Allen's Calculus Research Articles

On the Relevance of Conceptual Spaces for Spatial and Temporal Reasoning

This paper argues for the use of conceptual spaces in qualitative spatial and temporal reasoning. Conceptual spaces provide a natural framework for enriching the purely combinatorial and symbolic calculi such as Allen's calculus with a geometrical or topological structure. Recent work has shown that such enrichments are useful, since they provide simpler ways of characterizing tractable subclasses of the calculi. Hence part of the computational properties can be related to geometrical properties. The paper discusses a family of calculi (including Allen's calculus) for which substantial results have been obtained using this approach. It then examines other instances of calculi where the relationship has not yet been fully investigated and lists the main open questions which arise in this context.

Spatial and temporal reasoning: beyond Allen's calculus

Many formalisms for qualitative spatial and temporal reasoning fit into a pattern exemplified by Allen's temporal interval calculus. Constraint-based reasoning using Allen's calculus can benefit fr...

Spatial and temporal reasoning

Many formalisms for qualitative spatial and temporal reasoning fit into a pattern exemplified by Allen's temporal interval calculus. Constraint-based reasoning using Allen's calculus can benefit fr...

Solving hard qualitative temporal reasoning problems: Evaluating the efficiency of using the ORD-Horn class

While the worst-case computational properties of Allen's calculus for qualitative temporal reasoning have been analyzed quite extensively, the determination of the empirical efficiency of algorithms for solving the consistency problem in this calculus has received only little research attention. In this paper, we will demonstrate that using the ORD-Horn class in Ladkin and Reinefeld's backtracking algorithm leads to performance improvements when deciding consistency of hard instances in Allen's calculus. For this purpose, we prove that Ladkin and Reinefeld's algorithm is complete when using the ORD-Horn class, we identify phase transition regions of the reasoning problem, and compare the improvements of ORD-Horn with other heuristic methods when applied to instances in the phase transition region. Finally, we give evidence that combining search methods orthogonally can dramatically improve the performance of the backtracking algorithm.

An interval-based temporal relational calculus for events with gaps

Abstract 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 o...