On Kleene algebras and closed semirings
MFCS '90 Proceedings on Mathematical foundations of computer science 1990
Action logic and pure induction
JELIA '90 Proceedings of the European workshop on Logics in AI
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
On Finite Model Property of the Equational Theory of Kleene Algebras
Fundamenta Informaticae
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We present an infinitary logic ACT$_ω$ in the form of a Gentzen-style sequent system, which is equivalent to the equational theory of *-continuous action lattices [9]. We prove the cut-elimination theorem for ACT$_ω$ and, as a consequence, a theorem on the elimination of negative occurrences of *. This shows that ACT$_ω$ is $Π^0_1$, whence, by a result of Buszkowski [1], it is $Π^0_1$ complete.