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Models for polymorphic Lambek Calculus
1997An adaptation of string-semantic models to the Polymorphic Lambek Calculus is studied. We note that if quantifiers range over arbitrary sets of strings, the polymorphic calculus is incomplete. The semantics is refined so that quantifiers range over sets of strings that are the interpretation of categories, and we prove a completeness result.
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Dyadic Modalities and Lambek Calculus
1993The Lambek calculus is a logic on the one hand, and a grammar on the other. The system is studied in different disciplines, having their own interests. The logician studies relations with other systems, models in general, cut elimination etc. The linguist is interested in parsing properties, expressive power, and models that are useful for (natural ...
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Completeness Results for Lambek Syntactic Calculus
Mathematical Logic Quarterly, 1986We prove strong completeness of the Lambek syntactic calculus (with product) with respect to an algebraic semantics consisting of residuated semigroups spread over arbitrary semigroups. If the latter are free semigroups, strong completeness fails, but it is an open problem whether weak completeness holds.
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The Multimodal Lambek Calculus
2012The multimodal Lambek calculus extends the (non-associative) Lambek calculus in two ways. First, it provides a way of mixing different resource management possibilities — for example associative and non-associative or commutative and non-commutative — without collapse, that is to say that associativity can be valid for certain formulae but not for ...
Richard Moot, Christian Retoré
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Classical Conservative Extensions of Lambek Calculus
Studia Logica, 2002The paper concerns the Lambek Calculus (LC) and its extensions. The pure Lambek Calculus, which is LC without additive constants, is also distinguished. Two systems are considered: Noncommutative Multiplicative-Additive Linear Logic (NMALL), introduced by the author (in 1991), and Cyclic Multiplicative-Additive Linear Logic (CyMALL), introduced by ...
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Relational Semantics for the Lambek-Grishin Calculus
2010We study ternary relational semantics for LG: a symmetric version of the Lambek calculus with interaction principles due to Grishin [10]. We obtain completeness on the basis of a Henkin-style weak filter construction.
Kurtonina, N., Moortgat, M.J.
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Lambek calculus with restricted contraction and expansion
Studia Logica, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Language models for some extensions of the Lambek calculus
Information and Computation, 2022Stepan L Kuznetsov, Andre Scedrov
exaly
Conjoinability in 1-Discontinuous Lambek Calculus
2014In the present work we prove a conjoinability criterion for 1-discontinuous Lambek calculus. It turns out that types of this calculus are conjoinable if and only if they have the same sort and the same interpretation in the free abelian group generated by the primitive types.
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