The Role of Definitions in Construction and Analysis of Formal Ontologies

Logical Formalization of Commonsense Reasoning

Volume

Papers from the 2003 AAAI Spring Symposium

Contents

In this paper I make the case that formal characterisation of large conceptual vocabularies does not require the specification of large numbers of axioms but can be carried out primarily 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 construction. I give some results that generalise Tarski’s definability theorem to make it applicable to a much broader class of theories. I consider what primitives are necessary to formulate a theory of the physical world and specify a definitional reduction of concepts relating to "matter" to purely geometrical concepts.