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Home > Archive>Volume 23, Issue 12, 2012 >3074-3087. DOI:10.3724/SP.J.1001.2012.04212
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Quantitative Method for Multi-Value Modal Logics
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    Abstract:

    The concept of n-valued modal model for multi-value modal logics is introduced in this paper, and the corresponding semantics are constructed. The study points out this kind of semantics and generalizes the semantics for classical modal logics. The definition of 〈W,R〉n-typed frame is presented, under which the localized mappings induced by modal formulae are constructed, and the concept of localized truth degree for modal formulae is introduced. It is obtained that the localized truth degree for any modal formula can be computed as the one for some modal formula without modalities in the same possible world. Based on these, the concept of global truth degree for modal formulae is introduced. It has been shown that whenever a modal formula contains no modalities, its global truth degree coincides with its truth degree in the common propositional logics.

    Reference
    [1] Blackburn P, Rijke M, Venema Y. Modal Logic. New York: Cambridge University Press, 2001. 1-50.
    [2] Cresswell MJ, Hughes GE. A New Introduction to Modal Logic. London: Routledge, 1996. 19-46.
    [3] Wang GJ. Non-Classical Mathematical Logic and Approximate Reasoning. 2nd ed., Beijing: Science Press, 2008. 224-240 (inChinese).
    [4] Bergmann M. An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems. New York:Cambridge University Press, 2008. 71-96.
    [5] Dudois D, Prade H, Klement EP. Fuzzy Sets, Logics and Reasoning about Knowledge. Dordrecht: Kluwer Academic Publishers,1999. 7-17.
    [6] Hájek P. Metamathematics of Fuzzy Logic. Dordrecht: Kluwer Academic Publisher, 1998. 27-56.
    [7] Hájek P. On fuzzy modal logics S5(C). Fuzzy Sets and Systems, 2010,161:2389-2396. [doi: 10.1016/j.fss.2009.11.011]
    [8] Nossum R. A decidable multi-modal logic of context. Journal of Applied Logic, 2003,1:119-133. [doi: 10.1016/S1570-8683(03)00007-7]
    [9] Goldblatt R. Mathematical modal logic: A view of its evolution. Journal of Applied Logic, 2003,1:309-392. [doi: 10.1016/S1570-8683(03)00008-9]
    [10] Mironov AM. Fuzzy modal logics. Journal of Mathematical Sciences, 2005,128(6):3461-3483. [doi: 10.1007/s10958-005-0281-1]
    [11] Radzikowska AM, Kerre EE. Characterization of main classes of fuzzy relations using fuzzy modal operators. Fuzzy Sets andSystems, 2005,152:223-247. [doi: 10.1016/j.fss.2004.09.005]
    [12] Bou F, Esteva F, Godo L. Modal systems based on many-valued logics. In: Proc. of the EUSFLAT, Vol.1. 2007. 177-182.
    [13] Bou F, Esteva F, Godo L. Exploring a syntactic notion of modal many-valued logics. Mathware & Soft Computing, 2008,15:175-181.
    [14] Chen TY, Wang DG. The semantics of fuzzy modal propositional logic. Journal of Liaoning Normal University (Natural ScienceEdition), 2003,26(4):341-343 (in Chinese with English abstract).
    [15] Wang DG, Gu YD, Li HX. Generalized tautology in fuzzy modal propositional logic. Acta Electronica Sinica, 2007,35(2):261-264(in Chinese with English abstract).
    [16] Huynh VN, Nakamori Y, Ho TB, Resconi G. A context model for fuzzy concept analysis based upon modal logic. InformationSciences, 2004,160:111-129. [doi: 10.1016/j.ins.2003.08.010]
    [17] Morikawa O. An extended Gentzen-type formulation of a many-valued modal propositional logic based on Zadeh's similarityrelation. Fuzzy Sets and Systems, 1999,101:115-123. [doi: 10.1016/S0165-0114(97)00044-4]
    [18] Shi HX, Wang GJ. Lattice-Valued modal propositional logic and its completeness. Science China: Information Sciences, 2010,53(11):2230-2239. [doi: 10.1007/s11432-010-4098-2]
    [19] Kr?ger F, Merz S. Temporal Logic and State Systems. Berlin: Springer-Verlag, 2008. 19-63.
    [20] Prior AN. Past, Present, and Future. Oxford: Oxford University Press, 1967. 1-32.
    [21] Ohrstrom P, Hasle P. Temporal Logic: From Ancient Ideas to Artificial Intelligence. Dordrecht: Kluwer Academic Publisher, 1995.
    [22] Manna Z, Pnueli A. Temporal Verification of Reactive Systems. New York: Springer-Verlag, 1995. 42-54.
    [23] Manna Z, Pnueli A. The Temporal Logic of Reactive and Concurrent Systems: Specification. New York: Springer-Verlag, 1992.
    [24] Baier C, Katoen JP. Principles of Model Checking. London: The MIT Press, 2008. 229-252.
    [25] Clarke EM, Grumberg O, Peled DA. Model Checking. London: The MIT Press, 2000. 128-153.
    [26] Huth M, Ryan M. Logic in Computer Science: Modelling and Reasoning about Systems. 2nd ed., Cambridge: CambridgeUniversity Press, 2004. 175-186.
    [27] Sebastiani R, Tonetta S, Vardi MY. Symbolic systems, explicit properties: On hybrid approaches for LTL symbolic model checking.Int'l Journal of Softw Tools Technol Transfer, 2011,13:319-335. [doi: 10.1007/s10009-010-0168-4]
    [28] 王国俊,傅丽,宋建社.二值命题逻辑中命题的真度理论.中国科学(A 辑),2001,31(11):998-1008.
    [29] 王国俊,李璧镜.Lukasiwicz n 值命题逻辑中公式的真度理论和极限定理.中国科学(E 辑:信息科学),2005,35(6):561-569.
    [30] Li J, Wang GJ. Theory of α-truth degrees in n-valued G?del propositional logic. Journal of Software, 2007,18(1):33-39 (in Chinesewith English abstract). http://www.jos.org.cn/1000-9825/18/33.htm [doi: 10.1360/jos180033]
    [31] 李骏,王国俊.逻辑系统*Ln 中命题的真度理论.中国科学(E 辑:信息科学),2006,36(6):631-643.
    [32] Pei DW. On equivalent forms of fuzzy logic systems NM and IMTL. Fuzzy Sets and Systems, 2003,138:187-195. [doi: S0165-0114(02)00382-2]
    [33] Wang GJ. A universal theory of measure and integral on valuation spaces with respect to diverse implication operators. Science inChina (Series E), 2000,43(6):586-594.
    [34] Wang GJ, Leung Y. Integrated semantics and logic metric spaces. Fuzzy Sets and Systems, 2003,136:71-91. [doi: S0165-0114(02)00328-7]
    [35] Wang GJ, Zhou HJ. Quantitative logic. Information Sciences, 2009,179:226-247. [doi: 10.1016/j.ins.2008.09.008]
    [36] Wang GJ, Zhou HJ. Introduction to Mathematical Logic and Resolution Principle. Beijing: Science Press; Oxford: Alpha ScienceInternational Limited, 2009.
    [37] Wang GJ, Duan QL. Theory of (n) truth degrees of formulas in modal logic and a consistency theorem. Science in China (Series F):Information Sciences, 2009,52(1):70-83.
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时慧娴,王国俊.多值模态逻辑的计量化方法.软件学报,2012,23(12):3074-3087

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History
  • Received:January 05,2011
  • Revised:April 01,2012
  • Online: December 05,2012
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