Cybernetics and Systems Analysis

, Volume 55, Issue 2, pp 207–219 | Cite as

Proof of Theorems in Fuzzy Logic Based on Structural Resolution

  • Yu. Ya. SamokhvalovEmail author


An approach to proving theorems with fuzzy and not quite true argumentation is considered. Zadeh’s compositional rule of inference is used as the rule of provably correct reasoning, and its procedural implementation is enabled by a refutation mechanism. As such a mechanism, structural resolution (S-resolution) is proposed that 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 essential in S-resolution. They contain data used as control information in the process of inference. And similarity implies finding letters to obtain an S-resolvent. Combining Zadeh’s compositional rule of inference and S-resolution allows, on the one hand, to withdraw the problem of correctness of resolvents in fuzzy logic and, on the other hand, to ensure the regularity of the process of a proof in two-valued and fuzzy logics.


automatic proof of theorems fuzzy theorem principle of resolutions fuzzy logic approximate reasoning generalized rule of modus ponens composition rule fuzzy predicate fuzzy variable linguistic variable 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KyivKyivUkraine

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