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...

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...

In the paper, we introduce a new tree automata framework, called propositional tree automata, capturing the class of tree languages that are closed under an equational theory and Boolean operations. This framework originates in work on developing a su cient completeness checker for speci cations with rewriting modulo an equational theory. Propositional tree automata recognize regular equational...

Conditional equational theories can be built into logic programming using a generalized resolution rule which calls a universal uniication procedure. Such uniication procedures are often deened by sound and strongly complete sets of inference rules. In other words, to resolve upon two atoms requires to show-by means of the inference rules-that the corresponding arguments of the atoms are equal ...

Equational presentations with ordered sorts encompass partially deened functions and subtyping information in an algebraic framework. In this work we address the problem of computing in order-sorted algebras, with very few restrictions on the allowed presentations. We adopt an algebraic framework where equational, membership and existence formulas can be expressed. A complete deduction calculus...

We present an approach to the transformation of state machines from a restricted subclass of equational theories into rewrite theories, and show the transformation preserves invariant properties. Invariantpreservation of the transformation guarantees that a counterexample that is found to an invariant by model checking a generated rewrite theory is also the counterexample to the corresponding i...

A solution to the problem of specificity in a resource–oriented deductive approach to actions and change is presented. Specificity 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 specificity culminating in a completed equational logic program wi...