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Algebraic Kripke-Style Semantics for Weakly Associative Fuzzy Logics  

Yang, Eunsuk (Department of Philosophy & Institute of Critical Thinking and Writing, Chonbuk National University)
Publication Information
Korean Journal of Logic / v.21, no.2, 2018 , pp. 155-174 More about this Journal
Abstract
This paper deals with Kripke-style semantics, which will be called algebraic Kripke-style semantics, for weakly associative fuzzy logics. First, we recall algebraic semantics for weakly associative logics. W next introduce algebraic Kripke-style semantics, and also connect them with algebraic semantics.
Keywords
(Algebraic) Kripke-style semantics; weakening-free fuzzy logic; weak associativity; algebraic semantics; substructural logic;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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1 Cintula, P., Horcik, R., and Noguera, C. (2013), "Non-associative substructural logics and their semilinear extensions: axiomatization and completeness properties", Review of Symbol. Logic, 12, pp. 394-423.
2 Cintula, P., Horcik, R., and Noguera, C. (2015), "The quest for the basic fuzzy logic", Mathematical Fuzzy Logic, P. Hajek (Ed.), Springer.
3 Cintula, P. and Noguera, C. (2011), A general framework for mathematical fuzzy logic, Handbook of Mathematical Fuzzy Logic, vol 1, P. Cintula, P. Hajek, and C. Noguera (Eds.), London, College publications, pp. 103-207.
4 Galatos, N., Jipsen, P., Kowalski, T., and Ono, H. (2007), Residuated lattices: an algebraic glimpse at substructural logics, Amsterdam, Elsevier.
5 Horcik, R. (2011), Algebraic semantics: semilinear FL-algebras, Handbook of Mathematical Fuzzy Logic, vol 1, P. Cintula, P. Hajek, and C. Noguera (Eds.), London, College publications, pp. 283-353.
6 Kripke, S. (1963). "Semantic analysis of modal logic I: normal modal propositional calculi", Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9, pp. 67-96.   DOI
7 Kripke, S. (1965a) "Semantic analysis of intuitionistic logic I", in J. Crossley and M. Dummett (eds.) Formal systems and Recursive Functions, Amsterdam: North-Holland Publ Co, pp. 92-129.
8 Kripke, S. (1965b) "Semantic analysis of modal logic II", in J. Addison, L. Henkin, and A. Tarski (eds.) The theory of models, Amsterdam: North-Holland Publ Co, pp. 206-220.
9 Montagna, F. and Ono, H. (2002) "Kripke semantics, undecidability and standard completeness for Esteva and Godo's Logic MTL${\forall}$", Studia Logica, 71, pp. 227-245.   DOI
10 Montagna, F. and Sacchetti, L. (2003) "Kripke-style semantics for many-valued logics", Mathematical Logic Quaterly, 49, pp. 629-641.   DOI
11 Montagna, F. and Sacchetti, L. (2004) "Corrigendum to "Kripke-style semantics for many-valued logics", Mathematical Logic Quaterly, 50, pp. 104-107.   DOI
12 Yang, E. (2009) "Non-associative fuzzy-relevance logics: strong t-associative monoidal uninorm logics", Korean Journal of Logic, 12/1, pp. 89-110.
13 Yang, E. (2012) "Kripke-style semantics for UL", Korean Journal of Logic, 15 (1), pp. 1-15.
14 Yang, E. (2014a) "Algebraic Kripke-style semantics for weakening-free fuzzy logics", Korean Journal of Logic, 17 (1), pp. 181-195.
15 Yang, E. (2014b) "Algebraic Kripke-style semantics for relevance logics", Journal of Philosophical Logic, 43, pp. 803-826.   DOI
16 Yang, E. (2015a) "Weakening-free, non-associative fuzzy logics: micanorm-based logics", Fuzzy Sets and Systems, 276, pp. 43-58.   DOI
17 Yang, E. (2015b) "Some an axiomatic extension of the involutive micanorm logic IMICAL", Korean Journal of Logic, 18/2, pp. 197-215.
18 Yang, E. (2016a) "Algebraic Kripke-style semantics for substructural fuzzy logics", Korean Journal of Logic 19, pp. 295-322.
19 Yang, E. (2016b) "Weakly associative fuzzy logics", Korean Journal of Logic 19, pp. 437-461.
20 Yang, E. (2016c) "Basic substructural core fuzzy logics and their extensions: Mianorm-based logics", Fuzzy Sets and Systems 276, pp. 43-58.
21 Yang, E. (2017a) "Involutive basic substructural core fuzzy logics: Involutive mianorm-based logics", Fuzzy Sets and Systems, 320, pp. 1-16.   DOI
22 Yang, E. (2017b) "Some axiomatic extensions of the involutive mianorm Logic IMIAL", Korean Journal of Logic 20, pp. 295-322.
23 Yang, E. (2017c) "A non-associative generalization of continuous t-norm-based logics", Journal of Intelligent & Fuzzy Systems 33, pp. 3743-3752.   DOI