UDC 681.61
1 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
 yu1953@ukr.net
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PROOF OF THEOREMS IN FUZZY LOGIC ON THE BASIS OF STRUCTURAL RESOLUTION
Abstract. The author considers the approach to proof of theorems with fuzzy and not quite true argumentation.
In this approach, the Zadeh composition rule of correctness is used as a rule of evidence, and its procedural implementation
is carried out by refutation mechanism. As such a mechanism, a structural resolution (S -resolution) is proposed,
which is a generalization of the principle of resolutions to fuzzy statements. S -resolution is based on semantic indices of letters and their similarity.
Semantic indices are a key point of S -resolution. They contain information that is used as a control for the derivation process.
And similarity implies finding letters to get S -resolvent. Combining the Zadeh compositional derivation rule and S -resolution allows,
on the one hand, solving the problem of correctness of resolvents in fuzzy logic, and on the other hand, ensuring the regularity
of the proof process in both two-valued and fuzzy logic.
Keywords: automatic proof of theorems, fuzzy theorem, principle of resolutions, fuzzy logic, approximate reasoning, generalized rule of modus ponens, composition rule, fuzzy predicates, fuzzy and linguistic variables.
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