The Role of Definitions in Construction and Analysis of Formal Ontologies
Brandon Bennett · 2003
In this paper I make the case that formal characterisation of large conceptual vocabularies does not require the specifica-tion of large numbers of axioms but can be carried out pri-marily in terms of definitions. Axioms should be confined to describing the logical properties of a relatively small core of primitives. I examine some technical meta-logical notions and theorems relating to definitions and definability and show how these are relevant to the concerns of ontology construc-tion. I give some results that generalise Tarski’s definability theorem to make it applicable to a much broader class of the-ories. I consider what primitives are necessary to formulate a theory of the physical world and specify a definitional re-duction of concepts relating to ‘matter ’ to purely geometrical concepts.