Mechanical Theorem-Proving by Model Elimination

Author:

Loveland Donald W.1

Affiliation:

1. Mathematics and Computer Science Departments, Carnegie-Mellon University, Pittsburgh, Pa and New York University, New York

Abstract

A proof procedure based on a theorem of Herbrand and utilizing the matching technique of Prawitz is presented. In general, Herbrand-type proof procedures proceed by generating over increasing numbers of candidates for the truth-functionally contradictory statement the procedures seek. A trial is successful when some candidate is in fact a contradictory statement. In procedures to date the number of candidates developed before a contradictory statement is found (if one is found) varies roughly exponentially with the size of the contradictory statement. (“Size” might be measured by the number of clauses in the conjunctive normal form of the contradictory statement.) Although basically subject to the same rate of growth, the procedure introduced here attempts to drastically trim the number of candidates at an intermediate level of development. This is done by retaining beyond a certain level only candidates already “partially contradictory.” The major task usually is finding the partially contradictory sets. However, the number of candidate sets required to find these subsets of the contradictory set is generally much smaller than the number required to find the full contradictory set.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Reference8 articles.

1. CHINLUND T. DAVIS M. HTINMAN P . AND MCILROY M. D. Theorem-proving by matching. Submitted for publication. CHINLUND T. DAVIS M. HTINMAN P . AND MCILROY M. D. Theorem-proving by matching. Submitted for publication.

2. ELiminating the irrelevant from mechanical proofs;DA;Proc. Syrup. Appl. Math.,1963

3. A Semi-Decision Procedure for the Functional Calculus

4. An improved proof procedure;PRAWITZ D;Theoria,1960

5. A proof procedure for quantification theory;QUINE W.V;J. Symbolic Logic,1955

Cited by 132 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Subsumption-Linear Q-Resolution for QBF Theorem Proving;Logic, Language, Information, and Computation;2023

2. Eliminating Models During Model Elimination;Lecture Notes in Computer Science;2021

3. Machine Learning Guidance for Connection Tableaux;Journal of Automated Reasoning;2020-09-05

4. From Schütte’s Formal Systems to Modern Automated Deduction;The Legacy of Kurt Schütte;2020

5. Advances in Connection-Based Automated Theorem Proving;NASA Monographs in Systems and Software Engineering;2017

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3