Logics of time and computation
Logics of time and computation
Topological reasoning and the logic of knowledge
TARK '92 Proceedings of the fourth conference on Theoretical aspects of reasoning about knowledge
Reasoning about knowledge
Topological Semantics for Hybrid Systems
LFCS '97 Proceedings of the 4th International Symposium on Logical Foundations of Computer Science
A Topological Generalization of Propositional Linear Time Temporal Logic
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Reasoning about Knowledge on Computation Trees
JELIA '94 Proceedings of the European Workshop on Logics in Artificial Intelligence
Knowledge Theoretic Properties of Topological Spaces
International Conference Logic at Work on Knowledge Representation and Reasoning Under Uncertainty, Logic at Work
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
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Subsequently, we introduce a reasoning formalism which in particular allows to express that certain sets in a system of subsets of a given set are disjoint. The main purpose of considering such a family of subsets is to be able to investigate how knowledge grows as subsets shrink in the course of time. We actually introduce a trimodal logic: we have a system containing operators for knowledge and time, of which the latter corresponds to the effort of measurement and reminds of the nexttime operator of temporal logic; an operator separating sets is added then. So-called subset tree models appear as the relevant semantical structures.We present an axiomatization of the set of valid formulas encompassing the three operators and their interaction. Afterwards the completeness of the given axiomatization is proved. We also give arguments showing that the logic is decidable.