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Including the past in ‘topologic’. (English) Zbl 1132.03321
Artemov, Sergei N. (ed.) et al., Logical foundations of computer science. International symposium, LFCS 2007, New York, NY, USA, June 4–7, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-72732-3/pbk). Lecture Notes in Computer Science 4514, 269-283 (2007).
Summary: In this paper, we extend Moss and Parikh’s topological view of knowledge. We incorporate a further modality, denoted P, into the original system. This operator describes the increase of sets. Regarding the usual logic of knowledge, P corresponds to no learning of agents. In the context of ‘topologic’, however, P represents the reverse effort operator and is related to the past therefore. It is our objective to prove nice properties of the accompanying logic like soundness and completeness with respect to the intended class of structures, or decidability. To this end, we take up a hybrid logic point of view, among other things. This not only yields the desired results, but also has some interesting consequences with regard to applications.
For the entire collection see [Zbl 1121.03005].
03B42 Logics of knowledge and belief (including belief change)
03B44 Temporal logic
03B45 Modal logic (including the logic of norms)
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