Abstract
This paper deals with propositional fuzzy modal logic with evaluated syntax based on MV-algebras. We focus on its semantical theory from the viewpoint of Pavelka’s graded semantics of propositional fuzzy logic, investigate the L-tautologies based on different Kripke frames. We also define the notion of L-semantical consequence operation, its some basic properties are obtained. Finally, this paper considers the fuzzy decision implications in propositional fuzzy modal logic with evaluated syntax based on MV-algebras, and presents a kind of semantical characteristics of fuzzy decision implications. Moreover, we introduce the notions of possible and necessary fuzzy decision implication, and their semantical characteristics are presented as well.
Article PDF
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
R. Bělohlávek, M. Chlupová and V. Vychodil, Implications from data with fuzzy attributes, in Proceedings of AISTA 2004, Kirchberg, Luxembourg, November 2004, pp. 5.
R. Bělohlávek, V. Vychodil, Fuzzy attribute logic: syntactic entailment and completeness, in: JCIS 2005, 8th Joint Conference on Information Sciences, Salt Lake City, Utah USA, 2005, 78–81.
R. Bělohlávek, V. Vychodil, Reducing attribute implications from data tables with fuzzy attributes to tables with binary attributes, in: JCIS 2005, 8th Joint Conference on Information Sciences, 2005, 82–85.
R. Bělohlávek, V. Vychodil, Attribute implications in a fuzzy setting, in: ICFCA 2006, 2006, 45–60.
R. Bělohlávek, V. Vychodil, Pavelka-style fuzzy logic for attribute implications, in: JCIS 2006, 2006.
F. Bou, F. Esteva, Exploring a syntactic notion of modal many-valued logics, Mathware & Soft computing, 15(2008) 175–181.
F. Bou, L. Godo, F. Esteva, R.O. Rodriguez, On the minimum many-valued modal logic over a finite residuated lattice, Journal of Logic and Computation, 5(2011) 739–790.
C. C. Chang, Algebraic analysis of many-valued logics, Transactions of the American Mathematical Society, 88(1958) 476–490.
R. L. O. Cignoli, I.M.L. D’Ottaviano, D. Mundici, Algebraic foundations of many-valued reasoning, Kluwer, 2000.
M. C. Fitting, Many-valued modal logics, Fundamenta Informaticae, 15(1992) 235–254.
M. C. Fitting, Many-valued modal logics II, Fundamenta Informaticae, 17(1992) 55–73.
P. Hájek, On fuzzy modal logics S5(C), Fuzzy Sets Syst. 161(2010) 2389–2396.
A.M. Mironov, Fuzzy modal logics, Journal of Mathematical Sciences, 128(2005) 3461–3483.
V. Novák, I. Perfilieva, J. Močkoř, Mathematical principles of fuzzy logic, Kluwer Academic Publishers, Boston, 1999.
V. Novák, Which logic is the real fuzzy logic?, Fuzzy Sets Syst. 157(2006) 635–641.
V. Novák, Fuzzy logic with countable evaluated syntax revisited, Fuzzy Sets Syst. 158(2007) 929–936.
V. Novák, Reasoning about methematical fuzzy logic and its future, Fuzzy Sets Syst. 192(2012) 25–44.
J. Pavelka, On fuzzy logic I: Many-valued rules of inference, II: Enriched residuated lattices and semantics of propositional calculi, III: Semantical Conpleteness of some many-valued propositional calculi. Zeitschr F Math Logik Und Grundlagend Math, 25(1979) 45–52; 119–134; 447–464.
S. Pollandt, Fuzzy Begriffe: Formale Begriffsanalyse von unscharfen Daten, Springer-Verlag, Berlin-Heidelberg, 1997.
K.S. Qu, Y.H. Zhai, J.Y. Liang, M. Chen, Study of decision implications based on formal concept analysis, International Journal of General Systems, 36(2007) 147C–156.
G.J. Wang, MV-algebras, BL-algebras, R0-algebras, and multiple-valued logic, Fuzzy Systems and Mathematics, 16(2002) 1–15.(in Chinese)
Y. Xu, Lattice implication algebras, J. Southwest Jiaotong Univ. 28(1993)20–27.(in Chinese)
Y. Xu, D. Ruan, K.Y. Qin, J. Liu, Lattice-Valued Logic-An Alternative Approach to Treat Fuzziness and Incomparability, Springer-Verlag Berlin Heidelberg New York Press, 2003.
Y.H. Zhai, D.Y. Li, K.S. Qu, Fuzzy decision implications, Knowledge Based Systems, 37(2013) 230–236.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
About this article
Cite this article
Pan, X., Xu, Y. Semantics of Propositional Fuzzy Modal Logic with Evaluated Syntax and its Application to Fuzzy Decision Implications. Int J Comput Intell Syst 8 (Suppl 1), 85–93 (2015). https://doi.org/10.1080/18756891.2015.1129581
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1080/18756891.2015.1129581