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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 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 for Transformational Grammar
Research on Language and Computation, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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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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Versions of a Local Contraction Subexponential in the Lambek Calculus
Algebra i logika, 2022M. V. Valinkin
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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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