Uninorm logic: toward a fuzzy-relevance logic(2)
0
조회
0
다운로드
3
인용
0
참고문헌
키워드
초록
This paper first investigates several uninorm logics (introduced by Metcalfe and Montagna in [8]) as fuzzy-relevance logics. We first show that the uninorm logic UL and its extensions IUL, UML, and IUML are fuzzy-relevant; fuzzy in Cintula´s sense, i.e., the logic L is complete with respect to linearly ordered L-matrices; and relevant in the weak sense that φ→ψ is a theorem only if either (i) φ and ψ share a sentential variable or constant, or (ii) both ∼φ and ψ are theorems. We next expand these systems to those with △.
Abstract
This paper first investigates several uninorm logics (introduced by Metcalfe and Montagna in [8]) as fuzzy-relevance logics. We first show that the uninorm logic UL and its extensions IUL, UML, and IUML are fuzzy-relevant; fuzzy in Cintula´s sense, i.e., the logic L is complete with respect to linearly ordered L-matrices; and relevant in the weak sense that φ→ψ is a theorem only if either (i) φ and ψ share a sentential variable or constant, or (ii) both ∼φ and ψ are theorems. We next expand these systems to those with △.
참고문헌 (10)
- Anderson, A. R., "The pure calculus of entailment", The Journal of symbolic Logic, 27, pp.19~52 (1962)
- Cintula, P, "Weakly Implicative (Fuzzy) Logics I: Basic properties" (2006), Archive for Mathematical Logic
- Dunn, J. M, "Algebraic Completeness for R-Mingle and Its Extension", Journal of symbolic Logic, 35, pp.1~13 (1970)
- Esteva, F., "Monoidal t-norm based logic: towards a logic for left-continous t-norms", Fuzzy Sets and Systems, 124, pp.271~288 (2001)
- Esteva, F., "Residuated fuzzy logics with an involutive logics", Archive for Mathematical Logic, 39, pp.103~124 (2000)
- H?ek, P, "Metamathematics of Fuzzy Logic, Amsterdam, Kluwer", ~ (1998)
- Hohle, U, "Commutative, residuated l-monoids”, U. Hohle and E. P. Klement (eds.), Non-Classical Logics and Their Applications to Fuzzy Subsets, Amsterdam, Kluwer", 53~106 (1995)
- Metcalfe, G., "Substructural Fuzzy Logics", Journal of Symbolic Logic to appear (2007)
- Meyer, R. K., Dunn, J. M., and Leblanc, H, "Completeness of relevant quantification theories", Notre Dame Journal of Formal Logic, 15, pp.97~121 (1976)
- 양은석, "(weak) R-mingle: toward a fuzzy-relevance logic", 논리연구, 10(2), pp.125~146 (2007), 한국논리학회