By Donald Nute
Correct to philosophy, legislations, administration, and synthetic intelligence, those papers discover the applicability of nonmonotonic or defeasible good judgment to normative reasoning. The ensuing platforms purport to unravel famous deontic paradoxes and to supply a greater therapy than classical deontic common sense does of prima facie legal responsibility, conditional legal responsibility, and priorities of normative ideas.
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On the other hand, a treatment that allows unrestricted strengthening, such as those suggested by von Wright and Prior, will incorrectly yield O( -,F j A) from the first premise. What is needed, apparently, is a certain amount of strengthening, but not too much: in order to model prima facie reasoning, we want to allow oughts formulated explicitly only for very general circumstances to apply also by default in more specific situations, unless they are overridden in those situations. As far as I know, no treatment of conditional oughts based on any of the standard philosophical logics is able to model this kind of reasoning.
NONMONOTONIC FOUNDATIONS FOR DEONTIC LOGIC 31 We tum now to KD. Of course, anything can be derived in KD from an inconsistent set of oughts; and so, together with the following theorem, this shows that, as expected, KD is properly stronger than van Fraassen's theory. Theorem 4 Let r be a set of ought statements. Then if r that r rKD OA. rF OA, it follows Proof Suppose r r F OA. By Theorem 2, it follows that 9 r A for some subset 9 of I'; and so r (BI 1\ ... 1\ Bn) :J A, for some B I , ... , Bn E I'.
The notion ~SA of articulated skeptical consequence that reflects this reasoning strategy can be defined in the obvious way. Definition 6 r ~SA OA if and only if r* ~s OA. Focusing again on r 2, an agent reasoning with this new notion of consequence would have to abandon all the conclusions listed above except OB. 5. CONDITIONAL OUGHTS Much of our normative reasoning involves ought statements that are conditional rather than absolute, as in 'Given A, it ought to be that B', which we represent through the standard notation 0 (B / A).
Defeasible Deontic Logic by Donald Nute