A deontic logic framework allowing for factual detachment (Q545154)

Adaptive logics (AL) provide a nonmonotonic mechanism for reasoning with problematic rules, rules that seem intuitively correct yet sometimes yield unacceptable consequences. ALs allow some applications of the rule, but not all, in order to capture the sense of their correctness while avoiding their faults. It does this by regarding premise sets `as normal as possible', relative to a specified class of abnormalities or unacceptabilities. The present paper presents adaptive logics for dyadic deontic logic, the logic of conditional obligation. The problematic rule of concern is factual detachment (FD). It often seems correct to infer from the conditional obligation ``If \(A\) then it ought to be that \(B\)'', \(O(B/A)\), and the fact \(A\) to the absolute obligation ``It ought to be that \(B\)'', \(O(B)\). Yet this rule presents well-known problems, some related to inferences by strengthening the antecedent (SA), others regarding the familiar contrary-to-duty paradoxes. The author describes a general method for adaptively extending dyadic deontic logics to accommodate FD provisionally. This is effected by introducing a device to mark when a conclusion by FD is unacceptable, and also by distinguishing two sorts of absolute obligation, so-called `proper' and `instrumental' obligations. Detachment for each is appropriate under different conditions regarding violation and exception. To illustrate these methods, the author applies them to adaptive extensions of variations on \textit{L. Goble}'s logics CDPM (cf. [Lect. Notes Comput. Sci. 3065, 74--113 (2004; Zbl 1169.03335)]) that were designed to accommodate normative conflicts in a conditional setting and to resolve other puzzles for dyadic deontic logic, especially regarding SA.