A Modal Logic for Cantorian Subset Spaces
Based on a modification of Moss' and PARIKH 's topological modal language [MP], we generalize a weakly expressive fragment of propositional branching time logic. To be more precise, we restrict ourselves on binary branching. We define a trimodal logic comprising a knowledge - operator and two nexttime - operators. These operators are mterpreted in Cantorian subset spaces, which are generalizations of the well-known Cantor space of all infinite O - 1 - sequences. We present an axiomatization of the set T of theorems valid for this dass of semantical domains and prove - as the main result of the present paper - its completeness. Moreover, decidability of T is shown.
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