BRANCHING-TIME LOGIC WITH QUANTIFICATION OVER BRANCHES - THE POINT-OF-VIEW OF MODAL LOGIC

In Ockhamist branching-time logic [Prior 67], formulas are meant to be evaluated on a specified branch, or history, passing through the mome nt at hand. The linguistic counterpart of the manifoldness of future i s a possibility operator which Is read as 'at some branch, or history (passing through the moment at hand)'. Both the bundled-trees semantic s [Burgess 79] and the (moment, history) semantics [Thomason 84] for t he possibility operator involve a quantification over sets of moments. The Ockhamist frames are (3-modal) Kripke structures in which this se cond-order quantification is represented by a first-order quantificati on. The aim of the present paper is to investigate the notions of moda l definability, validity, and axiomatizability concerning 3-modal fram es which can be viewed as generalizations of Ockhamist frames.