Our view of computation is still evolving. The concrete theories for specific computational phenomena that are emerging encompass three aspects: specification and programming languages for describing computations, mathematical structures for modelling computations, and logics for reasoning about properties of computations. To make sense of this complexity, and also to compare and/or relate diff...

We present the details of a formalization of Equational Predicate Logic based on a propositional version of the Leibniz rule (PSL—Propositional Strong Leibniz), EQN (equanimity) and TR (transitivity). All the above rules are “strong”, that is, they are applicable to arbitrary premises (not just to absolute theorems). It is shown that a strong no-capture Leibniz (SLCS—Strong Leibniz with “Contex...

We show the completeness of an extension of SLDDresolution to the equational setting. This proves a conjecture of Laurent Fribourg and shows the completeness of an implementation of his. It is the rst completeness result for superposition of equational Horn clauses which reduces to SLD resolution in the nonnequational case. The inference system proved complete is actually more general than the ...

We present an algorithm for the generation of prime implicates in equational logic, that is, of the most general consequences of formulæ containing equations and disequations between first-order terms. This algorithm is defined by a calculus that is proved to be correct and complete. We then focus on the case where the considered clause set is ground, i.e., contains no variables, and devise a s...

Since rewriting logic has been introduced, it has shown its adequateness both as a semantic and a logical framework. But the numerous applications of the rewriting logic in the above two areas has shown the importance of increasing its expressive power. Therefore, in order to facilitate this work, we will study in this paper how to generalize the transformation that from the equational logic ha...

Various logic-based frameworks have been proposed for specifying the operational semantics of programming languages and concurrent systems, including inference systems in the styles advocated by Plotkin and by Kahn, Horn logic, equational specifications, reduction systems for evaluation contexts, rewriting logic, and tile logic. We consider the relationship between these frameworks, and assess ...

When one develops, implements, and studies type theories based on linear logic, for example, in the context of theorem proving, logic programming, and formal reasoning, one is immediately confronted with questions about their equational theory and how to deal with logic variables. In this paper, we propose linear contextual modal type theory that gives a mathematical account of the nature of lo...

Subset-logic programs are built up of three kinds of program clauses: subset, equational, and relational clauses. Using these clauses, we can program solutions to a broad range of problems of interest in logic programming and deductive databases. In an earlier paper Jay92], we discussed the implementation of subset and equational program clauses. This paper substantially extends that work, and ...

In this paper, we aim to contribute the knowledge about how imperative C functions can be transformed Maude functional and system modules respectively. is a formal specification language characterized by simplicity, expressivity good performance. It multi-paradigm meta-language based on rewriting logic equational theories used specify, simulate formally verify concurrent distributed systems. ha...