Man-machine theorem proving in graph theory

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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.

References (23)

  • Cvetković, D., Jovanović, M. and Kraus, L., Discussing graph theory with a computer, V: Graph theory bibliography...
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      In the last two decades, several systems have been designed for computer-aided or automated discovery of conjectures in graph theory, and assistance in construction of proofs. Some of them have been applied already to chemistry, and amongst the most successful of these are GRAPH [5,6], which makes rapid computations of graph invariants, and updates them interactively, and Graffiti[7,8] which generates large numbers of simple relations between graph invariants, then eliminates those refuted by data-base examples or judged uninteresting against various criteria. AutoGraphiX [9] is a system based upon a different principle.

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