@MISC{Hajek96basicfuzzy, author = {Petr Hajek}, title = {Basic fuzzy logic and BL-algebras}, year = {1996} }

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Abstract

The relation of the basic fuzzy logic BL to continuous t-norms is studied and two additional axioms are formulated such that the extended logic is complete with respect to tautologies over all logics given by continuous t-norms. Keywords Basic fuzzy logic, continuous t-norms, residuated lattices. 0.1 Introduction. Basic fuzzy logic BL, as developed and investigated in [3], is closely related to continuous t-norms; as summarized bellow, each continuous t-norm determines (1) a semantics of fuzzy propositional logic for which BL is sound, and (2) a particular linearly ordered BL-algebra, BL-algebras from a variety for which BL is sound and complete. Full treatment is found in [3]; bellow we summarize basic facts in Sections 1 - 3. At the end of Sect. 3 we formulate the main problem of completeness of BL with respect to BL-algebras given by continuous t-norms (t-algebras). In Sect. 4 we develop some algebra of linearly ordered BL-algebras. In Sect. 5 we exhibit two additional axioms (B...