Belief, awareness, and limited reasoning
Artificial Intelligence
A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
Reasoning about knowledge
Modal logic
Knowing Minimum/Maximum n Formulae
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Awareness and Forgetting of Facts and Agents
WI-IAT '09 Proceedings of the 2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology - Volume 03
On the interactions of awareness and certainty
AI'11 Proceedings of the 24th international conference on Advances in Artificial Intelligence
Epistemic profiles and belief structures
KES-AMSTA'12 Proceedings of the 6th KES international conference on Agent and Multi-Agent Systems: technologies and applications
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In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as "Ann knows that Bill is aware of something Ann is not aware of" - without using a stronger statement such as "Ann knows that Bill is aware of p and Ann is not aware of p", for some particular p. Recently, however, Halpern and Rêgo (2006) introduced a logic in which such statements about knowledge of unawareness can be expressed. The logic extends the traditional framework with quantification over formulae, and is thus very expressive. As a consequence, it is not decidable. In this paper we introduce a decidable logic which can be used to reason about certain types of unawareness. The logic extends the traditional framework with an operator expressing full awareness, i.e., the fact that an agent is aware of everything, and another operator expressing relative awareness, the fact that one agent is aware of everything another agent is aware of The logic is less expressive than Halpern's and Rêgo's logic. It is, however, expressive enough to express all of Halpern's and Rêgo's motivating examples. In addition to proving that the logic is decidable and that its satisfiability problem is PSPACE-complete, we present an axiomatisation which we show is sound and complete.