Modal Equivalence and Bisimilarity in Many-valued Modal Logics with Many-valued Accessibility Relations

• Autorzy: Diaconescu Denisa

Identyfikatory

DOI

10.3233/FI-2020-1920

• Języki publikacji: EN

Abstrakty

EN

In this paper we investigate the Hennessy-Milner property for models of many-valued modal logics defined based on complete MTL-chains having many-valued accessibility relations. Our main result gives a necessary and sufficient algebraic condition for the class of image-finite models for such modal logics to admit the Hennessy-Milner property.

Słowa kluczowe

EN

bisimulation; Hennessy-Milner property; many-valued logics; modal logics

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2020
• Tom: Vol. 173, nr 2-3
• Strony: 177--189
• Opis fizyczny: Bibliogr. 34 poz., rys.

Twórcy

autor

Diaconescu Denisa

• Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014, Bucharest, Romania

Bibliografia

• [1] Blackburn P, de Rijke M, Venema Y. Modal logic. Cambridge University Press, 2001. URL https://doi.org/10.1017/CBO9781107050884.
• [2] van Benthem J. Modal logic for Open Minds. CSLI Lecture Notes 199, 2010. ISBN: 9781575866987.
• [3] Huth M, Ryan M. Logic in Computer Science: Modelling and Reasoning About Systems. Cambridge University Press, 2004. ISBN-10:9780521543101, 13:978-0521543101.
• [4] Halpern JY, Moses Y. Knowledge and common knowledge in a distributed environment. Journal of the ACM, 1990. 37(3):549-587.
• [5] Hájek P, Harmancová D, Verbrugge R. A qualitative fuzzy possibilistic logic. International Journal of Approximate Reasoning, 1995. 12:1-19. URL https://doi.org/10.1016/0888-613X(94)00011-Q.
• [6] Godo L, Hájek P, Esteva F. A fuzzy modal logic for belief functions. Fundamenta Informaticae, 2003. 57(2-4):127-146.
• [7] Straccia U. Reasoning within Fuzzy Description Logics. Journal of Artificial Intelligence Research, 2001. 14:137-166. doi:10.1613/jair.813.
• [8] Hájek P. Making fuzzy description logic more general. Fuzzy Sets and Systems, 2005. 154(1):1-15. URL https://doi.org/10.1016/j.fss.2005.03.005.
• [9] Baader F, Borgwardt S, Peñaloza R. Decidability and Complexity of Fuzzy Description Logics. KI, 2017. 31(1):85-90. doi:10.1007/s13218-016-0459-3.
• [10] Diaconescu D, Georgescu G. Tense Operators on MV-Algebras and Łukasiewicz-Moisil Algebras. Fundamenta Informaticae, 2007. 81(4):379-408.
• [11] Schockaert S, Cock MD, Kerre E. Spatial reasoning in a fuzzy region connection calculus. Artificial Intelligence, 2009. 173(2):258-298. URL https://doi.org/10.1016/j.artint.2008.10.009.
• [12] Park D. Concurrency and automata on infinite sequences. Lecture Notes in Computer Science, 1981. 154:561-572.
• [13] Hennessy M, Milner R. On observing nondeterminism and concurrency. Lecture Notes in Computer Science, 1980. 85:299-309. doi:10.1007/3-540-10003-2_79.
• [14] van Benthem J. Correspondence theory. In: Gabbay D, Guenthner F (eds.), Handbook of Philosophical Logic, volume II. Reidel, 1984.
• [15] Kozen D. Automata and Computability. Springer, 1997. ISBN: 978-0-387-94907-9, 978-1-4612-7309-7.
• [16] Clarke EM, Grumberg O, Peled DA. Model Checking. MIT Press, 2000.
• [17] Hennessy M, Milner R. Algebraic laws for nondeterminism and concurrency. Journal of the ACM, 1985. 32:137-162. doi:10.1145/2455.2460.
• [18] Caicedo X, Rodríguez R. Standard Gödel Modal Logics. Studia Logica, 2010. 94(2):189-214. doi:10.1007/s11225-010-9230-1.
• [19] Caicedo X, Metcalfe G, Rodríguez R, Rogger J. A Finite Model Property for Gödel Modal Logics. In: Proceedings of WoLLIC 2013, Springer LNCS 8071, volume 8701 of LNCS. Springer, 2013 pp. 226-237. doi:10.1007/978-3-642-39992-3_20.
• [20] Hansoul G, Teheux B. Extending Łukasiewicz Logics with a Modality: Algebraic Approach to Relational Semantics. Studia Logica, 2013. 101(3):505-545. doi:10.1007/s11225-012-9396-9.
• [21] Marti M, Metcalfe G. Hennessy-Milner Properties for Many-Valued Modal Logics. In: Proceedings of AiML 2014. King’s College Publications, 2014 pp. 407-420. URL http://www.iam.unibe.ch/ltgpub/2014/mm14.pdf.
• [22] Metcalfe G, Marti M. Expressivity in chain-based modal logics. Archive for Mathematical Logic, 2018. 57(3-4):361-380. doi:10.1007/s00153-017-0573-4.
• [23] Bílková M, Dostál M. Expressivity of Many-Valued Modal Logics, Coalgebraically. In: WoLLIC. 2016 pp. 109-124. doi:10.1007/978-3-662-52921-8_8.
• [24] van Breugel F, Worrell J. A behavioural pseudometric for probabilistic transition systems. Theoretical Computer Science, 2005. 331(1):115-142. URL https://doi.org/10.1016/j.tcs.2004.09.035.
• [25] Balle B, Gourdeau P, Panangaden P. Bisimulation metrics for weighted automata. In: ICALP 2017, volume 103 pp. 1-14. doi:10.4230/LIPIcs.ICALP.2017.103.
• [26] Fan T, Liau C. Logical characterization of regular equivalence in weighted social networks. Artificial Intelligence, 2014. 214:66-88. URL https://doi.org/10.1016/j.artint.2014.05.007.
• [27] Esteva F, Godo L. Monoidal t-norm based logic: towards a logic for left-continuous t-norms. Fuzzy Sets and Systems, 2001. 124(3):271-288. URL https://doi.org/10.1016/S0165-0114(01)00098-7.
• [28] Hájek P. Metamathematics of Fuzzy Logic. Kluwer, Dordrecht, 1998. ISBN:978-0-7923-5238-9, 978-1-4020-0370-7.
• [29] Galatos N, Jipsen P, Kowalski T, Ono H. Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Elsevier, 2007. ISBN: 9780444521415, 9780080489643.
• [30] Bou F, Esteva F, Godo L, Rodríguez R. On the minimum many-valued logic over a finite residuated lattice. Journal of Logic and Computation, 2011. 21(5):739-790. doi:10.1093/logcom/exp062.
• [31] Cignoli R, D’Ottaviano IML, Mundici D. Algebraic Foundations of Many-Valued Reasoning, volume 7 of Trends in Logic. Kluwer, Dordrecht, 1999. ISBN: 978-0-7923-6009-4, 978-90-481-5336-7.
• [32] McNaughton R. A Theorem about infinite-valued Sentential Logic. Journal of Symbolic Logic, 1951. 16(1):1-13. doi:10.2307/2268660.
• [33] Cintula P, Menchón P, Noguera C. Toward a general frame semantics for modal many-valued logics. Soft Computing, 2019. 23(7):2233-2241. doi:10.1007/s00500-018-3369-5.
• [34] Cintula P, Noguera C. Neighborhood semantics for modal many-valued logics. Fuzzy Sets and Systems, 2018. 345:99-112. URL https://doi.org/10.1016/j.fss.2017.10.009.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).