A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
Reasoning about knowledge
Epistemic Logic for AI and Computer Science
Epistemic Logic for AI and Computer Science
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
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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Some natural epistemic properties which may arise in applications can only be expressed in standard epistemic logic by formulae which are exponentially long in the number of agents in the system. An example is the property "at least m agents know that at most n agents know φ". We present Epistemic Logic with Quantification over Coalitions (ELQC), where the standard common knowledge operator has been replaced allowing expressions of the form and [P]cφ where P is a coalition predicate, meaning that there is a coalition satisfying P which have common knowledge of φ and that all coalitions satisfying P have common knowledge of φ, respectively; and similarly for distributed knowledge and everybody-knows. While the language is no more expressive than standard epistemic logic, it is exponentially more succinct. We give a sound and complete axiomatisation for ELQC, and characterise the complexity of its model checking problem.