Gödel Homomorphisms as Gödel Modal Operators

• Autorzy: Fasching O.
• Języki publikacji: EN

Abstrakty

EN

We extend propositional Gödel logic by a unary modal operator, which we interpret as Gödel homomorphisms, i.e. functions [0, 1] → [0, 1] that distribute over the interpretations of the binary connectives of Gödel logic. We show weak completeness of the propositional fragment w.r.t. a simple superintuitionistic Hilbert-type proof system, and we prove that validity does not change if we use the function class of continuous, strictly increasing functions. We also give proof systems for restrictions to sub- and superdiagonal functions.

Słowa kluczowe

EN

Gödel logic; superintuitionistic logic; modal logic; truth stressers

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2013
• Tom: Vol. 123, nr 1
• Strony: 43--57
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Fasching O.

• Gudrunstrasse 5/1/15, 1110 Vienna, Austria

Bibliografia

• [1] Baaz M., Fasching O.: Gödel logics with monotone operators, Fuzzy Sets and Systems, 197, 2012, 3–13. http://dx.doi.org/10.1016/j.fss.2011.04.012, 2012.
• [2] Baaz M., Fasching O.: Monotone operators on Gödel logic, Archive for Mathematical Logic, accepted.
• [3] Bou F., Esteva F., Godo L., Rodrıguez R. O.: On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice, J. Log. Comput., 21, 2011, 739-790. http://dx.doi.org/10.1093/logcom/exp062.
• [4] Caicedo X., Rodr´ıguez R. O.: Bi-modal Gödel logic over [0,1]-valued Kripke frames. CoRR, abs/1110.2407, 2011. http://arxiv.org/abs/1110.2407.
• [5] Dummett M.: A propositional calculus with denumerable matrix. J. Symbolic Logic, 24, 1959, 97–106. http://www.jstor.org/stable/2964753.
• [6] Esteva F.; Godo L.; Noguera C.: Fuzzy logics with truth hedges revisited. 7th Conference of the European Society of Fuzzy Logic and Technology, EUSFLAT - LFA 2011, Atlantis Press, Aix-Les-Bains, 2011, 146–152.
• [7] Fasching O.: Operator extensions of Gödel logics, PhD thesis, Vienna University of Technology, http://permalink.obvsg.at/AC07810559, 2011.
• [8] Hájek P.: On very true. Fuzzy sets and systems, 124, 2001, 329–333. http://www.sciencedirect.com/science/article/pii/S0165011401001038.