A logic may be called local if each model may be used to deene the truth. In the proposition calculus each boolean algebra deene the truth by its greatest element. In the equational logic the equality between the algebra elements deene the truth. In the clause Horn logic the truth is given by the interpretation of the predicats in the model. We give a categorial framework for these logics and w...

We study two alternative bases for Belnap’s four-valued logic and provide complete equational axiomatizations for them. One is called conditional composition logic. It has a single, ternary if-then-else connective with a sequential, operational reading, and four constants for the truth values. The other logic is called guard logic. The main motivation for this logic lies in its technical proper...

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...

Presented is a completeness theorem for fuzzy equational logic with truth values in a complete residuated lattice: Given a fuzzy set Σ of identities and an identity p ≈ q, the degree to which p ≈ q syntactically follows (is provable) from Σ equals the degree to which p ≈ q semantically follows from Σ. Pavelka style generalization of well-known Birkhoff’s theorem is therefore established.

A solution to the problem of speciicity in a resource{oriented deductive approach to actions and change is presented. Speciicity 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 speciicity culminating in a completed equational logic program with ...

Introducing equality into standard Horn clauses leads to a programming paradigm known as Equational Logic Programming. We propose here a scheme for the evaluation of such equational logic programs combining two powerful operational techniques : directed narrowing for the equational part and linear completion for the logical part. Thus we provide a goal-oriented solving procedure, keeping the we...

Recently three approaches for solving planning problems deductively were proposed each of which does not require to state frame axioms explicitly. These approaches are based on the linear connection method, an equational logic programming language, and on linear logic. In this paper, we briefly review these approaches and show that they are equivalent. Moreover, we illustrate that these approac...

How can algebraic and coalgebraic specifications be integrated? How can behavioral equivalence be addressed in an algebraic specification language? The hidden-sorted approach, originating in work of Goguen and Meseguer in the early 80’s, and further developed into the hidden-sorted logic approach by researchers at Oxford, UC San Diego, and Kanazawa offers some attractive answers, and has been i...

This paper concerns the relation between process algebra and Hoare logic. We investigate question whether how a logic can be used for reasoning about data change in course of when equationally that process. introduce an extension ACP (Algebra Communicating Processes) with features are relevant to processes which involved, present considered this algebra, discuss use as complement pure equationa...