We study the problem of supervised learning of event classes in a simple temporal event-description language. We give lower and upper bounds and algorithms for the subsumption and generalization problems for two expressively powerful subsets of this logic, and present a positive-examples-only specific-to-general learning method based onthe resulting algorithms. We also present a polynomial-time 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. A companion paper shows that our methods can be applied to duplicate the performance of human-coded concepts in the substantial application domain of video event recognition.