Multiple-valued Logics Based on Hazy Structures
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 <$>n\le m<$>, 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.
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