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A logic for reasoning about knowledge of unawareness

Agotnes, Thomas; Alechina, Natasha

Authors

Thomas Agotnes

Natasha Alechina nza@cs.nott.ac.uk



Abstract

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. In Halpern and Rêgo (2006, 2009b) (revisited in Halpern and Rêgo (2009a, 2013)) Halpern and Rêgo 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. Our 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 the motivating examples in Halpern and Rêgo (2006, 2009b). 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.

Journal Article Type Article
Publication Date Jun 17, 2014
Journal Journal of Logic, Language and Information
Print ISSN 0925-8531
Electronic ISSN 0925-8531
Publisher Humana Press
Peer Reviewed Peer Reviewed
Volume 23
Issue 2
APA6 Citation Agotnes, T., & Alechina, N. (2014). A logic for reasoning about knowledge of unawareness. Journal of Logic, Language and Information, 23(2), doi:10.1007/s10849-014-9201-4
DOI https://doi.org/10.1007/s10849-014-9201-4
Publisher URL http://link.springer.com/article/10.1007%2Fs10849-014-9201-4
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information The final publication is available at Springer via http://dx.doi.org/10.1007/s10849-014-9201-4

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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