Обсуждение статьи Van der Hoek W., Meyer J.J. (1997) "A Complete Epistemic Logic for Multiple Agents"

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Van der Hoek W., Meyer J.J. 
"A Complete Epistemic Logic for Multiple Agents"

Аннотация:

We give one overall system for describing the knowledge in a group of m agents, in which distributed knowledge, everybody's knowledge and common knowledge can be dealt with at the same time. The canonical model for this complete epistemic logic for m agents appears to lack two desirable properties. We combine several validity-preserving techniques to transfer the satisfiability of an epistemic formula between classes of models; thus eventually proving completeness for the logic under consideration with respect to the class of models containing all the desired properties. Although the full procedure for achieving this seems, we admit, quite formidable, the method consists in essence of applying three standard techniques: firstly, we show how a filtration technique of Goldblatt can be used to gain one of the desired properties of the models. Next, we unravel this finite filtration, following ideas that were introduced by Sahlqvist for the mono-modal case. Finally, we use an equivalence relation to identify unravelled paths, the equivalence classes of this relation becoming the worlds that together constitute a new model. Thus, we eventually obtain a class of models for which, on the one hand, the given epistemic system is a sound and complete axiomatization, and on the other hand appealing mathematical properties can be proven. In passing, we prove the epistemic system to be decidable.   

Van der Hoek W., Meyer J.J. (1997) A Complete Epistemic Logic for Multiple Agents. In: Bacharach M., Gérard-Varet LA., Mongin P., Shin H.S. (eds) Epistemic Logic and the Theory of Games and Decisions. Theory and Decision Library (Series C: Game Theory, Mathematical Programming and Operations Research), vol 20. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1139-3_2

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