Algebraic Kripke-style Semantics for an Extension of HpsUL, CnHpsUL
1
조회
0
다운로드
3
인용
0
참고문헌
키워드
초록
This paper deals with Kripke-style semantics for weakening-free non-commutative fuzzy logics. As an example, we consider an algebraic Kripke-style semantics for an extension of the pseudo-uninorm based fuzzy logic HpsUL, CnHpsUL*. For this, first, we recall the system CnHpsUL*, define its corresponding algebraic structures CnHpsUL*-algebras, and algebraic completeness results for it. We next introduce a Kripke-style semantics for CnHpsUL*, and connect it with algebraic semantics.
Abstract
This paper deals with Kripke-style semantics for weakening-free non-commutative fuzzy logics. As an example, we consider an algebraic Kripke-style semantics for an extension of the pseudo-uninorm based fuzzy logic HpsUL, CnHpsUL*. For this, first, we recall the system CnHpsUL*, define its corresponding algebraic structures CnHpsUL*-algebras, and algebraic completeness results for it. We next introduce a Kripke-style semantics for CnHpsUL*, and connect it with algebraic semantics.
참고문헌 (27)
- Běhounek, L., "Fuzzy logics as the logics of chains", Fuzzy Sets and Systems, 157, pp.604~610 (2006)
- Cintula, P., "Weakly Implicative(Fuzzy)Logics I : Basic properties", Archive for Mathematical Logic, 45, pp.673~704 (2006)
- Cintula, P., "Non-associative substructural logics and their semilinear extensions : axiomatization and completeness properties", Review of Symbolic Logic, 6, pp.394~423 (2013)
- Cintula, P., "Petr Hájek on Mathematical Fuzzy Logic", pp.245~290 (2015), Springer
- Cintula, P., "Handbook of Mathematical Fuzzy Logic, 1", pp.103~207 (2011), College publications
- Diaconescu, D., "Kripke-style semantics for non-commutative monoidal t-norm logic", Journal of Multiple-Valued Logic and Soft Computing, 16, pp.247~263 (2010)
- Diaconescu, D., "On the forcing semantics for monoidal t-norm based logic", Journal of Universal Computer Science, 13, pp.1550~1572 (2007)
- Dunn, J. M., "A Kripke-style semantics for R-Mingle using a binary accessibility relation", Studia Logica, 35, pp.163~172 (1976)
- Dunn, J. M., "Partiality and its Dual", Studia Logica, 66, pp.5~40 (2000)
- Esteva, F., "Monoidal t-norm based logic : towards a logic for left-continuous t-norms", Fuzzy Sets and Systems, 124, pp.271~288 (2001)
- Galatos, N., "Residuated lattices : an algebraic glimpse at substructural logics" (2007), Elsevier
- Hájek, P., "Fuzzy logics with noncommutative conjunction", Journal of Logic and Computation, 13, pp.469~479 (2003)
- Hájek, P., "Observations on non-commutative fuzzy logic", Soft Computing, 8, pp.38~43 (2003)
- Metcalfe, G., "Substructural Fuzzy Logics", Journal of Symbolic Logic, 72, pp.834~864 (2007)
- Metcalfe, G., "Proof Theory for Fuzzy Logics" (2009), Springer
- Montagna, F., "Kripke semantics, undecidability and standard completeness for Esteva and Godo's Logic MTL∀", Studia Logica, 71, pp.227~245 (2002)
- Montagna, F., "Kripke-style semantics for many-valued logics", Mathematical Logic Quaterly, 49, pp.629~641 (2003)
- Montagna, F., "Corrigendum to “Kripke-style semantics for many-valued logics", Mathematical Logic Quaterly, 50, pp.104~107 (2004)
- Thomason, R. H., "A semantic study of constructive falsity", Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 15, pp.247~257 (1969)
- Tsinakis, C., "The structure of residuated lattices", International Journal of Algebra and Computation, 13, pp.437~461 (2003)
- Wang, S., "Logics for residuated pseudo-uninorms and their residua", Fuzzy Sets and Systems, 218, pp.24~31 (2013)
- Wang, S., "HpsUL is not the logic of pseudo-uninorms and their residua", Logic Journal of the IGPL, 17, pp.413~419 (2009)
- Yang, E., "(Star-based) four-valued Kripke-style Semantics for some neighbors of E, R, T", Logique et Analyse, 207, pp.255~280 (2009)
- 양은석, "Kripke-style Semantics for UL", 논리연구, 15(1), pp.1~15 (2012), 한국논리학회
- Yang, E., "(Star-based)three-valued Kripke-style semantics for pseudo-and weak-Boolean logics", Logic Journal of the IGPL, 20, pp.187~206 (2012)
- 양은석, "Algebraic Kripke-style semantics for weakening-free fuzzy logics", 논리연구, 17(1), pp.181~195 (2014), 한국논리학회
- Yang, E., "Algebraic Kripke-style semantics for relevance logics", Journal of Philosophical Logic, 43, pp.803~826 (2014)
