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Densification of FL Chains via Residuated Frames
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SYSNO ASEP 0438994 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Densification of FL Chains via Residuated Frames Author(s) Baldi, Paolo (UIVT-O) ORCID, RID
Terui, K. (JP)Source Title Algebra Universalis. - : Springer - ISSN 0002-5240
Roč. 75, č. 2 (2016), s. 169-195Number of pages 27 s. Language eng - English Country CH - Switzerland Keywords densifiability ; standard completeness ; residuated lattices ; residuated frames ; fuzzy logic Subject RIV BA - General Mathematics R&D Projects GAP202/10/1826 GA ČR - Czech Science Foundation (CSF) UT WOS 000375423100003 EID SCOPUS 84957958237 DOI 10.1007/s00012-016-0372-5 Annotation We introduce a systematic method for densification, i.e., embedding a given chain into a dense one preserving certain identities, in the framework of FL algebras (pointed residuated lattices). Our method, based on residuated frames, offers a uniform proof for many of the known densification and standard completeness results in the literature. We propose a syntactic criterion for densification, called semi-anchoredness. We then prove that the semilinear varieties of integral FL algebras defined by semi-anchored equations admit densification, so that the corresponding fuzzy logics are standard complete. Our method also applies to (possibly non-integral) commutative FL chains. We prove that the semilinear varieties of commutative FL algebras defined by knotted axioms x^m<=x^n (with m, n > 1) admit densification. It provides a purely algebraic proof to the standard completeness of uninorm logic as well as its extensions by knotted axioms. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2017
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