivation steps. This does not mean that linear sequences of derivation steps are a good representation for computer generated and computer manipulated proofs. And in fact, for various calculi there are alternative and more compact representations of proofs, for ...
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