Basic Conceptual Structures Theory

Although the theory of Conceptual Structures is over 10 years old, basic notions (like canonical graphs) are far from settled and are subject to constant extensions and refor-mulations. However, most of these are done in an informal way, which doesn't help in clarifying the issues involved. It is our hope that this paper will provide a rst step towards the complete and rigorous account of Conceptual Structures (CS) Theory, which is needed for ongoing standardization and implementation eeorts. Towards that goal, we present formal deenitions of some of the central notions of CS theory (type, referent, concept, relation, conceptual graph, canonical formation rules, canon, and canonical graph) in its simplest form, i.e. no contexts nor coreference links are allowed and referents must be individuals. We thereby introduce higher-order types in order to enable the use of conceptual graphs at the metalevel, the restriction operation of the canonical formation rules is extended to make use of the relation hierarchy, we show the relationship between denotation and conformity relation, and we give a rigorous meaning to the canonical basis, among other things.