A Deontic Counterpart of Lewis's S1

Notre Dame Journal of Formal Logic 46 (2):217-230 (2005)
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Abstract

In this paper we investigate nonnormal modal systems in the vicinity of the Lewis system S1. It might be claimed that Lewis's modal systems (S1, S2, S3, S4, and S5) are the starting point of modern modal logics. However, our interests in the Lewis systems and their relatives are not (merely) historical. They possess certain syntactical features and their frames certain structural properties that are of interest to us. Our starting point is not S1, but a weaker logic S1 (S1 without the schema [T]). We extend it to S1D, which can be considered as a deontic counterpart of the alethic S1. Soundness and completeness of these systems are then demonstrated within a prenormal idiom. We conclude with some philosophical remarks on the interpretation of our deontic logic

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Citations of this work

Hyperintensionality and Normativity.Federico L. G. Faroldi - 2019 - Cham, Switzerland: Springer Verlag.

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References found in this work

Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
New foundations for Lewis modal systems.E. J. Lemmon - 1957 - Journal of Symbolic Logic 22 (2):176-186.
Modal Logics in the Vicinity of S.Brian F. Chellas & Krister Segerberg - 1996 - Notre Dame Journal of Formal Logic 37 (1):1-24.
New Foundations for Lewis Modal Systems.E. J. Lemmon - 1958 - Journal of Symbolic Logic 23 (3):346-347.

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