In this paper we present the theorem prover SBR3 for equational logic and its application in the many-valued logic of Lukasiewicz. We give a new equational axiomatization of many-valued logic and we prove by SBR3 that it is equivalent to the classical equational presentation of such logic given by Wajsberg. We feel that our equational axiomatization of Wajsberg algebras is more suited for autom...

UCG-E (Hamel, 1991) is an equational logic programming system inspired by O’Donnell’s system (O’Donnell, 1985) and was designed to allow the integration of logic systems into imperative style programming environments. Equational logic systems are interesting, since they may be implemented very efficiently with term rewriting systems (Herman, 1991). Backtracking, a major source of inefficiencies...

It is well known that bisimulation on μ-expressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features beyond pure equational Horn logic: either rules that are impure by involving non-equational side-conditions, or rules that are schematically infinita...

We present an approach based on inductive theorem proving for verifying invariance properties of systems specified in Rewriting Logic, an executable specification language implemented (among others) in the Maude tool. Since theorem proving is not directly available for rewriting logic, we define an encoding of rewriting logic into its membership equational (sub)logic. Then, inductive theorem pr...

Functional logic programming languages combine the most important features of functional programming languages and logic programming languages. Functional logic programming applied to theMaude specification language would replace the functional viewpoint by an equational viewpoint while retaining the logic features. This paper tries to bridge the gap between functional logic languages and the c...

It is well known that bisimulation on μ-expressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features which go beyond pure equational Horn logic: either the rules are impure by involving non-equational side-conditions, or they are schematically infini...

Suppose that T is an equational theory of groups or of rings. If T is finitely axiomatizable, then there is a least number μ so that T can be axiomatized by μ equations. This μ can depend on the operation symbols that occur in T . In the 1960’s, Alfred Tarski and Thomas C. Green completely determined the values of μ for arbitrary equational theories of groups and of rings. While Tarski and Gree...

The idea to combine the advantages of function and logic programming has attracted many researches. Their work ranges from the integration of existing languages over higher-order logic to equational logic languages, where logic programs are augmented with equational theories. Recently, it has been proposed to handle those equational theories by complete sets of transformations. These transforma...

We introduce an abstract general notion of system of equations and rewrites between terms, called Term Equational Rewrite System (TERS), and develop a sound logical deduction system, called Term Equational Rewrite Logic (TERL), to reason about equality and rewriting. Further, we give an analysis of algebraic free constructions which together with an internal completeness result may be used to s...