This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finite-state agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571–595). The axiomatization is obtained by extending the general axioms of iteration theories (or iteration algebras), which characterize the equational p...

This paper exploits the point of view of constraint programming as computation in a logical system, namely constraint logic. We dene the basic ingredients of constraint logic, such as constraint models and generalised polynomials. We show that constraint logic is an institution , and we internalise the study of constraint logic to the framework of category-based equational logic. By showing tha...

This note shows that split-2 bisimulation equivalence (also known as timed equivalence) affords a finite equational axiomatization over the process algebra obtained by adding an auxiliary operation proposed by Hennessy in 1981 to the recursion free fragment of Milner’s Calculus of Communicating Systems. Thus the addition of a single binary operation, viz. Hennessy’s merge, is sufficient for the...

We explore the power of relational semantics and equational reasoning in the style of Kleene algebra for analyzing programs with mutable, statically scoped local variables. We provide (i) a fully compositional relational semantics for a first-order programming language with constructs for local variable declaration and destructive update; and (ii) an equational proof system based on Kleene alge...

The multiplicity of formalisms and corresponding verification systems makes the transformation useful for interoperations among them. We have proposed an approach to the transformation of state machines from a syntax-constrained class of equational theories into rewrite theories, which can be verified by Maude’s model checking facilities. However, the efficiency of model checking generated rewr...

This paper presents a complete account of positive and negative results on the finite axiomatizability of weak complete simulation semantics over the language BCCSP. We offer finite (un)conditional groundcomplete axiomatizations for the weak complete simulation precongruence. In sharp contrast to this positive result, we prove that, in the presence of at least one observable action, the (in)equ...

We consider the identities of a variety of semigroup-related algebras modeling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory interpret...

A solution to the problem of speciicity in a resource{oriented deductive approach to actions and change is presented. Speciicity originates in the problem of overloading methods in object oriented frameworks but can be observed in general applications of actions and change in logic. We give a uniform solution to the problem of speciicity culminating in a completed equational logic program with ...

A fundamental result in rewriting is : E |= s ≈ t ⇐⇒1 E ` s = t ⇐⇒2 s↔E t 1. is Birkhoff’s theorem expressing that semantic consequence (|=) coincides with syntactic consequence (`). 2. expresses that equality in equational logic (=) coincides with convertibility in rewriting (↔∗), a property known as logicality. We show that the result can be extended to hold for several sub-equational logics ...

Introducing equality into standard Horn clauses leads to a programming paradigm known as Equational Logic Programming. We propose here a scheme for the evaluation of such equational logic programs combining two powerful operational techniques : directed narrowing for the equational part and linear completion for the logical part. Thus we provide a goal-oriented solving procedure, keeping the we...