THE LOGIC OF PREDICTION

Giacomo Bonanno ()

Department of Economics from California Davis - Department of Economics

Abstract: When we make a non-trivial prediction about the future we select, among the conceivable future descriptions of the world, those that appear to us to be most likely. Within a branching-time framework we capture this by means of two binary relations, < c and < p. If t1 and t2 are different points in time, we interpret t1 < c t2 as saying that t2 is in the conceivable future of t1, while t1 < p t2 is interpreted to mean that t2 is in the predicted future of t1. We propose the following notion of "consistency of predictions." Suppose that at t1 some future moment t2 is predicted to occur, then (a) every moment t between t1 and t2 should also be predicted at t1 and (b) the prediction of t2 should continue to hold at every t between t1 and t2. We provide a sound and complete axiomatization for this notion of consistency.

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