Skolemization and Herbrand theorems for lattice-valued logics

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F19%3A00501613" target="_blank" >RIV/67985807:_____/19:00501613 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.tcs.2019.02.007" target="_blank" >http://dx.doi.org/10.1016/j.tcs.2019.02.007</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2019.02.007" target="_blank" >10.1016/j.tcs.2019.02.007</a>

Result language
angličtina
Original language name
Skolemization and Herbrand theorems for lattice-valued logics
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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