Notre Dame Journal of Formal Logic

A Deontic Counterpart of Lewis's S1

R. E. Jennings and Kam Sing Leung


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$^0$ (S1 without the schema [T]). We extend it to S1$^0$D, 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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Notre Dame J. Formal Logic Volume 46, Number 2 (2005), 217-230.

First available in Project Euclid: 2 June 2005

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Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}

modal logic deontic logic Lewis systems prenormal idiom


Leung, Kam Sing; Jennings, R. E. A Deontic Counterpart of Lewis's S1. Notre Dame J. Formal Logic 46 (2005), no. 2, 217--230. doi:10.1305/ndjfl/1117755151.

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