Notre Dame Journal of Formal Logic

A Deontic Counterpart of Lewis's S1

R. E. Jennings and Kam Sing Leung

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$^0$ (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.

Article information

Source
Notre Dame J. Formal Logic Volume 46, Number 2 (2005), 217-230.

Dates
First available in Project Euclid: 2 June 2005

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1117755151

Digital Object Identifier
doi:10.1305/ndjfl/1117755151

Mathematical Reviews number (MathSciNet)
MR2150953

Zentralblatt MATH identifier
1079.03011

Subjects
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}

Keywords
modal logic deontic logic Lewis systems prenormal idiom

Citation

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. http://projecteuclid.org/euclid.ndjfl/1117755151.


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References

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