Reasoning About Agent Types and the Hardest Logic Puzzle Ever

Minds and Machines 23 (1):123-161 (2013)
In this paper, we first propose a simple formal language to specify types of agents in terms of necessary conditions for their announcements. Based on this language, types of agents are treated as ‘first-class citizens’ and studied extensively in various dynamic epistemic frameworks which are suitable for reasoning about knowledge and agent types via announcements and questions. To demonstrate our approach, we discuss various versions of Smullyan’s Knights and Knaves puzzles, including the Hardest Logic Puzzle Ever (HLPE) proposed by Boolos (in Harv Rev Philos 6:62–65, 1996). In particular, we formalize HLPE and verify a classic solution to it. Moreover, we propose a spectrum of new puzzles based on HLPE by considering subjective (knowledge-based) agent types and relaxing the implicit epistemic assumptions in the original puzzle. The new puzzles are harder than the previously proposed ones in the literature, in the sense that they require deeper epistemic reasoning. Surprisingly, we also show that a version of HLPE in which the agents do not know the others’ types does not have a solution at all. Our formalism paves the way for studying these new puzzles using automatic model checking techniques.
Keywords Agent types  Public announcement logic  Questioning strategy  Knight and Knaves  The hardest logic puzzle ever
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DOI 10.1007/s11023-012-9287-x
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References found in this work BETA
Jelle Gerbrandy & Willem Groeneveld (1997). Reasoning About Information Change. Journal of Logic, Language and Information 6 (2):147-169.

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Citations of this work BETA
Johan van Benthem (2014). Natural Language and Logic of Agency. Journal of Logic, Language and Information 23 (3):367-382.

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Similar books and articles
Joshua Sack (2008). Temporal Languages for Epistemic Programs. Journal of Logic, Language and Information 17 (2):183-216.
Jelle Gerbrandy & Willem Groeneveld (1997). Reasoning About Information Change. Journal of Logic, Language and Information 6 (2):147-169.
George Boolos (1996). The Hardest Logic Puzzle Ever. The Harvard Review of Philosophy 6 (1):62-65.

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