Conceptual graphs and first-order logic

Wermelinger, Michel (1995). Conceptual graphs and first-order logic. In: Conceptual Structures: Applications, Implementation and Theory: Third International Conference on Conceptual Structures, ICCS '95 Santa Cruz, CA, USA, August 14–18, 1995 Proceedings, Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence), Springer, pp. 323–337.

DOI: https://doi.org/10.1007/3-540-60161-9_47

Abstract

Conceptual Structures (CS) Theory is a logic-based knowledge representation formalism. To show that conceptual graphs have the power of first-order logic, it is necessary to have a mapping between both formalisms. A proof system, i.e. axioms and inference rules, for conceptual graphs is also useful. It must be sound (no false statement is derived from a true one) and complete (all possible tautologies can be derived from the axioms). This paper shows that Sowa's original definition of the mapping is incomplete, incorrect, inconsistent, and unintuitive, and the proof system is incomplete too. To overcome these problems a new translation algorithm is given and a complete proof system is presented. Furthermore, the framework is extended for higher-order types.