Man-Machine Theorem Proving in Graph Theory

Abstract The interactive programming system GRAPH for the classification and extension of knowledge in the field of graph theory has been implemented during the period 1980–1984 at the University of Belgrade, Faculty of Electrical Engineering. The system consists of a computerized graph theory bibliography, a system for graph theoretic algorithms and a mechanical theorem prover. This paper describes the theorem prover of the system at a conceptual level and reports first experiences with this system. Important characteristics of the prover are: a special formalization of graph theory, a new way of handling definition instantiations and rewriting by lemmas, and the possibility of using graph theoretic algorithms to test the validity of subgoals on concrete graphs. A complexity measure of a formula is introduced to help the selection of a proper definition or lemma.