Complexity of resolution proofs and function introduction

Annals of Pure and Applied Logic 57 (3):181-215 (1992)
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Abstract

The length of resolution proofs is investigated, relative to the model-theoretic measure of Herband complexity. A concept of resolution deduction is introduced which is somewhat more general than the classical concepts. It is shown that proof complexity is exponential in terms of Herband complexity and that this bound is tight. The concept of R-deduction is extended to FR-deduction, where, besides resolution, a function introduction rule is allowed. As an example, consider the clause P Q: conclude P) Q, where a, f are new function symbols extending Herbrand's universe. P ()Q from Q) and Skolemization). By modification of a construction of Statman it is shown that FR-deductions may be nonelementarily shorter than R-deductions . Finally it is proved that FR-deduction has weaker effects only if clausal logic is restricted to Horn logic

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Citations of this work

Proof Theory of Finite-valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
A Resolution Calculus For Shortening Proofs.Nicolas Peltier - 2005 - Logic Journal of the IGPL 13 (3):307-333.

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References found in this work

A Machine-Oriented Logic based on the Resolution Principle.J. A. Robinson - 1966 - Journal of Symbolic Logic 31 (3):515-516.
A Computing Procedure for Quantification Theory.Martin Davis & Hilary Putnam - 1966 - Journal of Symbolic Logic 31 (1):125-126.
On Different Concepts of Resolution.Alexander Leitsch - 1989 - Mathematical Logic Quarterly 35 (1):71-77.
On Different Concepts of Resolution.Alexander Leitsch - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (1):71-77.

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