Fuzzy Horn logic I |
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Authors: | Radim Bělohlávek Vilém Vychodil |
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Institution: | (1) Deptartment of Computer Science, Palacky University, Tomkova 40, 77900 Olomouc, Czech Republic |
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Abstract: | The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of
fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises
weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability
of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style
completeness theorem (degree of provability equals degree of truth) from which we get some particular cases by imposing restrictions
on the formulas under consideration. As a particular case, we obtain completeness of fuzzy equational logic. |
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Keywords: | Fuzzy logic Equational logic Horn logic Implication Degree of provability |
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