Carving Up Space: Existential Axioms for a Formal Theory of Spatial Regions
In this paper I investigate how one might arrive at a set of existential axioms that would specify a complete 1st-order theory of spatial regions. In such a theory all formulae would be true or false (given that constants are taken as existentially quantiied with widest scope). The RCC spatial logic based on the relation of connectedness, C, will be taken as the starting point. This theory is not complete, since it does not guarantee the realisation of all possible conngurations of regions. By adding extra existential axioms one would aim to ensure that the existence of any possible connguration is entailed by the theory. Thus the ontology of the theory would be strengthened from being relative to contingent facts (asserted in conjunction with the theory) to an absolute ontology characterising the domain of spatial regions as having a speciic structure. This is only an exploratory paper. I do not attempt to give an axiom set but only to shed some light on fundamental principles and problems relating to existential axioms in a spatial theory. I suggest a method of eliciting such axioms by considering the operations involved in constructing diagrams illustrating possible conngurations of regions.