Topological reasoning and the logic of knowledge
TARK '92 Proceedings of the fourth conference on Theoretical aspects of reasoning about knowledge
Temporal aspects of the modal logic of subset spaces
Theoretical Computer Science
Modal logic
Knowledge Theoretic Properties of Topological Spaces
International Conference Logic at Work on Knowledge Representation and Reasoning Under Uncertainty, Logic at Work
Proceedings of the Conference on Logic of Programs
Complete Axiomatizations for Reasoning about Knowledge and Time
SIAM Journal on Computing
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In this paper, we extend Moss and Parikh's topo-logical 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.