Resolution graphs

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Abstract

This paper introduces a new notation, called “resolution graphs”, for deductions by resolution in first-order predicate calculus. A resolution graph consists of groups of nodes that represent initial clauses of a deduction and links that represent unifying substitutions. Each such graph uniquely represents a resultant clause that can be deduced by certain alternative but equivalent sequences of resolution and factoring operations.

Resolution graphs are used to illustrate the significance of merges and tautologies in proofs by resolution. Finally, they provide a basis for proving the completeness of a proof strategy that combines the set of support, resolution with merging, linear format, and Loveland's subsumption conditions.

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Presently at Evans, Griffiths and Hart Inc., Lexington, Massachusetts.

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