Sequential Dynamic Logic

Abstract

We introduce a substructural propositional calculus of Sequential Dynamic Logic that subsumes a propositional part of dynamic predicate logic, and is shown to be expressively equivalent to propositional dynamic logic. Completeness of the calculus with respect to the intended relational semantics is established.

On the Complexity of Kleene Algebra with Domain

“…The scope of the present paper is also more general than those of [12] and [24]. We also strengthen the following relational completeness results: (i) Bochman and Gabbay [1] formulate a sequent system (generalizing Kozen and Tiuryn's [18] substructural logic of partial correctness S) that is sound and complete with respect to a fragment of the equational theory of relational aKAT, (ii) Hollenberg [11] gives an axiomatization of the equational theory of * -free relational aKAT, and (iii) McLean [20] (based on the work of Mbacke [19]) establishes a relational completeness result for * -free relational dKA.…”

“…In contrast to KA and KAT, completeness and complexity results for their extensions with dynamic tests are largely missing. 1 We fill this gap by proving relational completeness and (parametrized) guarded-language completeness results for dKA (KA with domain), aKA (KA with both domain and antidomain), dKAT (KAT with domain) and aKAT (KAT with both domain and antidomain), and EXPTIMEcompleteness results for aKAT and aKA.…”