Multiple-valued Logics Based on Hazy Structures

Author: GHEZELAYAGHE M.¹

Source: Multiple Valued Logic: An International Journal, Volume 8, Numbers 5-6, 1 January 2002 , pp. 659-672(14)

Publisher: Taylor and Francis Ltd

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Abstract:

We will use the notion of neighbourhood-spaces as the ranges of arbitrary hazy structures imposed on the set of truth values in a multiple-valued logic instead of a point-wise truth values. In light of this consideration, we can characterize and modify the indistinguishable formulas of the propositional or first order multiple-valued logics. Thus, any problem in any ordinary m-valued logic, for instance the problem of realizability of a formula <$>varphi<$>, can be reduced to that of a corresponding problem in n-valued logic where m might be a finite or transfinite ordinal number and <$>nle m<$>, that is to say that we can reduce the denumerable or even continuum valued logics to a finite n-valued logic such as Lukasiewicz 3-valued logic. In the final part of the paper we are using neighbourhood (nbd.) system or hazy structures for necessities and possibilities as relevant examples.

Keywords: Neighbourhood space; Hazy structures; Lattice; Fuzzy set

Document Type: Research article

Affiliations: 1: Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, Kerman, Iran

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