Abstract
This expository paper presents an application, to the modal logic S4, of the valuation semantics technique proposed by Loparić for the basic normal modal logic K. In previous works we presented a valuation semantics for the minimal temporal logic Kt and several other systems modal and temporal logic. How to deal with S4, however, was left as an open problem—although we arrived at a working definition of \(A_1,\ldots ,A_n\)-valuations, we were not able to prove an important lemma for correctness. In this paper we solve this, presenting valuations for S4.
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References
Loparić, A. M., The method of valuations in modal logic, in A.I. Arruda, N.C.A. Da Costa, and, R. Chuaqui, (eds.), Mathematical Logic: Proceedings of the First Brazilian Conference, Marcel Dekker, New York, 1977.
Loparić, A. M., and C. A. Mortari, Valuations in Temporal Logic, The Journal of Non-Classical Logic 2(1): 49–60, 1984.
Mortari, C. A., Valorações para alguns sistemas de lógica do tempo, Master thesis, Unicamp, 1982.
Mortari, C. A., Issues in epistemic and modal logics and their applications, PhD thesis, Eberhard-Karls-Universität Tübingen, 1991.
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Loparić, A.M., Mortari, C.A. Valuation Semantics for S4. Stud Logica (2024). https://doi.org/10.1007/s11225-024-10100-w
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DOI: https://doi.org/10.1007/s11225-024-10100-w