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A pragmatic approach to resolution-based theorem proving

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Abstract

Resolution theory offers a simple, complete method for proving theorems but is generally considered impractical. The theorems we are interested in proving arise in the analysis of programs and usually involve quantification. We have developed a system for proving these theorems using resolution, but have embedded in it a simplifier as the central component. The simplifier is an integrated collection of algorithms for normalizing arithmetic, relational, and logical expressions. The knowledge in the simplifier is encoded in procedures, rather than as axioms or rules. We use the simplifier to prove certain theorems, reduce the clutter in theorems, and reduce the cost of unification, Inherent in the normal form algorithms is the notion of strengthening (e.g., inferringa =b froma ⩽ b ANDb ⩽ a). We have incorporated the notion into the unification algorithm as well. The design of the system permits its use along a spectrum from pure resolution to resolution with interpretation of the arithmetic and relational operators. Strengthening is a heuristic that permits the movement along this spectrum. We call the approachi-resolution.i-resolution does not preserve completeness; it does define a means for approaching completeness efficiently and systematically. It thus attempts to provide a pragmatic approach to mechanical theorem proving.

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  1. Center for Research in Computing Technology, Harvard University, 02138, Cambridge, Massachusetts

    Judy A. Townley

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  1. Judy A. Townley
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Townley, J.A. A pragmatic approach to resolution-based theorem proving. International Journal of Computer and Information Sciences 9, 93–116 (1980). https://doi.org/10.1007/BF00982291

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