We present the theoretical foundations of the many-valued generalization of a technique for simplifying large non-clausal formulas in propositional logic, that is called removal of anti-links. Possible applications of anti-links include computation of prime implicates of large non-clausal formulas as required, for example, in diagnosis. Anti-links do not compute any normal form of a given formu...

It is well known that the standard 3-valued logic programs with constraints can be inconsistent. Because of that we can not use it for a data integration where mutually inconsistent information comes from different data sources. We argue that a natural way to answer to this challenge, without collapsing all sentences into inconsistency, is by passing to 4-valued bilattice-based logic (with logi...

By interpreting ‘p is impossible’ by ‘p is selfcontradictory’, and ‘p is always’ by ‘not p is self-contradictory’, this paper studies which of the three-valued systems of Łucasiewicz, Gödel, Kleene, Bochvar, and Post, do verify the Aristotle’s principles of Non-Contradiction (NC), and Excluded-Middle (EM). Keywords— Systems of three-valued logic, Non-Contradiction, Excluded-Middle.

In this paper von Wright’s truth-logic T′′ is considered. It seems that it is a De Morgan four-valued logic DM4 (or Belnap’s four-valued logic) with endomorphism e2. In connection with this many other issues are discussed: twin truth operators, a truth-logic with endomorphism g (or logic Tr), the lattice of extensions of DM4, modal logic V2, Craig interpolation property, von Wright–Segerberg’s ...

This paper presents an experiment with human subjects concerning the vague spatial relation ‘near’ in environmental space. After the topic is introduced and relevant previous work surveyed, the experiment is described. Three approaches to experimental analysis are presented and discussed: nearness neighbourhoods as regions with broad boundaries, fuzzy nearness and distance measures, and four-va...

| In this paper, we will present a framework for reasoning with vague and uncertain information by fuzzy truth-valued logics. It is shown that possibilistic logic, many-valued logic, and approximate reasoning can all be embodied in the uniform framework.

In this paper, we continue to explore many-valued disjunctive logic programs with probabilistic semantics. In particular, we newly introduce the least model state semantics for such programs. We show that many-valued disjunctive logic programs under the semantics of minimal models, perfect models, stable models, and least model states can be unfolded to equivalent classical disjunctive logic pr...

Kleene’s strong three-valued logic extends naturally to a four-valued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it four-valued analogs of Kleene’s weak three-valued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bi...