In response to a concern raised by Horty, this paper develops a two-tiered, preference-based semantic framework for modeling defeasible conditional obligations. The paper extends a Hansson–Lewis style preference semantics for dyadic deontic logic by incorporating a nonmonotonic reasoning mechanism that enables previously derived obligations to be withdrawn when new, potentially conflicting information comes in. The account is bi-preferential: two orderings-ideality and normality-on worlds are employed to address shortcomings in earlier approaches, with a separate ranking method for each. At the nonmonotonic layer, a number of postulates are considered, including antecedent strengthening, inclusion and no-drowning. A connection is established with so-called constrained input/output (I/O) logic-an existing standard for normative reasoning based on a different methodology.

Abstract This article provides a systematic analysis of the well-known notions of weak and strong permission in input/output (I/O) logic. We extend the account of permission initially put forward by Makinson and Van der Torre to the whole family of I/O systems developed during the last two decades. The main contribution is a series of characterization results for strong permission, based on establishing the so-called non-repetition property. We also study an input/output logic not yet covered in the literature. It supports reasoning by cases—a natural feature of human reasoning. The output is not closed under logical entailment. At the same time, it avoids excess output using a consistency check—a technique familiar from non-monotonic logic. This makes it well suited for contrary-to-duty reasoning. The axiomatic characterization is in terms of a generalized OR rule. We discuss the implications of all this for our understanding of the notion of the coherence of a normative system. Topics for future research are identified.1

Although permissions are of crucial importance in several settings, they have garnered less attention within the deontic logic community than obligations. In previous work we showed how to reconstruct deontic logic using Kelsen’s quasi-causal conception of norms, restricting ourselves to the notion of obligation. Here we extend the account to permission, and show how to analyse the notion of strong permission through a Kelsenian lens. In our framework various forms of conflicts between obligation and permission are disentangled.

Inspired by Kelsen’s view that norms establish causal-like connections between facts and sanctions, we develop a deontic logic in which a proposition is obligatory iff its complement causes a violation. We provide a logic for normative causality, define non-contextual and contextual notions of illicit and duty, and show that the logic of such duties is well-behaved and solves the main deontic paradoxes.

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.