Reasoning about knowledge
The size of a revised knowledge base
Artificial Intelligence
Modal logic
Temporal Logic with Forgettable Past
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Modal Logic and the Two-Variable Fragment
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
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
Dynamic Epistemic Logic
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
The comparative linguistics of knowledge representation
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
The Description Logic Handbook: Theory, Implementation and Applications
The Description Logic Handbook: Theory, Implementation and Applications
Foundations of instance level updates in expressive description logics
Artificial Intelligence
Succinctness of epistemic languages
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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
Succinctness Gap between Monadic Logic and Duration Calculus
Fundamenta Informaticae
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One way of comparing knowledge representation formalisms that has attracted attention recently is in terms of representational succinctness, i.e., we can ask whether one of the formalisms allows for a more 'economical' encoding of information than the other. Proving that one logic 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) [1], but we present them as games for one player, called Spoiler), games that are played on two sets of models, and that directly link the length of a play in which Spoiler wins the game with the size of a formula, i.e., a formula that is true in the first set of models but false in all models of the second set. Using formula size games, we prove the following succinctness results for m-dimensional modal logic, where one has a set I={i"1,...,i"m} of indices for m modalities: (1) on general Kripke models (and also on binary trees), a definition [@?"@C]@f=@?"i"@?"@C[i]@f (with @C@?I) makes the resulting logic exponentially more succinct for m1; (2) several modal logics use such abbreviations [@?"@C]@f, e.g., in description logics the construct corresponds to adding role disjunctions, and an epistemic interpretation of it is 'everybody in @C knows'. Indeed, we show that on epistemic models (i.e., S"5-models), the logic with [@?"@C]@f becomes more succinct for m3; (3) the results for the logic with 'everybody knows' also hold for a logic with 'somebody knows', and (4) on epistemic models, Public Announcement Logic is exponentially more succinct than epistemic logic, if m3. The latter settles an open problem raised by Lutz (2006) [18].