Neighbourhood Semantics for Graded Modal Logic

• Autorzy: Jinsheng Chen , Hans van Ditmarsch , Giuseppe Greco , Apostolos Tzimoulis

Abstrakty

EN

We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We also obtain a new definition of graded bisimulation with respect to Kripke frames by modifying the definition of monotonic bisimulation.

Słowa kluczowe

EN

Graded modal logic; neighbourhood frames; bisimulation

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2021
• Tom: 50
• Numer: 3
• Strony: 373-395

Daty

wydano

2021

Twórcy

autor

Jinsheng Chen

• Zhejiang University, Department of Philosophy

autor

Hans van Ditmarsch

• LORIA, CNRS, University of Lorraine

• https://orcid.org/0000000345268687

autor

Giuseppe Greco

• Vrije Universiteit Amsterdam, School of Business and Economics, Ethics, Governance and Society

• https://orcid.org/0000000248453821

autor

Apostolos Tzimoulis

• Vrije Universiteit Amsterdam, School of Business and Economics, Ethics, Governance and Society

• https://orcid.org/0000000262284198

Bibliografia

• [1] L. Aceto, A. Ingolfsdottir, J. Sack, Resource bisimilarity and graded bisimilarity coincide, Information Processing Letters, vol. 111(2) (2010), pp. 68–76, DOI: https://doi.org/10.1016/j.ipl.2010.10.019
• [2] C. Cerrato, General canonical models for graded normal logics (Graded modalities IV), Studia Logica, vol. 49(2) (1990), pp. 241–252, DOI: https://doi.org/10.1007/BF00935601
• [3] C. Cerrato, Decidability by filtrations for graded normal logics (graded modalities V), Studia Logica, vol. 53(1) (1994), pp. 61–74, DOI: https://doi.org/10.1007/BF01053022
• [4] B. F. Chellas, Modal logic: an introduction, Cambridge University Press (1980).
• [5] J. Chen, G. Greco, A. Palmigiano, A. Tzimoulis, Non normal logics: semantic analysis and proof theory, [in:] Proc. of WoLLIC, vol. 11541 of LNCS, Springer (2019), pp. 99–118, DOI: https://doi.org/10.1007/978-3-662-59533-6_7
• [6] F. De Caro, Graded modalities, II (canonical models), Studia Logica, vol. 47(1) (1988), pp. 1–10, DOI: https://doi.org/10.1007/BF00374047
• [7] M. de Rijke, A note on graded modal logic, Studia Logica, vol. 64(2) (2000), pp. 271–283, DOI: https://doi.org/10.1023/A:1005245900406
• [8] K. Fine, In so many possible worlds., Notre Dame Journal of formal logic, vol. 13(4) (1972), pp. 516–520, DOI: https://doi.org/10.1305/ndjfl/1093890715
• [9] L. F. Goble, Grades of modality, Logique et Analyse, vol. 13(51) (1970), pp. 323–334.
• [10] H. H. Hansen, Monotonic modal logics, ILLC Report Nr: PP-2003-24, University of Amsterdam (2003).
• [11] D. Kaplan, S5 with multiple possibility, Journal of Symbolic Logic, vol. 35(2) (1970), p. 355, DOI: https://doi.org/10.2307/2270571
• [12] M. Ma, K. Sano, How to update neighbourhood models, Journal of Logic and Computation, vol. 28(8) (2018), pp. 1781–1804, DOI: https://doi.org/10.1093/logcom/exv026
• [13] M. Ma, H. van Ditmarsch, Dynamic Graded Epistemic Logic, The Review of Symbolic Logic, vol. 12(4) (2019), pp. 663–684, DOI: https://doi.org/10.1017/S1755020319000285
• [14] E. Pacuit, Neighborhood semantics for modal logic, Short Textbooks in Logic, Springer (2017), DOI: https://doi.org/10.1007/978-3-319-67149-9
• [15] W. van der Hoek, On the semantics of graded modalities, Journal of Applied Non-Classical Logics, vol. 2(1) (1992), pp. 81–123.
• [16] W. van der Hoek, J.-J. C. Meyer, Graded modalities in epistemic logic, [in:] International Symposium on Logical Foundations of Computer Science, Springer (1992), pp. 503–514, DOI: https://doi.org/10.1007/BFb0023902

Identyfikatory

DOI

10.18778/0138-0680.2021.12

nonstd.3pn.id

2033856