Antony Galton

A critical examination of Allen's theory of action and time

Abstract J.F. Allens theory of time and action is examined and found to be unsuitable for representing facts about continuous change. A series of revisions to Allens theory is proposed in order to accommodate this possibility. The principal revision is a diversification of the temporal ontology to include instants on the same footing as intervals; a distinction is also made between two kinds of property, called states of position and states of motion, with respect to the logic of their temporal incidence. As a consequence of these revisions, it is also found necessary to diversify the range of predicates specifying temporal location. Finally, it is argued that Allens category of processes is superfluous, since it can be assimilated with the category of properties. The implications of this assimilation for the representation of sentences containing verbs in the progressive aspect are discussed.

Fields and Objects in Space, Time, and Space-time

The well-known distinction between field-based and object-based approaches to spatial information is generalised to arbitrary locational frameworks, including in particular space, time and space-time. We systematically explore the different ways in which these approaches can be combined, and address the relative merits of a fully four-dimensional approach as against a more conventional ‘three-plus-one’-dimensional approach. We single out as especially interesting in this respect a class of phenomena, here called multiaspect phenomena, which seem to present different aspects when considered from different points of view. Such phenomena (e.g., floods, wildfires, processions) are proposed as the most natural candidates for treatment as fully four-dimensional entities (‘hyperobjects’), but it remains problematic how to model them so as to do justice to their multi-aspectual nature. The paper ends with a range of important researchable questions aimed at clearing up some of the difficulties raised.

Two Approaches to Event Definition

We compare two approaches to event definition, deriving from the Active Database and Knowledge Representation communities. We relate these approaches by taking a system of the former kind, displaying some of its shortcomings, and rectifying them by remodelling the system in the latter style. We further show the extent to which the original system can be recreated within the remodelled system. This bridge between the two approaches should provide a starting point for fruitful interaction between the two communities.

Towards a qualitative theory of movement

The phenomenon of movement arises whenever the same object occupies different positions in space at different times. Therefore a theory of movement must contain theories of time, space, objects, and position. We provide a theoretical basis for describing movement events in terms of the conditions for their occurrence, which refer to the holding or not holding of various positional fluents at different times. For this we need to bring together a formal model of time with a formal model of space. By attending closely to the constraints imposed by continuity on the temporal behaviour of different fluents we develop theory of dominance, which enables us to generate ab initio the perturbation relation on the full set of positional relations.

A unifying semantics for time and events

We give a formal semantics for a highly expressive language for representing temporal relationships and events. This language, which we call Versatile Event Logic (VEL), provides a general temporal ontology and semantics encompassing many other representations. The system incorporates a number of features that have not been widely employed in AI formalisms. It has the ability to describe alternative histories using a modal operator. It provides a semantics for individuals that explicitly models their identity through time and across alternative possible histories; and enables one to distinguish between necessary and extensional identity of individuals. In virtue of its treatment of individuals and count nouns, the formalism offers a solution to certain puzzles of identity, which arise when individuals are described in different ways. We propose that VEL can be used as a foundational interlingua for comparing and interfacing different AI languages and illustrate this by considering how Situation Calculus and Event Calculus can be represented within VEL.

The water falls but the waterfall does not fall: New perspectives on objects, processes and events

We challenge the widespread presumption that matter and objects are ontologically prior to processes and events, and also the less widespread but increasingly popular view that processes and events are ontologically prior to matter and objects. Instead we advance a third view according to which each of these pairs of categories is ontologically dependent on the other. In particular, taking a cue from an ontology of devices, we identify the object as an interface between those processes which are internal to it and those which are external to it and which it may be said to enact, thereby linking objects intrinsically to the processes in which they are involved as well as providing a more powerful determinant of object identity than more traditional, non-dynamic criteria based on demarcation from the environment. The internal processes are themselves external processes in relation to the components of the object which enact them, leading to a potentially open-ended recursive decomposition of both objects and processes in a complex web of mutual interdependency. We also discuss how matter is related to objects, and processes to events, bringing the four categories together in a diagram which clarifies the relations between them - often considered problematic - and establishes a framework for a highly general top-level ontology.

