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Implicit Definability of Truth Constants in Łukasiewicz Logic
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SYSNO ASEP 0503661 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Implicit Definability of Truth Constants in Łukasiewicz Logic Tvůrce(i) Haniková, Zuzana (UIVT-O) SAI, RID, ORCID Zdroj.dok. Soft Computing. - : Springer - ISSN 1432-7643
Roč. 23, č. 7 (2019), s. 2279-2287Poč.str. 9 s. Jazyk dok. eng - angličtina Země vyd. DE - Německo Klíč. slova propositional logic ; fuzzy logic ; Łukasiewicz Logic ; rational truth constants ; implicit definability ; computational complexity Vědní obor RIV BA - Obecná matematika Obor OECD Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) CEP GBP202/12/G061 GA ČR - Grantová agentura ČR Způsob publikování Omezený přístup Institucionální podpora UIVT-O - RVO:67985807 UT WOS 000461580400013 EID SCOPUS 85053265965 DOI 10.1007/s00500-018-3461-x Anotace In the framework of propositional Łukasiewicz logic, a suitable notion of implicit definability, tailored to the intended real-valued semantics and referring to the elements of its domain, is introduced. Several variants of implicitly defining each of the rational elements in the standard semantics are explored, and based on that, a faithful interpretation of theories in Rational Pavelka logic in theories in Łukasiewicz logic is obtained. Some of these results were already presented in Hájek (Metamathematics of fuzzy logic, 1998) as technical statements. A connection to the lack of (deductive) Beth property in Łukasiewicz logic is drawn. Moreover, while irrational elements of the standard semantics are not implicitly definable by finitary means, a parallel development is possible for them in infinitary Łukasiewicz logic. As an application of definability of the rationals, it is shown how computational complexity results for Rational Pavelka logic can be obtained from analogous results for Łukasiewicz logic. The complexity of the definability notion itself is studied as well. Finally, we review the import of these results for the precision/vagueness discussion for fuzzy logic, and for the general standing of truth constants in Łukasiewicz logic. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2020 Elektronická adresa http://dx.doi.org/10.1007/s00500-018-3461-x
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