TOWARDS AN ONTOLOGICAL THEORY OF PHYSICAL OBJECTS Stefano Borgo, Nicola Guarino, and Claudio Masolo National Research Council, LADSEB-CNR Corso Stati Uniti, 4 - I-35127 Padova, Italy guarino@ladseb.pd.cnr.it ABSTRACT We present a logical theory based on a fundamental distinc- tion between objects and their substrates, i.e. chunks of mat- ter and regions of space, whose purpose is to establish the basis of a general ontology of space, matter and physical objects for the domain of mechanical artifacts. An extensio- nal mereological framework is assumed for substrates, while physical objects are allowed to change their spatial and ma- terial substrate while keeping their identity. Besides the parthood relation, simple self-connected regions and con- gruence are adopted as primitives for the description of spa- ce. Only tridimensional regions are assumed in the domain. 1. INTRODUCTION Many knowledge based systems applied in the automation of engineering tasks require explicit models of mechanical ar- tifacts. Such models are often developed with a specific task in mind, and therefore only the relevant knowledge is repre- sented. However, the high costs associated to their de- velopment motivate the introduction of general, task-inde- pendent ontologies, suitable to support very basic kinds of reasoning like those related to space, matter, time, or units of measure [20]. In this case, it is important to make explicit the ontological assumptions underlying the primitives a- dopted, restricting their possible interpretations in such a way to exclude (at least some) non-intended models [12]. The aim of this paper is to introduce and characterize, by means of logical axioms, the basic ontological distinctions needed to reason about physical objects. In our opinion, such dis- tinctions should account for the following intuitions: • Physical objects are located in space, can move across space; when an object moves, it occupies a different re- gion of space. So the space occupied by an object is dif- ferent from the object itself. • Most physical objects are made of matter, but this matter is different from the object itself: when a gold ring is melted to form a kettle, a new object is created out of the same matter, and the previous object is destroyed. • Some physical objects are immaterial (like a hole), but still they do not coincide with the space they occupy [4]. • The prominent way to explore and perceive space is by filling (or covering) it with matter. Hence points do not seem to be parts of space: we often refer to corners, edges and surfaces as if they were physical bodies [25]. The main position we take in this paper regards the dis- tinction between objects and their substrates, i.e. the space they occupy and the matter they are made of. The reason of this distinction lies in the different identity criteria of the entities involved. Consider for instance the gold ring in the example above: we recognize its concrete existence in a given situation on the basis of certain properties, like hav- ing a certain form and dimension, being made of a certain material, and so on. By verifying the satisfaction of these properties we are also able to recognize the same ring in an- other situation, where maybe its spatial location has changed or even a tiny piece has been lost. On the other hand, when focusing our attention on the matter the ring is made of, we shall use different criteria to recognize the existence of that particular amount of matter, which will be the same as long as no piece of it is removed independently of any properties regarding shape, physical integrity and so on. The formal characterisation of identity criteria for enti- ties like artifacts is notoriously a very difficult problem [28,23]. Specifically, functional properties are often in- cluded in such criteria. We don’t attempt here an ontological analysis of functional properties (which are often task- dependent), limiting ourselves to the properties of objects bound to their spatio-material configuration: that is, the mereo-topological and morphological properties of the re- gion they occupy, and the mereological properties of the matter they are composed of. In the following, we present a logical theory 1 based on a fundamental distinction between objects, chunks of matter and regions of space, whose purpose is to establish the basis of a general ontology of space, matter and physical objects, to be mainly used in the domain of mechanical artifacts. Such a theory is an ontological theory, in the sense dis- cussed in [13]. It is a rich theory in terms of axioms and definitions (in the spirit of [14]), since its main purpose is to convey meaning, in such a way as to characterize unambi- guously the intended models of a logical vocabulary suitable to be used in concrete applications; it is not intended there- fore to be directly implemented in a reasoning system. In the next section we discuss the general assumptions underlying our approach; in Section 3 we introduce the common mereological framework adopted for space and mat- ter, while in Section 4 we present our axiomatic chara- cterization of space, innovative in many points with respect to theories adopting the topological connection ‘C’ as a primitive [21,1]; in section 5 we introduce objects as a fur- ther subdomain, and discuss the various relations holding between objects, matter, and space; finally, in section 6 we show how various useful ontological distinctions among physical objects can be made within our framework. 2. GENERAL A SSUMPTIONS According to the principles discussed above, our basic as- sumption is a sharp distinction between physical objects and their substrates. The simplified world we have in mind i s characterised by the concrete existence of a certain quantity of matter (all of the same kind), that can assume different configurations within a given tridimensional space. We limit ourselves to the properties of physical objects bound to their spatio-material configuration, assuming that an ob- ject can be described by the set of its admittable spatio- material configurations. A particular solid cube, for in- stance, may be described by the class of all (roughly) cube- 1 As costumary in AI, a logical theory is intended here as a set of logical axioms closed under formal deduction.