We consider a constrained equational logic where the constraints are membership conditions t 2 s where s is interpreted as a regular tree language. Our logic includes a fragment of second order equational logic (without projections) where second order variables range over regular sets of contexts. The problem with constrained equational logics is the failure of the critical pair lemma. That is ...

A logic is developed in which function symbols are allowed to represent partial functions. It has the usual rules of logic (in the form of a sequent calculus) except that the substitution rule has to be modi ed. It is developed here in its minimal form, with equality and conjunction, as partial Horn logic . Various kinds of logical theory are equivalent: partial Horn theories, quasi-equational ...

This paper considers compositions of conditional term rewriting systems as a basis for a modular approach to the design and analysis of equational logic programs. In this context, an equational logic program is viewed as consisting of a set of modules, each module defining a part of the program’s functions. We define a compositional semantics for conditional term rewriting systems which we show...

PAM is a general proof tool for process algebras. It allows users to deene their own calculi and then perform algebraic style proofs in these calculi by directly manipulating process terms. The logic that PAM implements is equational logic plus recursion, with some features tailored to the particular requirements of process algebras. Equational reasoning is implemented by rewriting, while recur...

A sound and complete approach for encoding the action description language A developed by M. Gelfond and V. Lifschitz in an equational logic program is given. Our results allow the comparison of the resource-oriented equational logic based approach and various other methods designed for reasoning about actions, most of them based on variants of the situation calculus, which were also related to...

Fiore and Hur [10] recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This work completes the foundations of the subject from the vie...

The algebraic approach originally concentrated on the use of equational logic as the basic formalism for specification. This use was successful in many senses. In particular, the good behaviour of equational logic with respect to a number of semantic constructs has helped to facilitate the study of new specification concepts and constructs. At the same time, the categorical techniques used for ...