Statements not only update our current knowledge, but also have other dynamic effects. In particular, suggestions or commands 'upgrade' our preferences by changing the current order among worlds. We present a complete logic of knowledge update plus preference upgrade that works with dynamic-epistemic-style reduction axioms. This system can model changing obligations, conflicting commands, or 'regret'. We then show how to derive reduction axioms from arbitrary definable relation changes. This style of analysis also has a product update version with preferences between actions, as well as worlds. Some illustrations are presented involving defaults and obligations. We conclude that our dynamic framework is viable, while admitting a further extension to more numerical 'utility update'.

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This article proposes a systematic application of recent developments in the logic of preference to a number of topics in deontic logic. The key junction is the well-known Hansson conditional for dyadic obligations. These conditionals are generalized by pairing them with reasoning about syntactic priority structures. The resulting two-level approach to obligations is tested first against standard scenarios of contrary-to-duty obligations, leading also to a generalization for the Kanger-Anderson reduction of deontic logic. Next, the priority framework is applied to model two intuitively different sorts of deontic dynamics of obligations, based on information changes and on genuine normative events. In this two-level setting, we also offer novel takes on vexed issues such as the Chisholm paradox and modelling strong permission. Finally, the priority framework is shown to provide a unifying setting for the study of operations on norms as such, in particular, adding or deleting individual norms, and even merging whole norm systems in different manners. Accordingly, deontic logic has long considered models involving betterness ordering of worlds or states, going back at least to Hansson (1969). There, statements of dyadic obligation like "it ought to be the case that φ under condition ψ" (in symbols, O(φ | ψ)) were interpreted in terms of a binary relation s t between states s, t -representing that t is at least as ideal as s -according to the following semantics: bs_bs_banner THEORIA, 2014, 80, 116-152 1 In this article only the single-agent case will be considered. Extensions to multi-agent deontic scenarios, which would not pose any technical difficulty, require indexing the ideality relations by different agents.2 Lewis (1974) is an overview of various moves in the early literature on dyadic obligation. PRIORITY STRUCTURES IN DEONTIC LOGIC3 One can also construe the order of properties differently with not-touching on top, and marrying as second best. We return to options in extracting priorities below. 118 JOHAN VAN BENTHEM ET AL.