Reasoning about Knowledge on Computation Trees

This paper presents a bimodal logic for reasoning about knowledge during knowledge acquisition. One of the modalities represents (effort during) non-deterministic time and the other represents knowledge. The semantics of this logic are tree-like spaces which are a generalization of semantics used for modelling branching time and historical necessity. A finite system is shown to be canonically complete for the formentioned spaces. A characterization of the satisfaction relation implies the small model property and decidability for this system.

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