Logic, Rationality and Intelligent Interaction

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Title: Muddy Children Playground: Number Triangle, Internal Complexity, and Quantifiers

Abstract: In this talk we will generalize Muddy Children puzzle to account for a large class of possible public announcements with various quantifiers. We identify conditions for solvability of the extended puzzle, with its classical version as a particular case. The characterization suggests a novel way of modeling multi-agent epistemic reasoning. The framework is based on the concept of number triangle. The advantage of our approach over more general formalizations in epistemic logics, like Dynamic Epistemic Logic, is that it gives models of linear size w.r.t. the number of agents. Therefore, it is computationally plausible for modeling agents' internal perspective.

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