Given the above procedures for computing , , , , , and , one can now define a procedure for computing . This procedure takes a model M along with an event-logic expression and computes a set of normalized spanning intervals that represents the set I of intervals for which is true. The model M is a set of atomic event-occurrence formulae of the form , where is a ground primitive event-logic expression and is a normalized spanning interval. A model entry indicates that the primitive event occurred during all intervals in the extension of .
The procedure performs structural induction on . It computes a set of normalized spanning intervals to the represent the occurrence of each atomic event-logic expression in and recursively combines the sets so computed for each child subexpression to yield the sets for each parent subexpression. An important property of this inference procedure is that for any finite model M, , the set I of intervals for which is true, can be represented by a finite set of normalized spanning intervals. Nominally, the number of normalized spanning intervals in can be exponential in the subexpression depth of because each step in the structural induction can introduce a constant factor growth in the size of the set. However, in practice, such exponential growth does not occur. Computing for all of the event types given in Figure 10 for all of the movies that have been tried so far have yielded sets of fewer than a dozen normalized spanning intervals.