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OBLIGATION AS WEAKEST PERMISSION: A STRONGLY COMPLETE AXIOMATIZATION

Published online by Cambridge University Press:  01 April 2016

FREDERIK VAN DE PUTTE
FREDERIK VAN DE PUTTE*
Affiliation:
Centre for Logic and Philosophy of Science Ghent University
*
*CENTRE FOR LOGIC AND PHILOSOPHY OF SCIENCE GHENT UNIVERSITY E-mail: frederik.vandeputte@ugent.be
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Abstract

In (Anglberger et al., 2015, Section 4.1), a deontic logic is proposed which explicates the idea that a formula φ is obligatory if and only if it is (semantically speaking) the weakest permission. We give a sound and strongly complete, Hilbert style axiomatization for this logic. As a corollary, it is compact, contradicting earlier claims from Anglberger et al. (2015). In addition, we prove that our axiomatization is equivalent to Anglberger et al.’s infinitary proof system, and show that our results are robust w.r.t. certain changes in the underlying semantics.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 2 , June 2016 , pp. 370 - 379
Copyright
Copyright © Association for Symbolic Logic 2016 

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References

BIBLIOGRAPHY

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