Invariance Properties of Quantifiers and Multiagent Information Exchange

Abstract
The paper presents two case studies of multi-agent information exchange involving generalized quantifiers. We focus on scenarios in which agents successfully converge to knowledge on the basis of the information about the knowledge of others, so-called Muddy Children puzzle and Top Hat puzzle. We investigate the relationship between certain invariance properties of quantifiers and the successful convergence to knowledge in such situations. We generalize the scenarios to account for public announcements with arbitrary quantifiers. We show that the Muddy Children puzzle is solvable for any number of agents if and only if the quantifier in the announcement is positively active (satisfies a version of the variety condition). In order to get the characterization result, we propose a new concise logical modeling of the puzzle based on the number triangle representation of generalized quantifiers. In a similar vein, we also study the Top Hat puzzle. We observe that in this case an announcement needs to satisfy stronger conditions in order to guarantee solvability. Hence, we introduce a new property, called bounded thickness, and show that the solvability of the Top Hat puzzle for arbitrary number of agents is equivalent to the announcement being 1-thick.
Keywords Muddy Children Puzzle  Top Hat Puzzle  generalized quantifiers  number triangle  epistemic logic
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 Translate to english
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 10,731
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

No references found.

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.
Analytics

Monthly downloads

Added to index

2011-06-05

Total downloads

14 ( #112,475 of 1,098,619 )

Recent downloads (6 months)

1 ( #285,544 of 1,098,619 )

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.