van Benthem, J.

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International Migration, Integration and Social Cohesion online publications

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)UvA-DARE (Digital Academic Repository)Foundational Issues in Logical Dynamicsvan Benthem, J.Publication date2012Document VersionFinal published versionPublished inAdvances in Modal LogicLink to publicationCitation for published version (APA):van Benthem, J. (2012). Foundational Issues in Logical Dynamics. In T. Bolander, T. Braüner,S. Ghilardi, & L. Moss (Eds.), Advances in Modal Logic: AiML 9 (pp. 95-96). CollegePublications. http://www.aiml.net/volumes/volume9/Benthem.pdfGeneral rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an opencontent license (like Creative Commons).Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, pleaselet the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the materialinaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letterto: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. Youwill be contacted as soon as possible.Download date:10 Mar 2023Foundational Issues in Logical DynamicsJohan van Benthem 1Amsterdam and StanfordA healthy field combines two driving forces, extension of coverage and the-oretical reflection – and modal logic is no exception. In this talk, we look atsome broader theoretical issues raised by recent developments in dynamic logicsof information flow, whose main technical feature is the modal study of defin-able model change. Our pilot system will be public announcement logic PAL,the base calculus of update with hard information. We identify several generalthemes behind the particulars of its design. These include model-theoretic is-sues like the balance of expressive power for the static and dynamic componentsof the language, and learnability results in the form of preservation theorems.But we also discuss PAL’s calculus of reasoning, via correspondence analysisof its axioms as constraints on update functions in domains of inquiry, showinghow this leads to two recent extensions: protocol versions where no reductionto the static base language occurs, and substitution-closed core versions of thesystem. Both moves exemplify more general operations on modal logics.Next, we consider other dynamic-epistemic logics, and amplify on the abovethemes, while adding some new ones. First, we discuss event models andproduct update in DEL, a calculus of model construction that shows analogieswith process algebra, but also with the epistemic µ–calculus. Then we turnto dynamic logics for belief change under incoming hard and soft informationthat upgrade plausibility relations without eliminating worlds. We discuss whatlogical format best captures the generality needed to avoid a jungle of revisionpolicies. In this setting also, we look at the general phenomenon of definingnew static modalities by dynamic considerations.While all this broadens our view of single-step model transformations, an-other conspicuous dimension in current research is the global temporal horizonof a process of inquiry, a conversation, or a game, adding procedural informa-tion to local updates. We discuss representation results linking local dynamicand global temporal logics, while also pointing at specific model-theoretic issuesarising with concrete processes involving iterated hard or soft announcements,and their limit behavior. Here we link up with modal fixed-point logics, thoughthe general situation is far from clear. As a very concrete instance of merginglocal and global perspectives, we discuss some recent links between dynamicepistemic logics and formal learning theory, where modal models acquire a newmeaning as priors pre-encoding learning methods.1 http://staff.science.uva.nl/~johan96 Foundational Issues in Logical DynamicsDrawing these threads together, we will discuss what it means to be adynamic logic, looking for postulates on model transformations at the level ofabstract model theory.This survey by no means exhausts the foundational themes behind currentdynamic logics of information and agency. We refer to the cited literaturefor further issues of logic combination and entanglement of modal operatorsin areas of agency such as games, with new questions about expressivenessand computational complexity for modal languages capturing reasoning aboutbest action in interactive social settings. Likewise, recent work has questionedthe use of standard relational models, using more finely-grained neighborhoodmodels generalizing many of the above concerns. A final general theme areinterfaces between modal and probabilistic approaches, which are emergingnaturally across many of the areas discussed in this lecture.Our presentation will refer to earlier literature plus talks at AiML 2012,but its main sources are J. van Benthem, 1996, Exploring Logical Dynamics,CSLI Publications, Stanford, 2011, Logical Dynamics of Information and In-teraction, Cambridge University Press, Cambridge, 2012, Logic in Games, TheMIT Press, Cambridge Mass.

Foundational Issues in Logical Dynamics

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