David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Brian Rabern & Landon Rabern (2008). A Simple Solution to the Hardest Logic Puzzle Ever. [REVIEW] Analysis 68 (2):105-112.
Gabriel Uzquiano (2010). How to Solve the Hardest Logic Puzzle Ever in Two Questions. Analysis 70 (1):39-44.
Tim S. Roberts (2001). Some Thoughts About the Hardest Logic Puzzle Ever. Journal of Philosophical Logic 30 (6):609-612.
Gregory Wheeler & Pedro Barahona (2012). Why the Hardest Logic Puzzle Ever Cannot Be Solved in Less Than Three Questions. Journal of Philosophical Logic 41 (2):493-503.
Stefan Wintein (2012). On the Behavior of True and False. Minds and Machines 22 (1):1-24.
Nina Gierasimczuk & Jakub Szymanik (2011). A Note on a Generalization of the Muddy Children Puzzle. In K. Apt (ed.), Proceeding of the 13th Conference on Theoretical Aspects of Rationality and Knowledge. ACM.
Nina Gierasimczuk & Jakub Szymanik (2011). Invariance Properties of Quantifiers and Multiagent Information Exchange. In M. Kanazawa (ed.), Proceedings of the 12th Meeting on Mathematics of Language, Lecture Notes in Artificial Intelligence 6878. Springer.
Joshua Sack (2008). Temporal Languages for Epistemic Programs. Journal of Logic, Language and Information 17 (2):183-216.
Stefan Wintein (2011). A Framework for Riddles About Truth That Do Not Involve Self-Reference. Studia Logica 98 (3):445-482.
Jelle Gerbrandy & Willem Groeneveld (1997). Reasoning About Information Change. Journal of Logic, Language and Information 6 (2):147-169.
Nicholas Asher & Alex Lascarides (2011). Reasoning Dynamically About What One Says. Synthese 183 (S1):5-31.
George Boolos (1996). The Hardest Logic Puzzle Ever. The Harvard Review of Philosophy 6 (1):62-65.
Hans van Ditmarsch & Jan van Eijck (2010). Verifying One Hundred Prisoners and a Lightbulb. Journal of Applied Non-Classical Logics 20 (3):173-191.
J. Gerbrandy (2007). The Surprise Examination in Dynamic Epistemic Logic. Synthese 155 (1):21 - 33.
Added to index2012-09-21
Total downloads15 ( #88,836 of 1,008,710 )
Recent downloads (6 months)1 ( #64,702 of 1,008,710 )
How can I increase my downloads?