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Logic and Logical Philosophy

KD45 with Propositional Quantifiers
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KD45 with Propositional Quantifiers

Authors

  • P. Maurice Dekker Institute for Logic, Language and Computation, University of Amsterdam

DOI:

https://doi.org/10.12775/LLP.2023.018

Keywords

modal logic, propositional quantifier, KD45_{\Box}

Abstract

Steinsvold (2020) has provided two semantics for the basic modal language enriched with propositional quantifiers (∀p). We define an extension EM of the system KD45_{\Box} and prove that EM is sound and complete for both semantics. It follows that the two semantics are equivalent.

References

Balbiani, Ph., and T. Tinchev, 2018, “Elementary unification in modal logic KD45”, Journal of Logics and their Applications 5: 301–317.

Chagrov, A., and M. Zakharyaschev, 1997, Modal Logic, Clarendon press Oxford.

Ding, Y., 2021, “On the logic of belief and propositional quantification”, Journal of Philosophical Logic 50: 1143–1198. DOI: http://dx.doi.org/10.1007/s10992-021-09595-8

Fine, K., 1969, For some proposition and so many possible worlds, PhD thesis, University of Warwick.

French, T., 2006, Bisimulation quantifiers for modal logic, PhD thesis, University of Western Australia.

Harvey, F. R., 1963, “The derived set operator”, American Mathematical Monthly 70: 1085–1086. DOI: http://dx.doi.org/10.2307/2312842

Gabai, H., 1964, “The exterior operator and boundary operator”, American Mathematical Monthly 71: 1029–1031. DOI: http://dx.doi.org/10.2307/2311925

Ghilardi, S., and M. Zawadowski, 1995, “Undefinability of propositional quantifiers in the modal system S4”, Studia Logica 55: 259–271. DOI: http://dx.doi.org/10.1007/BF01061237

Nagle, M. C., 1981, “The decidability of normal K5 logics”, Journal of Symbolic Logic 46: 319–328. DOI: http://dx.doi.org/10.2307/2273624

Pietruszczak, A., 2009, “Simplified Kripke style semantics for modal logics K45, KB4 and KD45”, Bulletin of the Section of Logic 38: 163–171.

Segerberg, K., 1968, “Decidability of four modal logics”, Theoria 34: 21–25. DOI: http://dx.doi.org/10.1111/j.1755-2567.1968.tb00336.x

Spira, R., 1967, “Derived-set axioms for topological spaces”, Portugaliae mathematica 26: 165–167.

Steinsvold, Ch., 2007, Topological models of belief logics, PhD thesis, City University of New York.

Steinsvold, Ch., 2008, “A grim semantics for logics of belief”, Journal of Philosophical Logic 37: 45–56. DOI: http://dx.doi.org/10.1007/s10992-007-9055-1

Steinsvold, Ch., 2020, “Some formal semantics for epistemic modesty”, Logic and Logical Philosophy 29: 381–413. http://dx.doi.org/DOI: 10.12775/LLP.2020.002

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Published

2023-08-24

How to Cite

1.
DEKKER, P. Maurice. KD45 with Propositional Quantifiers. Logic and Logical Philosophy. Online. 24 August 2023. pp. 1-28. [Accessed 1 December 2023]. DOI 10.12775/LLP.2023.018.
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Copyright (c) 2023 P. Maurice Dekker

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This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

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