The Manchester twins : conflicts between directed obligations

Term-modal logic uses modal operators that are indexed with terms of the language,which allows for quantification over these operators. Term-modal deontic logics (TMDL) can capture reasoning with rules, directed, and undirected obligations. Us-ing the rich language of TMDL, we identify different types of deontic conflicts between directed obligations and describe reasoning in the face of these conflicts. We develop several monotonic logics in the TMDL family and show that none is capable of cap-turing all plausible deontic principles, while also being conflict-tolerant. To remedythis we develop several non-monotonic extensions in the format of adaptive logics.We end by isolating one of these,TMDLm, and commenting on it

Adaptive logic characterizations of input/output logic

We translate unconstrained and constrained input/output logics as introduced by Makinson and van der Torre to modal logics, using adaptive logics for the constrained case. The resulting reformulation has some additional benefits. First, we obtain a proof-theoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our framework naturally gives rise to useful variants and allows to express important notions that go beyond the expressive means of input/output logics, such as violations and sanctions

A logic for prioritized normative reasoning

In this article 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 article 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 defined in the format of lexicographic adaptive logics from [34], 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