Modal Kleene Algebra and Applications --- A Survey ---
J. Desharnais, B. Möller and G. Struth
Modal Kleene algebras are Kleene algebras with forward and backward
modal operators, defined via domain and codomain operations. They
provide a concise and convenient algebraic framework that subsumes
various popular calculi and allows treating quite a number of areas. We
survey the basic theory and some prominent applications. These include,
on the system semantics side, wlp and wpc calculus, PDL
(Propositional Dynamic Logic), predicate transformer semantics,
temporal logics and termination analysis of rewrite systems and state
transition systems. On the derivation side we apply the framework to
game analysis and greedy-like algorithms.
Journal on Relation Methods in Computer Science, Vol. 1, pp. 93-131,
2004