ENRICHED INTERVAL BILATTICES AND PARTIAL MANY-VALUED LOGICS: AN APPROACH TO DEAL WITH GRADED TRUTH AND IMPRECISION

Author:

ESTEVA FRANCESC1,GARCIA-CALVÉS PERE1,GODO LLUÍS1

Affiliation:

1. Institut d'Investigació en Intel. ligència Artificial, Centre d'Estudis Avançats de Blanes (CSIC), Camí de Sta. Bàrbara s/n, 17300 Blanes, Girona, Spain

Abstract

Within the many-valued approach for approximate reasoning, the aim of this paper is two-fold. First, to extend truth-values lattices to cope with the imprecision due to possible incompleteness of the available information. This is done by considering two bilattices of truth-value intervals corresponding to the so-called weak and strong truth orderings. Based on the use of interval bilattices, the second aim is to introduce what we call partial many-valued logics. The (partial) models of such logics may assign intervals of truth-values to formulas, and so they stand for representations of incomplete states of knowledge. Finally, the relation between partial and complete semantical entailment is studied, and it is provedtheir equivalence for a family of formulas, including the so-called free well formed formulas.

Publisher

World Scientific Pub Co Pte Lt

Subject

Artificial Intelligence,Information Systems,Control and Systems Engineering,Software

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