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On Product Logic with Truth-Constants
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SYSNO ASEP 0045161 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On Product Logic with Truth-Constants Title O produktové logice s pravdivostními konstantami Author(s) Savický, Petr (UIVT-O) SAI, RID, ORCID
Cignoli, R. (AR)
Esteva, F. (ES)
Godo, L. (ES)
Noguera, C. (ES)Source Title Journal of Logic and Computation - ISSN 0955-792X
Roč. 16, č. 2 (2006), s. 205-225Number of pages 21 s. Language eng - English Country GB - United Kingdom Keywords non-classical logic ; fuzzy logic ; product logic ; truth-constants ; standard completeness Subject RIV BA - General Mathematics R&D Projects 1M0545 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) UT WOS 000236613800004 EID SCOPUS 33645746903 DOI 10.1093/logcom/exi075 Annotation Product Logic is an axiomatic extension of Hájek's Basic Fuzzy Logic BL coping with the 1-tautologies when the strong conjunction and implication are interpreted by the product of reals in [0, 1] and its residuum respectively. In this paper we investigate expansions of Product Logic by adding into the language a countable set of truth-constants, for example one truth-constant for each rational number in [0, 1], and by adding the corresponding book-keeping axioms for the truth-constants. We first show that the corresponding logics are algebraizable, and hence complete with respect to the variety of corresponding algebras. The main result of the paper is the canonical standard completeness of these logics, that is, theorems of them are exactly the 1-tautologies of the algebra defined over the real unit interval where the truth-constants are interpreted as their own values. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2007
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