Affiliation:
1. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Abstract
Action logic is the algebraic logic (inequational theory) of residuated Kleene lattices. One of the operations of this logic is the Kleene star, which is axiomatized by an induction scheme. For a stronger system that uses an
-rule instead (infinitary action logic), Buszkowski and Palka (2007) proved
-completeness (thus, undecidability). Decidability of action logic itself was an open question, raised by Kozen in 1994. In this article, we show that it is undecidable, more precisely,
-complete. We also prove the same undecidability results for all recursively enumerable logics between action logic and infinitary action logic, for fragments of these logics with only one of the two lattice (additive) connectives, and for action logic extended with the law of distributivity.
Funder
Ministry of Science and Higher Education of the Russian Federation
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
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