Kripke semantics, undecidability and standard completeness for Esteva and Godo's logic MTL∀

Studia Logica

Volumn 71, Issue 2, 2002, Pages 227-245

  Montagna, Franco ^a   Ono, Hiroakira ^b  

^a UNIVERSITY OF SIENA   (Italy)

^b JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY   (Japan)

Author keywords

Kripke semantics; Left continuous t norms; Logics without contraction; Many valued logics

Indexed keywords

EID: 0042905373     PISSN: 00393215     EISSN: 15728730     Source Type: Journal    
DOI: 10.1023/A:1016500922708     Document Type: Article

References (21)

1. R. CIGNOLI, F. ESTEVA, L. GODO and A. TORRENS, 'Basic fuzzy logic is the logic of continuous t-norms and their residua', Soft Computing 4 (2000) 106-112.
2. R. CIGNOLI, D. MUNDICI and I. M. L. D'OTTAVIANO, Algebraic Foundations of Many-Valued Reasoning, Kluwer 2000.
3. K. DOŠEN, 'Sequent systems and groupoid models I', Studia Logica XLVII (1988) 353-385.
4. K. DOŠEN, 'Sequent systems and groupoid models II', Studia Logica XLVIII (1989) 41-65.
5. F. ESTEVA and L. GODO, 'Monoidal t-norm based logic: towards a logic for left-continuous t-norms', Fuzzy Sets and Systems 114 (2001), 271-288.
6. F. ESTEVA, L. GODO, J. GISPERT and F. MONTAGNA, 'On the standard and rational completeness of some axiomatic extensions of the monoidal t-norm logic', Studia Logica, this volume, 393-420.
7. P. HÁJEK, Metamathematics of Fuzzy Logic, Kluwer, 1998.
8. P. HÁJEK, 'Fuzzy logic and arithmetical hierarchy III', Studia Logica 68, 1 (2001), 129-142.
9. S. JENEI and F. MONTAGNA, 'A proof of standard completeness for Esteva's and Godo's logic MTL', Studia Logica 70, 2 (2002), 183-192.
10. E. KIRIYAMA and H. ONO, 'The contraction rule and decision problems for logics without structural rules', Studia Logica L, 2 (1991), 299-319.
11. E. P. KLEMENT, R. MESIAR and E. PAP, Triangular Norms, Kluwer Academic Publishers, Dordrecht (2000).
12. Y. KOMORI, 'Pedicate logics without the structure rules', Studia Logica 45 (1986), 393-404.
13. J. LAMBEK, 'The mathematics of sentence structure', American Mathematical Monthly 12 (1958), 166-178.
14. F. MONTAGNA, 'Three complexity problems in predicate fuzzy logic', Studia Logica 68, 1 (2001), 143-152.
15. H. ONO, 'Semantical analysis of predicate logics without the contraction rule', Studia Logica 44, 2 (1985), 187-196.
16. H. ONO, 'Structural rules and a logical hierarchy', in: Mathematical Logic, Proceedings of the Summer School and Conference on Mathematical Logic, Heyting'88, P.P. Petkov (ed.), Plenum Press, 1990, pp. 95-104.
17. H. ONO, 'Semantics for substructural logics', in: Sub structural Logics, eds. by K. Došen and P. Schroeder-Heister, Oxford University Press, 1993, pp. 259-291.
18. H. ONO, 'Logics without the contraction rule and residuated lattices I', Festschrift on the occasion of R. K. Meyer's 65th birthday (forthcoming).
19. H. ONO and Y. KOMORI, 'Logics without the contraction rule', Journal of Symbolic Logic 50 (1985), 169-201.
20. M. E. RAGAZ, Arithmetische Klassification von Formelnmenge der unendlichwertigen Logik, ETH Zürich, (1981) Thesis.
21. A. S. TROELSTRA and D. VAN DALEN, Constructivism in Mathematics. An Introduction vol.II, Studies in Logic and the Foundations of Mathematics, vol. 123, North-Holland, 1988.