
Undecidability of the Lambek calculus with subexponential and bracket modalities
The Lambek calculus is a wellknown logical formalism for modelling natu...
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Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality (Extended Abstract)
We develop a categorical compositional distributional semantics for Lamb...
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A Light Modality for Recursion
We investigate the interplay between a modality for controlling the beha...
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Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality
We develop a categorical compositional distributional semantics for Lamb...
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Dialectica Categories for the Lambek Calculus
We revisit the old work of de Paiva on the models of the Lambek Calculus...
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Iterative division in the Distributive Full Nonassociative Lambek Calculus
We study an extension of the Distributive Full Nonassociative Lambek Ca...
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Iterative division in the productfree Distributive Full Nonassociative Lambek Calculus
We study an extension of the productfree Distributive Full Nonassociat...
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Undecidability of the Lambek calculus with a relevant modality
Morrill and Valentin in the paper "Computational coverage of TLG: Nonlinearity" considered an extension of the Lambek calculus enriched by a socalled "exponential" modality. This modality behaves in the "relevant" style, that is, it allows contraction and permutation, but not weakening. Morrill and Valentin stated an open problem whether this system is decidable. Here we show its undecidability. Our result remains valid if we consider the fragment where all division operations have one direction. We also show that the derivability problem in a restricted case, where the modality can be applied only to variables (primitive types), is decidable and belongs to the NP class.
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