Logic Journal of IGPL

Logic Journal of IGPL Advance Access published online on September 9, 2009
Logic Journal of IGPL, doi:10.1093/jigpal/jzp050

This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions Google Scholar Articles by Parent, X. Social Bookmarking          What's this?

© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

A complete axiom set for Hansson's deontic logic DSDL2

Xavier Parent

Individual and Collective Reasoning Group, Department of Computer Science and Communications, University of Luxembourg.
E-mail: xavier.parent{at}uni.lu

The main contribution of this paper is a (strong) completeness result for an axiomatization of Hansson [13]'s deontic system DSDL2, whose semantics involves a non-necessarily transitive betterness relation. Reference is made to a deductive system put forth by Åqvist [2, 3].

Key Words: deontic logic • completeness • Hansson's system DSDL2 • non-transitive betterness relation • optimality language for dyadic deontic logic

Received for publication 6 September 2008. Revision received 27 June 2009.

References

[1]  Åqvist L. Modal logic with subjunctive conditionals and dispositional predicates. Journal of Philosophical Logic (1973) 2(1):1–76.[CrossRef]

[2]  Åqvist. L. An Introduction to Deontic logic and the Theory of Normative Systems. (1987) Naples: Biliopolis.

[3]  Åqvist. L. Deontic logic. 147–264. Gabbay and Guenthner [10].

[4]  Ardeshir M, Nabavi F. On some questions of L. Åqvist. Logic Jnl IGPL (2006) 14(1):1–13.[Abstract/Free Full Text]

[5]  Bezzazi H, Makinson D, Pérez R. Beyond rational monotony: some strong non-horn rules for nonmonotonic inference relations. Journal of Logic and Computation (1997) 7(5):605–631.[Abstract/Free Full Text]

[6]  Carmo J, Jones. A.JI. Deontic logic and contrary-to-duties. 265–343. Gabbay and Guenthner [10].

[7]  Chellas. BF. Modal Logic (1980) Cambridge: Cambridge University Press.

[8]  Chernoff H. Rational selection of decision functions. Econometrica (1954) 22:422–443.[CrossRef][Web of Science]

[9]  Gabbay DM. Reactive kripke models and contrary-to-duty obligations. 155–173. van der Meyden and van der Torre [27].

[10]  Gabbay DM, Guenthner F, eds. Handbook of Philosophical Logic. (2002) 2nd edition. Dordrecht, Holland: Kluwer Academic Publishers. volume 8.

[11]  Goble L. Preference semantics for deontic logics. Part I: Simple models. Logique & Analyse (2003) 46(183-184):383–418.

[12]  Goble L. Preference semantics for deontic logics. Part II: Multiplex models. Logique & Analyse (2004) 47(185-188):335–363.

[13]  Hansson B. An analysis of some deontic logics. Noûs (1969) 3:373–398.

[14]  Humberstone IL. Two merits of the circumstantial operator language for conditional logics. Australasian Journal of Philosophy (1978) 56(1):21–24.[CrossRef][Web of Science]

[15]  Lewis. DK. Counterfactuals (1973) Oxford: Blackwell.

[16]  Loewer B, Belzer M. Dyadic deontic detachment. Synthese (1983) 54(2):295–318.[CrossRef][Web of Science]

[17]  Makinson DC. Five faces of minimality. Studia Logica (1993) 52(3):339–379.[CrossRef]

[18]  Mott PL. On Chisholm's paradox. Journal of Philosophical Logic (1973) 2(2):197–211.

[19]  Nute D, editor. Defeasible Deontic Logic (1997) Dordrecht: Kluwer Academic Publishers.

[20]  Parent X. Remedial interchange, contrary-to-duty obligation and commutation. Journal of Applied Non-Classical Logics (2003) 13(3/4):345–375.[CrossRef]

[21]  Parent. X. On the strong completeness of Åqvist's dyadic deontic logic G. 189–202. van der Meyden and van der Torre [27].

[22]  Prakken H, Sergot. MJ. Dyadic deontic logic and contrary-to-duty obligation. 223–262. Nute [19].

[23]  Sen A. Choice functions and revealed preference. Review of Economic Studies (1971) 38:307–317.[CrossRef][Web of Science]

[24]  Spohn W. An analysis of Hansson's dyadic deontic logic. Journal of Philosophical Logic (1975) 4(2):237–252.[CrossRef][Web of Science]

[25]  Temkin LS. Intransitivity and the mere addition paradox. Philosophy and Public Affairs (1987) 16(2):138–187.

[26]  Tomberlin JE. Contrary-to-duty imperatives and conditional obligation. Noûs (1981) 15(3):357–375.[Web of Science]

[27]  van der Meyden R, van der Torre. L, eds. 9th International Conference, DEON 2008, Luxembourg, July 15-18. In: Deontic Logic in Computer Science (2008) Berlin Heidelberg: Springer.

[28]  van der Torre L.WN, tan Y-H. The many faces of defeasibility in defeasible deontic logic. 79–121. Nute [19].

CiteULike    Connotea    Del.icio.us    What's this?

This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions Google Scholar Articles by Parent, X. Social Bookmarking          What's this?