Algebraic Routley-Meyer-style semantics for the involutive monoidal t-norm logic IMTL
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Routley-Meyer-style semantics, called algebraic Routley-Meyer-style semantics, was investigated for the fuzzy logic system MTL. This paper extends this investigation to involutive systems. More precisely, as an example, we consider such semantics for the fuzzy logic system IMTL. First, we recall the involutive monoidal t-norm logic IMTL and its algebraic semantics. We next introduce algebraic Routley-Meyer-style semantics for it and then connect this semantics with algebraic semantics.
Abstract
Routley-Meyer-style semantics, called algebraic Routley-Meyer-style semantics, was investigated for the fuzzy logic system MTL. This paper extends this investigation to involutive systems. More precisely, as an example, we consider such semantics for the fuzzy logic system IMTL. First, we recall the involutive monoidal t-norm logic IMTL and its algebraic semantics. We next introduce algebraic Routley-Meyer-style semantics for it and then connect this semantics with algebraic semantics.
참고문헌 (25)
- Ciabattoni, A, "T-norm-based logics with n-contraction", Special Issue on SOFSEM2002of Neural Network World, 12, pp.453~460 (2002)
- Cintula, P, "Weakly Implicative (Fuzzy) Logics I: Basic properties", Archive for Mathematical Logic, 45, pp.673~704 (2006)
- Diaconescu, D, "On the forcing semantics for monoidal t-norm based logic", Journal of Universal Computer Science, 13, pp.1550~1572 (2007)
- Galatos, N, "Residuated lattices: an algebraic glimpse at substructural logics" (2007), Elsevier
- Hájek, P, "Metamathematics of Fuzzy Logic" (1998), Kluwer
- Jenei, S, "A Proof of Standard completeness for Esteva and Godo's Logic MTL", Studia Logica, 70, pp.183~192 (2002)
- Kripke, S, "Semantic analysis of modal logic I: normal modal propositional calculi", Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 9, pp.67~96 (1963)
- Kripke, S, "Formal systems and Recursive Functions", pp.92~129 (1965), North-Holland Publ Co
- Kripke, S, "The theory of models", pp.206~220 (1965), North-Holland Publ Co
- Montagna, F, "Kripke semantics, undecidability and standard completeness for Esteva and Godo's Logic IMTL", 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)
- Urquhart, A, "Handbook of Philosophical Logic, vol. 3", pp.71~116 (1986), Reidel Publ Co
- Wang, S, "Uninorm logic with the n-potency axiom", Fuzzy Sets and Systems, 205, pp.116~126 (2012)
- Wang, S, "Involutive uninorm logic with the n-potency axiom", Fuzzy Sets and Systems, 218, pp.1~23 (2013)
- 양은석, "Algebraic Kripke-style semantics for weakening-free fuzzy logics", 논리연구, 17(1), pp.181~195 (2014), 한국논리학회[DOI]
- Yang, E, "Algebraic Kripke-style semantics for relevance logics", Journal of Philosophical Logic, 43, pp.803~826 (2014)
- 양은석, "Algebraic Kripke-style Semantics for Three-valued Paraconsistent Logic", 논리연구, 17(3), pp.441~460 (2014), 한국논리학회
- 양은석, "Algebraic Kripke-style semantics for substructural fuzzy logics", 논리연구, 19(2), pp.295~322 (2016), 한국논리학회[DOI]
- 양은석, "Weakly associative fuzzy logics", 논리연구, 19(3), pp.437~461 (2016), 한국논리학회[DOI]
- Yang, E, "Basic substructural core fuzzy logics and their extensions: Mianorm-based logics", Fuzzy Sets and Systems, 276, pp.43~58 (2016)
- 양은석, "Set-theoretic Kripke-style Semantics for Involutive Monoidal T-norm (Based) Logics", 철학사상, pp.79~88 (2017), 철학사상연구소[DOI]
- Yang, E, "A non-associative generalization of continuous t-norm-based logics", Journal of Intelligent & Fuzzy Systems, 33, pp.3743~3752 (2017)
- 양은석, "Algebraic Routley-Meyer-style semantics for the fuzzy logic MTL", 논리연구, 21(3), pp.353~371 (2018), 한국논리학회[DOI]
- Yang, E, "Mianorm-based logics with n-contraction and n-mingle axioms", Journal of Intelligent & Fuzzy Systems, 37, pp.7895~7907 (2019)
