We discuss the declarative and computational issues in combining equa-tional, subset, and relational assertions in a logic programming language. The novel feature in this work is the subset assertion, whose interactions with equational and relational assertions are discussed in this paper. The semantics of subset assertions incorporate a collect all capability, which is expressed formally by th...

Birkhoff’s completeness theorem of equational logic asserts the coincidence of the model-theoretic and proof-theoretic consequence relations. Goguen and Meseguer, giving a sound and adequate system of inference rules for finitary many-sorted equational deduction, generalized the completeness theorem of Birkhoff to the completeness of finitary many-sorted equational logic and provided simultaneo...

Among others we will see that the equational theory of ω dimensional representable polyadic equality algebras (RPEAω’s) is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is finite schema-axiomatizable (and hence the equational theory of this class is finite schemaaxi...

In this paper we propose an equational specification of UML+OCL static class diagrams that provides a formal foundation for automatically validating UML object diagrams with respect to OCL constraints. Basically, class and object UML diagrams are specified as membership equational theories, and OCL expressions are represented as terms over extensions of those theories. Then, validating object d...

‎‎The investigation of equational compactness was initiated by‎ ‎Banaschewski and Nelson‎. ‎They proved that pure injectivity is‎ ‎equivalent to equational compactness‎. ‎Here we define the so‎ ‎called sequentially compact acts over semigroups and study‎ ‎some of their categorical and homological properties‎. ‎Some‎ ‎Baer conditions for injectivity of S-acts are also presented‎.

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 a new class of fuzzy open sets called fuzzy $bigwedge_e$ sets which includes the class of fuzzy $e$-open sets. We also define a weaker form of fuzzy $bigwedge_e$ sets termed as fuzzy locally $bigwedge_e$ sets. By means of these new sets, we present the notions of fuzzy $bigwedge_e$ continuity and fuzzy locally $bigwedge_e$ continuity which are weaker than fuzzy $e$-continuity and f...

Nominal unification is a generalisation of first-order unification that takes α-equivalence into account. In this paper, we study nominal unification in the context of equational theories. We introduce nominal narrowing and design a general nominal E-unification procedure, which is sound and complete for a wide class of equational theories. We give examples of application. 1998 ACM Subject Clas...