Understanding the semantics of conceptual graphs

In this paper, we propose a simple and well established semantics for conceptual graphs. This model theoretic semantics is an alternative to previous approaches, where a game theoretical semantics has been suggested. In addition to that, we thoroughly compare conceptual graphs with First Order Predicate Logic (FOPL). The comparison is based on semantics. Based on this comparison, we present some clarifying remarks on the semantics of conceptual graphs. The comparison of the expressive power of FOPL and conceptual graphs is carried out by a consideration of translation algorithms. John Sowa’s algorithm translates an arbitrary conceptual graph into a FOPL formula. The algorithm that we shall outline in this paper translates an arbitrary closed FOPL formula into a conceptual graph. On the basis of the algorithms, it can be claimed that the expressive power of conceptual graphs (with limited syntax) equals to that of a slightly limited FOPL. Without the syntactic limitations, the expressive power of conceptual graphs would probably exceed the expressive power of FOPL. We also provide a set of knowledge representation examples using both FOPL and conceptual graphs. The examples indicate that in some cases conceptual graph formalism is harder to read than FOPL.