Numerous examples of temporal reasoning involve a process of abstraction from the number of times an event is to occur or the number of times events stand in a temporal relation. For example, scheduling a recurring event such as one's office hours may consider things like the relative temporal ordering of the office hours and a number of other events in a given work day. The number of times office hours will actually be held may be unknown, even irrelevant, at the time of scheduling them. The objective of this article is to formulate a domain‐independent framework for reasoning about recurring events and their relations. To achieve this end, we propose an ontology of recurrence based on the model‐theoretic structure underlying collective predication using plural noun phrases. We offer a calculus of binary temporal relations for temporal collections based on a well‐defined transformation of interval temporal relations into recurrence relations. Finally, we describe a reasoning framework based on manipulating knowledge stored in temporal relation networks, which is in turn a specialization of the CSP (constraint satisfaction problem) framework. The reasoner manipulates recurrence relations in the network to determine the network's consistency or to generate scenarios.

Building planning systems that operate in real domains requires coping with both uncertainty and time pressure. This article describes a model of reaction plans, which are generated using a formalization of actions and of state descriptions in probabilistic logic, as a basis for anytime planning under uncertainty. the model has the following main features. At the action level, we handle incomplete and ambiguous domain information, and reason about alternative action effects whose probabilities are given. On this basis, we generate reaction plans that specify different courses of action, reflecting the domain uncertainty and alternative action effects; if generation time was insufficient, these plans may be left unfinished, but they can be reused, incrementally improved, and finished later. At the planning level, we develop a framework for measuring the quality of plans that takes domain uncertainty and probabilistic information into account using Markov chain theory; based on this framework, one can design anytime algorithms focusing on those parts of an unfinished plan first, whose completion promises the most “gain”. Finally, the plan quality can be updated during execution, according to additional information acquired, and can therefore be used for on-line planning. © 1995 John Wiley & Sons, Inc.