A modal logic for reasoning about knowledge and time on binary subset trees

  • Bernhard Heinemann
Accepted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1244)


We introduce a modal logic in which one of the operators expresses properties of points (knowledge states) in a neighbourhood of a given point (the actual set of alternatives), and other operators speak about shrinking such neighbourhoods gradually (representing the change of the set of states in time). Based on a modification of the topological language due to Moss and Parikh [Moss and Parikh 1992] we generalize a certain fragment of prepositional branching time logic to the logic of knowledge in this way. To keep the notation simple we confine ourselves to binary branching. Thus we define a trimodal logic comprising one knowledge-operator and two nexttime-operators. The formulas are interpreted in binary ramified subset tree models. We present an axiomatization of the set T of theorems valid for this class of semantical domains and prove its completeness as the main result of the paper. Furthermore, decidability of T is shown, and its complexity is determined.


Modal Logic Canonical Model Logical Language Semantical Domain Cantor Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Bernhard Heinemann
    • 1
  1. 1.FernUniversitätHagenGermany

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