Reasoning About Agent Types and the Hardest Logic Puzzle Ever

Minds and Machines 23 (1):123-161 (2013)
Abstract
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)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 12,088
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA
George Boolos (1996). The Hardest Logic Puzzle Ever. The Harvard Review of Philosophy 6 (1):62-65.
Jelle Gerbrandy & Willem Groeneveld (1997). Reasoning About Information Change. Journal of Logic, Language and Information 6 (2):147-169.
Wesley H. Holliday & Thomas F. Icard (2010). Moorean Phenomena in Epistemic Logic. In Lev Beklemishev, Valentin Goranko & Valentin B. Shehtman (eds.), Advances in Modal Logic 8. College Publications.

View all 13 references

Citations of this work BETA
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.
Analytics

Monthly downloads

Added to index

2012-09-21

Total downloads

22 ( #83,083 of 1,102,035 )

Recent downloads (6 months)

7 ( #41,676 of 1,102,035 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.