Dynamic vs. Classical Consequence
نویسنده
چکیده
The shift of interest in logic from just reasoning to all forms of information flow has considerably widened the scope of the discipline, as amply illustrated in Johan van Benthem’s recent book Logical Dynamics of Information and Interaction. But how much does this change when it comes to the study of traditional logical notions such as logical consequence? We propose a systematic comparison between classical consequence, explicated in terms of truth preservation, and a dynamic notion of consequence, explicated in terms of information flow. After a brief overview of logical consequence relations and the distinctive features of classical consequence, we define classical and dynamic consequence over abstract information frames. We study the properties of information under which the two notions prove to be equivalent, both in the abstract setting of information frames and in the concrete setting of Public Announcement Logic. The main lesson is that dynamic consequence diverges from classical consequence when information is not persistent, which is in particular the case of epistemic information about what we do not yet know. We end by comparing our results with recent work by Rothschild and Yalcin on the conditions under which the dynamics of information updates can be classically represented. We show that classicality for consequence is strictly less demanding than classicality for updates.
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