Equational logic is one of the most important domains of research in computer science. Specifications of types of data structures and assertions about the behaviour of programs are naturally written in equational form. Programs made of equations are called equational programs and appear in functional programming, logic programming and in most combinations of high level programming paradigms [19...

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...

We propose and study a logic able to state and reason about equational constraints, by combining aspects of classical propositional logic, equational logic, and quantifiers. The logic has a classical structure over an algebraic base, and a form of universal quantification distinguishing between local and global validity of equational constraints. We present a sound and complete axiomatization f...

We show that the generalized variant of formal systems where the underlying equational specifications are membership equational theories, and where the rules are conditional and can have equations, memberships and rewrites in the conditions is reflective. We also show that membership equational logic, many-sorted equational logic, and Horn logic with equality are likewise reflective. These resu...

derivations, equational logic and interpolation Gerard R. Renardel de Lavalette Department of Mathematics and Computing Science University of Groningen, the Netherlands Abstract. We define abstract derivations for equational logic and use them to prove the interpolation property. We define abstract derivations for equational logic and use them to prove the interpolation property.

derivations, equational logic and interpolation (extended abstract) Gerard R. Renardel de Lavalette Department of Mathematics and Computing Science University of Groningen, the Netherlands Abstract. We define abstract derivations for equational logic and use them to prove the interpolation property. We define abstract derivations for equational logic and use them to prove the interpolation prop...