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Prediction in Branching Time Logic
Author(s) -
Bonanno Giacomo
Publication year - 2001
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200105)47:2<239::aid-malq239>3.0.co;2-r
Subject(s) - mathematics , consistency (knowledge bases) , branching (polymer chemistry) , moment (physics) , binary number , path (computing) , discrete mathematics , computer science , arithmetic , physics , materials science , classical mechanics , composite material , programming language
When we make a prediction we select, among the conceivable future descriptions of the world, those that appear to us to be most plausible. We capture this by means of two binary relations, ≺ c and ≺ p : if t 1 and t 2 are points in time, we interpret t 1 ≺ c t 2 as sayingthat t 2 is in the conceivable future of t 1 , while t 1 ≺ p t 2 is interpreted to mean that t 2 isin the predicted future of t 1 . Within a branching‐time framework we propose the following notion of “consistency of prediction”. Suppose that at t 1 some future moment t 2 is predicted to occur, then (a) every moment t on the unique path from t 1 to t 2 should also be predicted at t 1 and (b) the prediction of t 2 should continue to hold at every such t . A sound and complete axiomatization is provided.