The pragmatic oddity in norm-based deontic logics

Abstract

The ideal worlds of a possible worlds semantics may satisfy both a primary obligation and an associated secondary obligation, for example the obligation to keep a promise and the obligation to apologise for not keeping it. This is known as the pragmatic oddity introduced by Prakken and Sergot. We argue that an adequate treatment of the pragmatic oddity within a norm-based semantics can be obtained, by not allowing primary and secondary obligations to aggregate, because they are obligations of a different kind. On the basis of this conceptual analysis, we introduce two logics, depending on the stance taken on the representation of normative conflicts, and we present sound and complete proof systems for these logics. We then give a formal analysis, discuss extensions, and highlight various topics for further research.