On Action Logic
نویسنده
چکیده
Pratt [22] defines action algebras as Kleene algebras with residuals and action logic as the equational theory of action algebras. In opposition to Kleene algebras, action algebras form a (finitely based) variety. Jipsen [9] proposes a Gentzen-style sequent system for action logic but leaves it as an open question if this system admits cut-elimination and if action logic is decidable. We show that Jipsen’s system does not admit cutelimination. We prove that the equational theory of *-continuous action algebras and the simple Horn theory of *-continuous Kleene algebras are not recursively enumerable and they possess FMP, but action logic does not possess FMP.
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