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COMPLETENESS OF ÅQVIST’S SYSTEMS E AND F

Published online by Cambridge University Press:  27 November 2014

XAVIER PARENT
XAVIER PARENT*
Affiliation:
Université Aix-Marseille, CNRS, CEPERC UMR 7304
*
*UNIVERSITÉ AIX-MARSEILLE, CNRS, CEPERC UMR 7304, AIX-EN-PROVENCE, 13629, FRANCE E-mail: [email protected]
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Abstract

This paper tackles an open problem posed by Åqvist. It is the problem of whether his dyadic deontic systems E and F are complete with respect to their intended Hanssonian preference-based semantics. It is known that there are two different ways of interpreting what it means for a world to be best or top-ranked among alternatives. This can be understood as saying that it is optimal among them, or maximal among them. First, it is established that, under either the maximality rule or the optimality rule, E is sound and complete with respect to the class of all preference models, the class of those in which the betterness relation is reflexive, and the class of those in which it is total. Next, an analogous result is shown to hold for F. That is, it is established that, under either rule, F is sound and complete with respect to the class of preference models in which the betterness relation is limited, the class of those in which it is limited and reflexive, and the class of those in which it is limited and total.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 1 , March 2015 , pp. 164 - 177
Copyright
Copyright © Association for Symbolic Logic 2014 

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