Detachment and defeasibility in deontic logic
This paper presents a deontic logic designed to formalize concepts of both defeasible and indefeasible duties, where each may be either categorical or conditional. Defeasible conditional duties are distinguished from their indefeasible counterparts in that principles for strengthening the antecedent and of deontic modus ponens should both fail for the former and both be valid for the latter. Standard conditional deontic logic validates the first principle but not the second; hence it is inadequate for either sort of statement of conditional duties. This paper builds deontic logic upon a logic of defeasible conditionals, \(A>B\), by adding the standard deontic operator \(O\), according to which statements \(OA\) assert that \(A\) holds in all ideal worlds. This represents indefeasible categorical, or actual, duties. Statements of indefeasible conditional duties, \(O(A|B)\) are defined as \(B\Rightarrow OA\), where `\(\Rightarrow\)' represents alethic strict implication. By contrast, statements of defeasible conditional duties, \(Od(A|B)\), are defined in terms of the defeasible conditional, \(B>OB\), and statements of defeasible categorical duties, prima facie duties, \(Od(A)\), are defined as \(Od(A|T)\), i.e., \(T>OA\), where \(T\) is any tautology. These concepts are all defined precisely by means of a possible-worlds semantics, and shown to have desirable properties.
scientific article; zbMATH DE number 929960