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arXiv · 1408.5956

Kleene Algebras, Regular Languages and Substructural Logics

Christian Wurm
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Abstract

We introduce the two substructural propositional logics KL, KL+, which use disjunction, fusion and a unary, (quasi-)exponential connective. For both we prove strong completeness with respect to the interpretation in Kleene algebras and a variant thereof. We also prove strong completeness for language models, where each logic comes with a different interpretation. We show that for both logics the cut rule is admissible and both have a decidable consequence relation.

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Christian Wurm. 2014-08-26. Kleene Algebras, Regular Languages and Substructural Logics. https://doi.org/10.4204/eptcs.161.7

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