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(weak) R-mingle: toward a fuzzy-relevance logic
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This paper investigates the relevance system R-mingle (RM) as a fuzzy-relevance logic. It shows that RM is fuzzy in Cintula's sense, i.e., RM is complete with respect to linearly ordered L-matrices (or L-algebras). More exactly, we first introduce RM and its weak versions wwRM and wRM. We next provide algebraic and matrix completeness results for them.
Abstract
This paper investigates the relevance system R-mingle (RM) as a fuzzy-relevance logic. It shows that RM is fuzzy in Cintula's sense, i.e., RM is complete with respect to linearly ordered L-matrices (or L-algebras). More exactly, we first introduce RM and its weak versions wwRM and wRM. We next provide algebraic and matrix completeness results for them.
참고문헌 (8)
- 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", Archive for Mathematical Logic (2006), Archive for Mathematical Logic
- Dunn, J. M, "Algebraic Completeness for R-Mingle and Its Extension", Journal of symbolic Logic, 35, pp.13~13 (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)
- Hájek, P.(, "Metamathematics of Fuzzy Logic" (1998), Amsterdam, Kluwer
- Höhle, U, "Commutative, residuated l-monoids (Non-Classical Logics and Their Applications to Fuzzy Subsets)", pp.53~106 (1995), Amsterdam, Kluwer
- Meyer, R. K, "Completeness of relevant quantification theories", Notre Dame Journal of Formal Logic, 15, pp.97~121 (1976)
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