A spectrum of applications of automated reasoning.
The likelihood of an automated reasoning program being of substantial assistance for a wide spectrum of applications rests with the nature of the options and parameters it offers on which to base needed strategies and methodologies. This article focuses on such a spectrum, featuring W. McCune's program OTTER, discussing widely varied successes in answering open questions, and touching on some of the strategies and methodologies that played a key role. The applications include finding a first proof, discovering single axioms, locating improved axiom systems, and simplifying existing proofs. The last application is directly pertinent to the recently found (by R. Thiele) Hilbert's twenty-fourth problem--which is extremely amenable to attack with the appropriate automated reasoning program, a problem concerned with proof simplification. The methodologies include those for seeking shorter proofs and for finding proofs that avoid unwanted lemmas or classes of term, a specific option for seeking proofs with smaller equational or formula complexity, and a different option to address the variable richness of a proof. The type of proof one obtains with the use of OTTER is Hilbert-style axiomatic, including details that permit one sometimes to gain new insights. We include questions still open and challenges that merit consideration.
- Research Organization:
- Argonne National Lab., IL (US)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- W-31-109-ENG-38
- OSTI ID:
- 793070
- Report Number(s):
- ANL/MCS/CP-106778; TRN: US200206%%204
- Resource Relation:
- Conference: 2002 AMS and MAA Spring Southeastern Section Meeting, Atlanta, GA (US), 03/08/2002--03/10/2002; Other Information: PBD: 1 Feb 2002
- Country of Publication:
- United States
- Language:
- English
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