0491819 20240103220301.820180727235959.9 85049671436 000461580400009 10.1007/s00500-018-3369-5 9 s. P cav_un_epca*02583681432-7643237 (2019)2233-2241Springer Modal many-valued logics Mathematical fuzzy logic Neighborhood frames Kripke semantics General frames cav_un_auth*0100737 Cintula Petr UIVT-O Oddělení teoretické informatiky Department of Theoretical Computer Science Department of Theoretical Computer Science Ústav informatiky AV ČR, v. v. i. cav_un_auth*0362702 Menchón P. AR cav_un_auth*0293476 Noguera Carles UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory K Ústav teorie informace a automatizace AV ČR, v. v. i. http://dx.doi.org/10.1007/s00500-018-3369-5 cav_un_auth*0349495 GA17-04630S GA ČR Frame semantics, given by Kripke or neighborhood frames, do not give completeness theorems for all modal logics extending, respectively, K and E. Such shortcoming can be overcome by means of general frames, i.e., frames equipped with a collection of admissible sets of worlds (which is the range of possible valuations over such frame). We export this approach from the classical paradigm to modal many-valued logics by defining general A-frames over a given residuated lattice AA (i.e., the usual frames with a collection of admissible A-valued sets). We describe in detail the relation between general Kripke and neighborhood A-frames and prove that, if the logic of A is finitary, all extensions of the corresponding logic E of A are complete w.r.t. general neighborhood frames. Our work provides a new approach to the current research trend of generalizing relational semantics for non-classical modal logics to circumvent axiomatization problems. BA 10000 10200 10201 2020 UTIA-B 10000 10100 10101 4 A O 4a 4o 4a 20231122143315.9 RVO:67985807 RVO:67985556 http://hdl.handle.net/11104/0285436 S 1* Article Biochemistry Molecular Biology|Chemistry Multidisciplinary C COMPUTERSCIENCE.INTERDISCIPLINARYAPPLICATIONS|COMPUTERSCIENCE.ARTIFICIALINTELLIGENCE 2.988 1.125 3 0.01198 0.499 8859 120 0.705 40.95 3.41 5282 Q2 2.638 893 Q2 32.106 63.5 Q3 Q4 0.87 Q2 63.761 2019 Soubory v repozitáři: 0491819a2.pdf, a0491819prep.pdf, a0491819.pdf 85049671436 SCOPUS PUBMED 000461580400009 WOS cav_un_epca*0258368 Soft Computing 1432-7643 1433-7479 Roč. 23 č. 7 2019 2233 2241 Springer