. "V\u00FDsledky studia Hornovy logiky."@cs . . . "49"^^ . "Fuzzy Hornova logika I: d\u016Fkaz teorie"@cs . "B\u011Blohl\u00E1vek, Radim" . . . "RIV/61989592:15310/06:00002566" . "Vychodil, Vil\u00E9m" . "Fuzzy Horn logic I: proof theory"@en . "Archive for Mathematical Logic" . "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."@en . "0933-5846" . "1" . . . . "Fuzzy Horn logic I: proof theory"@en . "Fuzzy Horn logic; proof theory"@en . "2"^^ . "Fuzzy Horn logic I: proof theory" . . "Fuzzy Hornova logika I: d\u016Fkaz teorie"@cs . . "RIV/61989592:15310/06:00002566!RIV07-AV0-15310___" . . "476577" . . "Fuzzy Horn logic I: proof theory" . "2"^^ . "P(KJB1137301), Z(MSM6198959214)" . "15310" . "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." . . "45" . . . "[C17A4F599B1C]" . "DE - Spolkov\u00E1 republika N\u011Bmecko" . "3-51" . . .