Reasoning about knowledge
Epistemic Logic for AI and Computer Science
Epistemic Logic for AI and Computer Science
An n! lower bound on formula size
ACM Transactions on Computational Logic (TOCL)
Complexity and succinctness of public announcement logic
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
On the relative succinctness of two extensions by definitions of multimodal logic
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Reasoning About Agent Types and the Hardest Logic Puzzle Ever
Minds and Machines
On the succinctness of some modal logics
Artificial Intelligence
Coalgebraic announcement logics
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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Proving that one language is more succinct than another becomes harder when the underlying semantics is stronger. We propose to use Formula-Size Games (as put forward by Adler and Immerman, 2003), games that are played on two sets of models, and that directly link the length of play with the size of the formula. Using FSGs, we prove three succinctness results for m-dimensional modal logic: (1) In system Km, a notion of 'everybody knows' makes the resulting language exponentially more succinct for m 1 (2) In S5m, the same language becomes more succinct for m 3 and (3) Public Announcement Logic is exponentially more succinct than S5m, if m 3. The latter settles an open problem raised by Lutz, 2006.