This article looks at so-called dynamic consequence relations for models of soft information change. We provide a sound, complete calculus for one-step soft dynamic consequence relations. We then study a generalization to sequences of updates, for which we show a number of valid and invalid structural rules.Keywords: Dynamic epistemic logic, substructural logic, soft information.Dynamic consequence relations are consequence relations generated by concrete information update procedures. Here we study soft information updates, which are updates that are reversible and not necessarily truthful. We provide a sound and complete axiomatization for dynamic consequence relations generated by a large class of such updates. The calculus covers one-shot updates. It describes the effect of a ψ-type of update in contexts where φ holds. Towards the end of the article we generalize this calculus to cover sequences of information updates, also known as iterated revisions. We show a number of valid inferences in that calculus, and use them to compare dynamic and classical consequence relations.
Why dynamic consequence relationsRational belief change can be seen as licensing specific kinds of inferences, that is, inducing a specific kind of consequence relation. In the words of [12], belief change and non-classical inferences are 'two sides of the same coin'. This idea, by now widely accepted in default logic, also underlies the notion of dynamic consequence.This article focuses on one specific framework for the study of information change in multiagent settings: dynamic epistemic logic (DEL). See [26] and [22] for an in-depth presentation. The gist of DEL is to enrich propositional modal languages with operators that describe the effects or consequences of certain 'epistemic actions' in a given situation. Epistemic actions are events that only affect the information available in a given situation, such as observing certain states of affairs or learning about them from a truthful and trusted source.