Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-22T21:13:28.470Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Anglberger, Albert J. J., Gratzl, Norbert, & Roy, Olivier. (2015). Obligation, free choice, and the logic of weakest permissions, this Review, 8(4), 807–827.Google Scholar
Dong, Huimin, & Roy, Olivier. (2015). Three deontic logics for rational agency in games. In Studies in Logic, Vol. 8. College Publications, London, pp. 7–31.Google Scholar
Gargov, George, & Passy, Solomon. (1990). A note on boolean modal logic. In Petrov Petkov, Petio, editor. Mathematical Logic. US: Springer, pp. 299–309.Google Scholar
Passy, Solomon, & Tinchev, Tinko. (1991). An essay in combinatory dynamic logic. Information and Computation, 93(2), 263–332.Google Scholar
Roy, Olivier, Anglberger, Albert J. J., & Gratzl, Norbert. (2012). The logic of obligation as weakest permission. In Agotnes, Thomas, Broersen, Jan, & Elgesem, Dag, editors. Deontic Logic in Computer Science. Lecture Notes in Computer Science, Vol. 7393. Berlin, Heidelberg: Springer, pp. 139–150.CrossRefGoogle Scholar
Roy, Olivier, Anglberger, Albert J. J., & Gratzl, Norbert. (2014). The logic of best actions from a deontic perspective. In Baltag, Alexandru, & Smets, Sonja, editors. Johan van Benthem on Logic and Information Dynamics. Outstanding Contributions to Logic, Vol. 5. Springer International Publishing, Switzerland, Cham, pp. 657–676.CrossRefGoogle Scholar
Van De Putte, Frederik. That will do: Logics for deontic necessity and sufficiency. Under review, 2016.Google Scholar