
Summary: We give a probabilistic interpretation of first-order formulas based on Valiant's model of pac-learning. We study the resulting notion of probabilistic or approximate truth and take some first steps in developing its model theory. In particular we show that every fixed error parameter determining the precision of universal quantification gives rise to a different class of tautologies. Finally we study the inductive inference of first-order formulas from atomic truths.
approximate truth, inductive inference of first-order formulas from atomic truths, Learning and adaptive systems in artificial intelligence, pac-learning, probabilistic logic, Probability and inductive logic
approximate truth, inductive inference of first-order formulas from atomic truths, Learning and adaptive systems in artificial intelligence, pac-learning, probabilistic logic, Probability and inductive logic
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