Concept Types and Coreference in Simple Conceptual Graphs

This paper tackles the question of representing and reasoning with types and coreference in simple conceptual graphs (SGs). It presents a framework integrating a number of previous works. This proposal is guided by the usability of CGs in practice. In other words, notions should be easy to use in knowledge representation and operations for doing reasoning have to be efficiently realizable. We propose to use conjunctive concept types, which are conjunctions of primitive types. The conjunctive concept type set is defined by means of a primitive type set and a set of banned conjunctive types. For efficiency reasons our framework is based on projection. However it has been shown that projection is complete (w.r.t. logical deduction) only when SGs are in normal form. In some situations the original form of the SGs has to be kept; we thus define an extension of projection, called coref-projection, which is complete for SGs of any form. Coref-projection is in particular suitable for frameworks where it is not assumed that coreferent nodes are mergeable.