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Enriched interval bilattices and partial many-valued logics: an approach to deal with graded truth and imprecision. (English) Zbl 1232.03013

Summary: Within the many-valued approach for approximate reasoning, the aim of this paper is twofold. First, to extend truth-value 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 we prove their equivalence for a family of formulas, including the so-called free well-formed formulas.

MSC:

03B50 Many-valued logic
03B52 Fuzzy logic; logic of vagueness
03G10 Logical aspects of lattices and related structures
68T30 Knowledge representation
68T37 Reasoning under uncertainty in the context of artificial intelligence
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