Archive for Mathematical Logic

, Volume 45, Issue 1, pp 3–51 | Cite as

Fuzzy Horn logic I

  • Radim Bělohlávek
  • Vilém Vychodil


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.

Key words or phrases

Fuzzy logic Equational logic Horn logic Implication Degree of provability 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Deptartment of Computer SciencePalacký UniversityOlomoucCzech Republic

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