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Dynamic Versus Classical Consequence
Stockholm University, Faculty of Humanities, Department of Philosophy.
Number of Authors: 2
2014 (English)In: Johan van Benthem on Logic and Information Dynamics / [ed] Baltag, A.; Smets, S., Dordrecht: Springer, 2014, Vol. 5, 837-854 p.Chapter in book (Refereed)
Abstract [en]

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. Johan van Benthem's recent book Logical Dynamics of Information and Interaction [8] can be seen as a passionate plea for a radically new view of logic. To be sure, the book is not a philosophical discussion of what logic is but rather an impressive series of illustrations of what logic can be, with presentations of numerous logical languages and a wealth of meta-logical results about them. The view is called simply Logical Dynamics, and contrasted with more traditional views of logic, and also with the earlier view from e.g. [5], now called Pluralism, in which logic was seen as the study of consequence relations. According to Logical Dynamics, logic is not only about reasoning, about what follows from what, but about all aspects of information flow among rational agents. Not just proof and inference, but observations, questions, announcements, communication, plans, strategies, etc. are first-class citizens in the land of Logic. And not only the output of these activities belong to logic, but also the processes leading up to it. This is a fascinating and inspiring view of logic. But how different is it from a more standard view? In particular, what does it change for the analysis of logical consequence, which had been the focus of traditional logical enquiry? This paper attempts some answers to the latter question, with a view to get clearer about the former.

Place, publisher, year, edition, pages
Dordrecht: Springer, 2014. Vol. 5, 837-854 p.
, Outstanding Contributions to Logic, 5
National Category
Computer and Information Science Philosophy
URN: urn:nbn:se:su:diva-117755DOI: 10.1007/978-3-319-06025-5_32ISI: 000351548700034ISBN: 978-3-319-06025-5ISBN: 978-3-319-06024-8OAI: diva2:816930
Available from: 2015-06-04 Created: 2015-06-01 Last updated: 2015-06-04Bibliographically approved

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Westerståhl, Dag
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