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Skolemization and Herbrand theorems for lattice-valued logics
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SYSNO ASEP 0501613 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Skolemization and Herbrand theorems for lattice-valued logics Tvůrce(i) Cintula, Petr (UIVT-O) RID, ORCID, SAI
Diaconescu, D. (RO)
Metcalfe, G. (CH)Zdroj.dok. Theoretical Computer Science. - : Elsevier - ISSN 0304-3975
Roč. 768, 10 May (2019), s. 54-75Poč.str. 22 s. Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova Skolemization ; Herbrand theorems ; Non-classical logics ; Lattices 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 000466456500003 EID SCOPUS 85061573241 DOI 10.1016/j.tcs.2019.02.007 Anotace Skolemization and Herbrand theorems are obtained for first-order logics based on algebras with a complete lattice reduct and operations that are monotone or antitone in each argument. These lattice-valued logics, defined as consequence relations on inequations between formulas, typically lack properties underlying automated reasoning in classical first-order logic such as prenexation, deduction theorems, or reductions from consequence to satisfiability. Skolemization and Herbrand theorems for the logics therefore take various forms, applying to the left or right of consequences, and restricted classes of inequations. In particular, in the presence of certain witnessing conditions, they admit sound “parallel” Skolemization procedures where a strong quantifier is removed by introducing a finite disjunction or conjunction of formulas with new function symbols. A general expansion lemma is also established that reduces consequence in a lattice-valued logic between inequations containing only strong occurrences of quantifiers on the left and weak occurrences on the right to consequence between inequations in the corresponding propositional logic. If propositional consequence is finitary, this lemma yields a Herbrand theorem for the logic. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2020 Elektronická adresa http://dx.doi.org/10.1016/j.tcs.2019.02.007
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