Planning and model checking are similar in concept. They both deal with reaching a goal state from an initial state by applying specified rules that allow for the transition from one state to another. Exploring the relationship between them is an interesting new research area. We are interested in planning frameworks that combine both planning and scheduling. For that, we focus our attention on real time model checking. As a first step, we developed a mapping from planning domain models into timed automata. Since timed automata are the representation structure of real-time model checkers, we are able to exploit what model checking has to offer for planning domains. We present the mapping algorithm, which involves translating temporal specifications into timed automata, and list some of the planning domain questions someone can answer by using model checking.

A number of reasoning problems involving the manipulation of temporal information can naturally be viewed as implicitly inducing an ordering of potential local decisions involving time (specifically, associated with durations or orderings of events) on the basis of preferences. For example, a pair of events might be constrained to occur in a certain order and, in addition, it might be preferable that the delay between the start times of each of them be as large, or as small, as possible. Sometimes, however, it is more natural to view preferences as something initially ascribed to complete solutions to temporal reasoning problems, rather than to local decisions. For example, in classical scheduling problems, the preference for solutions which minimize makespan is a global, rather than a local, condition. In such cases, it might be useful to learn the local preferences that contribute to globally preferred solutions. This information could be used in heuristics to guide the solver to more promising solutions. To address the potential requirement for information about local preferences, we propose to apply learning techniques to infer local preferences from global ones. The preliminary work proposes an approach based on the notion of learning a set of soft temporal constraints, given a training set of solutions to a Temporal CSP, and an objective function for evaluating each solution in the set.

Effective manipulation of temporal information about periodic events is required for solving complex problems such as long‐range scheduling or querying temporal information. Furthermore, many problems involving repeating events involve the optimization of temporal aspects of these events (e.g., minimizing make‐span in job‐shop scheduling). In this paper, a constraint‐based formulation of reasoning problems with repeating events is presented, and its complexity is analyzed for a range of problems. Optimization constraints are interpreted formally using the Semiring CSPs (SCSP) representation of optimization in constraint reasoning. This allows for familiar algorithms such as branch‐and‐bound to be applied to solving them.

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.

Traditional interval-based representations of time assume interval convexity, i.e., that intervals are uninterrupted. This assumption makes it difficult to represent the common sense notion of a single event with ‘gaps’. Having a representation of this species of event contributes favorably to the ability of the human or machine to solve certain tasks, such as planning or database retrieval. This paper defines two kinds of discourse and knowledge object which comprise collections of convex intervals. Although other researchers have suggested the need for a relaxation of the assumption of convexity in event representation, there has been no attempt to offer a concise representation of gapped events. The formulation employed here to introduce gapped events is an extension of James Allen's interval-based approach to time representation. Allen's calculus of thirteen binary relations defined between two convex intervals is generalized to a matrix of binary relations between each pair of subintervals of pairs of non-convex intervals. A primary goal of this paper is to show that this extension of the interval-based approach increases the expressive power of the calculus, while retaining its computational advantages.