Paper Info
Title
Automated reasoning contributes to mathematics and logic
Abstract
In this article, we present some results of our research focusing on the use of our newest automated reasoning program OTTER to prove theorems from Robbins algebra, equivalential calculus, implicational calculus, combinatory logic, and finite semigroups. Included among the results are answers to open questions and new shorter and less complex proofs to known theorems. To obtain these results, we relied upon our usual paradigm, which heavily emphasizes the role of demodulation, subsumption, set of support, weighting, paramodulation, hyperresolution, and UR-resolution. Our position is that all of these components are essential, even though we can shed little light on the relative importance of each, the coupling of the various components, and the metarules for making the most effective choices. Indeed, without these components, a program will too often offer inadequate control over the redundancy and irrelevancy of deduced information. We include experimental evidence to support our position, examples producing success when the paradigm is employed, and examples producing failure when it is not. In addition to providing evidence that automated reasoning has made contributions to both mathematics and logic, the theorems we discuss also serve nicely as challenge problems for testing the merits of a new idea or a new program and provide interesting examples for comparing different paradigms.
Year
DOI
Venue
1990
10.1007/3-540-52885-7_109
CADE
Keywords
Field
DocType
automated reasoning,artificial intelligent
Automated reasoning,Combinatory logic,Computer science,Robbins algebra,Algorithm,Automation,Mathematical proof,Boolean algebra,Rule of inference,Mathematical logic
Conference
Volume
ISBN
Citations 
449
0-387-52885-7
18
PageRank 
References 
Authors
3.53
6
7
Name
Order
Citations
PageRank
L Wos111529.69
S Winker27924.44
William McCune315045.05
Ross A. Overbeek428138.97
E Lusk5277.71
R. Stevens6194.22
Rick L. Stevens71327135.40