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2005 A Deontic Counterpart of Lewis's S1
R. E. Jennings, Kam Sing Leung
Notre Dame J. Formal Logic 46(2): 217-230 (2005). DOI: 10.1305/ndjfl/1117755151


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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R. E. Jennings. Kam Sing Leung. "A Deontic Counterpart of Lewis's S1." Notre Dame J. Formal Logic 46 (2) 217 - 230, 2005.


Published: 2005
First available in Project Euclid: 2 June 2005

zbMATH: 1079.03011
MathSciNet: MR2150953
Digital Object Identifier: 10.1305/ndjfl/1117755151

Primary: 03B45

Rights: Copyright © 2005 University of Notre Dame


Vol.46 • No. 2 • 2005
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