Thesis Overview 1.1 Topic

The topic of this thesis is the study of computational complexity of temporal and spatial reasoning 1. Much of the work within the area of Artiicial Intelligence (and elsewhere) has been recognised as including the notions of time and space, naturally, since these are fundamental aspects of the real world. It is clear that capabilities of modelling and computing with facts about time and space will be needed for any reasonably exible system interacting with its environment. The areas of temporal and spatial reasoning in AI have developed from this recognition. In this thesis, the focus is on temporal reasoning, and the results on spatial reasoning can largely be considered as by-products of the research on temporal reasoning. Vila 1994] has written an overview of the general uses of temporal reasoning in AI. The thesis contributes to the problem of computing with temporal and spatial information, as opposed to the task of modelling temporal and spatial phenomena. The modelling problem consists of deciding what are the ideal primitive concepts and what is the appropriate formalism to use for a given application. Once it is decided how to model a class of phenomena, methods can be devised for computing facts given information expressed in the chosen formalism. Attacking the problem of computation certainly requires a choice of modelling formalism, and in order for the solutions to the computational problems to be relevant, here formalisms that are well established and uncontroversial have been used, at least for the temporal case, where the basis is Allen's interval algebra Allen, 1983], both in its original form and extended with constructs for expressing metric temporal information. For the spatial case, however, the modelling language used is the spatial algebra, RCC-5 Bennett, 1994], taken from the RCC approach to spatial reasoning Randell and Cohn, 1989; Randell et al., 1992b], about which there is still some controversy whether or when it correctly models spatial phenomena Lemon, 1996]. 1 Instead of temporal reasoning, sometimes the expression temporal constraint reasoning is used to distinguish the eld from that of reasoning about action, which deals with the problem of inferring what propositions hold at what time points when it is known that certain actions have been performed (see e.g. Sandewall, 1994] and paper V of this thesis). I think that this use is unfortunate, since in line with this, any reasoning task having a temporal component could be called temporal …