David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 57 (1):91 - 115 (1996)
We investigate under what conditions contrary-to-duty (CTD) structures lacking temporal and action elements can be given a coherent reading. We argue, contrary to some recent proposals, that CTD is not an instance of defeasible reasoning, and that methods of nonmonotonic logics are inadequate since they are unable to distinguish between defeasibility and violation of primary obligations. We propose a semantic framework based on the idea that primary and CTD obligations are obligations of different kinds: a CTD obligation pertains to, or pre-supposes, a certain context in which a primary obligation is already violated. This framework is presented initially as an extension of Standard Deontic Logic (SDL), a normal modal logic of type KD, and is illustrated by application to a series of examples. The concluding section is concerned with some resemblances between CTD and defeasible reasoning. We show first that the SDL-based framework contains a flaw and must be adjusted. A discussion of possible adjustments, including an alternative treatment in terms of a preference-based semantics, reveals difficulties that are reminiscent of problems in defeasible reasoning and intensional accounts of defeasible conditionals.
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Mathijs Boer, Dov M. Gabbay, Xavier Parent & Marija Slavkovic (2012). Two Dimensional Standard Deontic Logic [Including a Detailed Analysis of the 1985 Jones–Pörn Deontic Logic System]. Synthese 187 (2):623-660.
M. Abraham, D. M. Gabbay & U. Schild (2011). Obligations and Prohibitions in Talmudic Deontic Logic. Artificial Intelligence and Law 19 (2-3):117-148.
Thomas Ågotnes, Wiebe Van Der Hoek, Juan A. Rodríguez-Aguilar, Carles Sierra & Michael Wooldridge (2009). Multi-Modal CTL: Completeness, Complexity, and an Application. Studia Logica 92 (1):1 - 26.
Thomas Ågotnes, Wiebe Van der Hoek, Juan A. Rodríguez-Aguilar, Carles Sierra & Michael Wooldridge (2009). Multi-Modal CTL: Completeness, Complexity, and an Application. [REVIEW] Studia Logica 92 (1):1-26.
José Júlio Alferes, Ricardo Gonçalves & João Leite (2013). Equivalence of Defeasible Normative Systems. Journal of Applied Non-Classical Logics 23 (1-2):25-48.
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