A generalized topological view of motion in discrete space

In several areas of Computer Science, one is interested in using abstract mathematical structures as a basis for modelling certain phenomena of the real world. This interest is particularly strong in the knowledge representation sub*eld of arti*cial intelligence (AI), and amongst the phenomena studied in this *eld, those concerned with time, space, motion, and change have enjoyed a special prominence over the last 20 years or so [2,4,16,18]. The standard approach to these phenomena in the natural sciences has always been to use the well-developed theory of functions over the real numbers as the most appropriate starting point. Time is regarded as isomorphic, in point of its ordering and metric properties, with the real line R, and n-dimensional space is likewise modelled as Rn. In the *eld of AI this approach has often been regarded as problematic on account of a perceived mismatch between the forms of representation and reasoning naturally arising from it and the forms employed in everyday qualitative thinking, which it is part of the purpose of AI to emulate. As a result of this, AI researchers have tended to espouse theories based on qualitative descriptions of the phenomena. In practice, this often means discrete rather than continuous descriptions, a typical approach being to describe the state of the world in terms of some small *nite set of possible situations collectively constituting a discrete space of qualitative possibilities. Motion and change are then described with respect to this discrete space [7]. Discrete phenomena have also been studied by researchers interested in formulating a systematic and rigorous theory of digital images [12,13,14]. This work has proceeded largely in isolation from the AI work mentioned above, but in recent years a certain rapprochement between the two areas has arisen as a result of a number of researchers’ beginning to explore the common ground between them [19,10]. In particular, it has become apparent that by generalizing certain topological notions it may be possible to provide a unifying framework within which all the disparate forms of discrete space that have engaged the attention of workers in these *elds may be described [17].

Operators vs. Arguments: The Ins and Outs of Reification

So-called ‘reified temporal logics’ were introduced by researchers in Artificial Intelligence (AI) in the early 1980s, and gave rise to a long-running series of debates concerning the proper way to represent states, events, causation, action, and other notions identified as crucial to the knowledge representation needs of AI. These debates never resulted in a definitive resolution of the issues under discussion, and indeed continue to produce aftershocks to the present day; none the less, we are now sufficiently far removed in time from their heyday for it to be a worthwhile exercise to stand back and review them as a connected piece of history.

Desiderata for a Spatio-temporal Geo-ontology

We survey the manifold variety of kinds of phenomena which come within the purview of geography and GI Science, and identify three key desiderata for a fully spatio-temporal geo-ontology which can do justice to those phenomena. Such a geo-ontology must (a) provide suitable forms of representation and manipulation to do justice to the rich network of interconnections between field-based and object-based views of the world; (b) extend the field-based and object-based views, and the forms of representation developed to handle them, into the temporal domain; and (c) provide a means to develop different views of spatio-temporal extents and the phenomena that inhabit them, especially with reference to those phenomena such as storms, floods, and wildfires which seem to present dual aspects as both object-like and process-like.

Space, Time, and Movement

Mathematical physics provides an exact, quantitative account of motion which has enabled us to send spacecraft to distant planets and to aim our missiles with deadly accuracy. It becomes unwieldy, perhaps even impotent, when dealing with less tidy situations such as the flow of traffic through the streets of a city, the movement of people about an office, or the procession of weather systems around the globe. The degree of idealization required even to describe these phenomena in mathematical terms inevitably leaves out many factors which are in fact instrumental in determining how they happen. In our everyday life, too, our predictive abilities are sorely limited, yet we have evolved a workable, and in some respects quite refined network of commonsense notions which enable us to get by most of the time. In disciplines such as philosophy and artificial intelligence (Davis, 1990; Hobbs and Moore, 1985) there is an intense interest in laying bare and systematising the conceptual schemes underlying our everyday competence in handling such notions as time, space, and movement, and this chapter is intended to contribute to that enterprise.