We develop, analyze, and evaluate a novel, supervised, specific-to-general learner for a simple temporal logic and use the resulting algorithm to learn visual event definitions from video sequences. First, we introduce a simple, propositional, temporal, event-description language called AMA that is sufficiently expressive to represent many events yet sufficiently restrictive to support learning. We then give algorithms, along with lower and upper complexity bounds, for the subsumption and generalization problems for AMA formulas. We present a positive-examples-only specific-to-general learning method based on these algorithms. We also present a polynomialtime-computable "syntactic" subsumption test that implies semantic subsumption without being equivalent to it. A generalization algorithm based on syntactic subsumption can be used in place of semantic generalization to improve the asymptotic complexity of the resulting learning algorithm. Finally, we apply this algorithm to the task of learning relational event definitions from video and show that it yields definitions that are competitive with hand-coded ones.1. In our formal analysis, we will use two different notions of generality (semantic and syntactic). In this section, we ignore such distinctions. We note, however, that the algorithm we informally describe later in this section is based on the syntactic notion of generality. each timeline of © ¼ subsumes ©. This implies © © ¼ . ¾We can now characterize the AMA LGG using IS and IG.Theorem 14. IG´Ë ©¾¦ IS´©µµ is an AMA LGG of the set ¦ of AMA formulas.Proof: Let ¦ © ½ © Ò and © ½ ¡ ¡ ¡ © Ò . We know that the AMA LGG of ¦ must subsume , or it would fail to subsume one of the © . Using "and-to-or" we can represent as a disjunction of MA timelines given by ´Ï IS´© ½ µµ ¡ ¡ ¡ ´Ï IS´© Ò µµ. Any AMALGG must be a least-general formula that subsumes -i.e., an AMA LGG of the set of MA timelines Ë IS´©µ © ¾ ¦ . Theorem 13 tells us that an LGG of these timelines is given by IG´Ë IS´©µ © ¾ ¦ µ. ¾ 9. There must be at least one such timeline, the timeline where the only state is ØÖÙ © ½ ℄ syn © ¾ ℄µ. Using this property, it is straightforward to show how to compute the syntactic AMA LGG using the syntactic AMA LGG algorithm.Proposition 28. For any AMA formulas © ½ © Ñ , let © be the syntactic AMA LGG of © ½ ℄ © Ñ ℄ . Then, ½ ©℄ is the unique syntactic AMA LGG of © ½ © Ñ .Proof: We know that for each , © ℄ syn ©-thus, since ½ preserves syntactic subsumption, we have that for each , © syn ½ ©℄. This shows that ½ ©℄ is a generalization of the inputs.We now show that ½ ©℄ is the least such formula. For the sake of contradiction assume that ½ ©℄ is not least. It follows that there must be a © ¼ ¾ AMA such that © ¼ ×ÝÒ ½ ©℄ and for each , © syn © ¼ . Combining this with the fact that preserves syntactic subsumption, we get that © ¼ ℄ ×ÝÒ © and for each , © ℄ © ¼ ℄. But this contradicts the fact that © is an LGG; so we must have that ½ ©℄ is a syntactic AMA LGG. As argued elsewhere, the uniqueness of this LGG follows from the f...