Merging Frameworks for Interaction

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic event models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of An early version of this paper was presented at TARK XI [14]. J. van Benthem (B) Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands e-mail: [email protected] J. van Benthem School of Humanities and Social Sciences, Tsinghua University, Beijing, China J. van Benthem · T. Hoshi · E. Pacuit Department of Philosophy, Stanford University, Stanford, CA, USA T. Hoshi e-mail: [email protected] E. Pacuit e-mail: [email protected] J. Gerbrandy Departimento di Informatica, University of Torino, Turin, Italy e-mail: [email protected] J. van Benthem et al. ETL models corresponding to DEL protocols in terms of notions of Perfect Recall, No Miracles, and Bisimulation Invariance. We then focus on new issues of completeness. One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL.