Characterization of strongly equivalent logic programs in intermediate logics

Characterization of Strongly Equivalent Logic Programs in Intermediate Logics

Truth Values and Connectives in Some Non-Classical Logics

The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...

Applications of Intuitionistic Logic in Answer Set Programming

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove properties of answer sets. A character...

On the Propositional SLDNF-Resolution

We consider propositional logic programs with negations. We deene notions of constructive transformation and constructive completion of a program. We use these notions to characterize SLDNF-resolution in classical, intuitionistic and intermediate logics, and also to derive a characterization in modal logics of knowledge. We show that the three-valued and four-valued x-point or declarative seman...

EQ-logics with delta connective

In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...