PP-2007-08: Merging Frameworks for Interaction: DEL and ETL

PP-2007-08: van Benthem, Johan and Gerbrandy, Jelle and Pacuit, Eric (2007) Merging Frameworks for Interaction: DEL and ETL. [Report]

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Abstract

Many logical systems today describe behaviour of intelligent interacting agents over time. Frameworks include Interpreted Systems (IS, Fagin et al.), Epistemic-Temporal Logic (ETL, Parikh & Ramanujam), STIT (Belnap et al.), Process Algebra and Game Semantics (Abramsky). This proliferation is an asset, as different modeling tools can be fine-tuned to specific applications. But it may also be an obstacle, when barriers between paradigms and schools go up. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow in multi-agent systems. One is IS/ETL (IS and ETL are basically the same up to model transformations), which uses linear or branching time models with added epistemic structure induced by agents' different capabilities for observing events. These models provide a Grand Stage where histories of some process unfold constrained by a protocol, and a matching epistemic-temporal language describes what happens. The other framework is Dynamic Epistemic Logic (DEL) which describes interactive processes in terms of epistemic event models which may occur inside modalities of the language. Temporal evolution is then computed from some initial epistemic model through a process of successive 'product updates'. It has long been unclear how to best compare IS/ETL and DEL. Other papers have investigated various aspects, but in this paper, we strengthen the interface to a considerable extent. We first show how to transform DEL protocols into classes of ETL models, leading to a simple language translation from dynamic modalities to temporal operators. Next, we prove a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall, No Miracles, and Bisimulation Invariance. These describe the sort of idealized agent presupposed in standard DEL. Next, we consider further assumptions on agents, and introduce a new technique of modal correspondence analysis relating special properties of DEL protocols to corresponding ETL-style properties. Finally, we how the DEL ETL analogy suggests new issues of completeness. Our new 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. Once again, we are not reducing one framework to another. We show rather how ETL and DEL lead to interesting new issues when merged as accounts of intelligent agents.

Item Type: Report
Report Nr: PP-2007-08
Series Name: Prepublication (PP) Series
Year: 2007
Uncontrolled Keywords: Dynamic Epistemic Logic; Epistemic Temporal Logic
Depositing User: epaquit1
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/242

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