Abstract
We explore the basic fuzzy logic BL as well as propositional fuzzy logics with modalities □ and ◊ and a total accessibility relation. Formulations and proofs are given to replacement theorems for BL. A basic calculus of modal fuzzy logic is introduced. For this calculus and its extensions, we prove replacement and deduction theorems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic Publ., Dordrecht (1998).
M. Baaz and H. Veith, “Quantifier elimination in fuzzy logic,” in Computer Science Logic, Proc. 12th Int. Workshop, CSL’98, Lect. Notes Comp. Sc., Vol. 1584, Springer-Verlag, Berlin (1999), pp. 399–414.
M. Baaz and H. Veith, “Interpolation in fuzzy logic,” Arch. Math. Log., 38, No. 7, 461–489 (1999).
O. V. Zeevald, “Fuzzy logics and ω +-valued logic,” Vestnik NGU, Mat., Mekh., Inf., 4, Nos. 3/4, 33–44 (2004).
Author information
Authors and Affiliations
Additional information
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools, project NSh-4787.2006.1.
__________
Translated from Algebra i Logika, Vol. 45, No. 6, pp. 731–757, November–December, 2006.
Rights and permissions
About this article
Cite this article
Zeevald, O.V. Fuzzy logics with modalities. Algebr Logic 45, 415–430 (2006). https://doi.org/10.1007/s10469-006-0038-z
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10469-006-0038-z