Believing in default rules: inclusive default reasoning

Abstract This paper argues for the reasonableness of an inclusive conception of default reasoning. The inclusive conception allows untriggered default rules to influence beliefs: Since a default “from $$\varphi $$ , infer $$\psi $$ ” is a defeasible inference rule, it by default warrants a belief in the material implication $$\varphi \rightarrow \psi $$ , even if $$\varphi $$ is not believed. Such inferences are not allowed in standard default logic of the Reiter tradition, but are reasonable by analogy to the Deduction Theorem for classical logic. Our main contribution is a formal framework for inclusive default reasoning. The framework has a solid philosophical foundation, it draws conclusions non-trivially different from non-inclusive frameworks, and it exhibits a host of benchmark properties deemed desirable in the literature—e.g., that extensions always exist and are consistent.