A Logic for prioritized normative reasoning

In this paper we present the logic MP⊏ that explicates reasoning on the basis of prioritized obligations. Although formal criteria to handle prioritized obligations have been formulated in the literature, little attention has been paid to the actual (non-monotonic) reasoning that makes use of these criteria. The dynamic proof theory of MP⊏ fills this lacuna. This paper focuses on premise sets consisting of possibly conflicting prima facie obligations that have a modular order. MP⊏ allows to derive –inter alia– the actual, all-things-considered obligations from such premise sets. It is an adaptive logic defined in the new generic format from [35], whence a rich meta-theory is immediately available (e.g. soundness and completeness, idempotence, reflexivity, etc.). In addition, we establish some meta-theoretic results that are specific to the context of prioritized obligations. With the aid of concrete examples, we illustrate properties of MP⊏ which improve on other existing criteria for prioritized obligations. Finally, we show how this logic may also be applied to the context of prioritized belief bases. keywords: prioritized obligations; adaptive logics; deontic conflicts