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The predicate elimination strategy in theorem proving

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Raymond ReiterAuthors Info & Claims

STOC '70: Proceedings of the second annual ACM symposium on Theory of computing

Pages 180 - 183

https://doi.org/10.1145/800161.805163

Published: 04 May 1970 Publication History

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Abstract

The predicate elimination strategy is a complete resolution proof strategy for multi-predicate formulas. Essentially, the procedure focuses on one of the predicate symbols P, and attempts to deduce clauses independent of P by means of resolution in which only predicates in P are “resolved away” from parent clauses. The completeness theorem states that one can in this way, deduce an unsatisfiable P-independent set of clauses, provided the given set is unsatisfiable.

The strategy is then extended to a suitable form of semantic resolution. This leads to the following strategy: in the attempt to deduce an unsatisfiable P-independent set of clauses, apply elementary resolution to “resolve away” predicates in P only from parent clauses, one of which has all of its predicates in P positive (negative).

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Friedman, J., A new decision procedure in logic with a computer realization. Ph.D. Thesis, Harvard University, 1964.

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Green, C. C., Theorem proving by resolution as a basis for question-answering systems, Machine Intelligence 4, D. Michie and B. Meltzer, Eds. (Edinburgh University Press, Edinburgh, Scotland, 1969).

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Loveland, D. W., Mechanical theorem-proving by model elimination. JACM, 15 (1968), pp. 236-251.

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Luckham, D., Some tree paring strategies for theorem proving, Machine Intelligence 3, D. Michie ed., Edinburgh University Press, 1968, pp. 95-112.

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Cited By

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Kaushik SWinsborough WWijesekera DAmmann P(2006)Policy Transformations for Preventing Leakage of Sensitive Information in Email Systems20th Annual IFIP WG 11.3 Working Conference on Data and Applications Security on Data and Applications Security XX - Volume 412710.5555/3127142.3127154(163-178)Online publication date: 31-Jul-2006
https://dl.acm.org/doi/10.5555/3127142.3127154
Kaushik SWinsborough WWijesekera DAmmann P(2006)Policy Transformations for Preventing Leakage of Sensitive Information in Email SystemsData and Applications Security XX10.1007/11805588_12(163-178)Online publication date: 2006
https://doi.org/10.1007/11805588_12
Gelperin D(1976)A Resolution-Based Proof Procedure Using Deletion-Directed SearchIEEE Transactions on Computers10.1109/TC.1976.167461225:4(323-327)Online publication date: 1-Apr-1976
https://dl.acm.org/doi/10.1109/TC.1976.1674612
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Index Terms

The predicate elimination strategy in theorem proving
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Theorem proving algorithms
2. Theory of computation
  1. Logic
  2. Models of computation
    1. Computability

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Published In

STOC '70: Proceedings of the second annual ACM symposium on Theory of computing

May 1970

234 pages

ISBN:9781450374699

DOI:10.1145/800161

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 04 May 1970

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STOC '70 Paper Acceptance Rate 27 of 70 submissions, 39%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Kaushik SWinsborough WWijesekera DAmmann P(2006)Policy Transformations for Preventing Leakage of Sensitive Information in Email Systems20th Annual IFIP WG 11.3 Working Conference on Data and Applications Security on Data and Applications Security XX - Volume 412710.5555/3127142.3127154(163-178)Online publication date: 31-Jul-2006
https://dl.acm.org/doi/10.5555/3127142.3127154
Kaushik SWinsborough WWijesekera DAmmann P(2006)Policy Transformations for Preventing Leakage of Sensitive Information in Email SystemsData and Applications Security XX10.1007/11805588_12(163-178)Online publication date: 2006
https://doi.org/10.1007/11805588_12
Gelperin D(1976)A Resolution-Based Proof Procedure Using Deletion-Directed SearchIEEE Transactions on Computers10.1109/TC.1976.167461225:4(323-327)Online publication date: 1-Apr-1976
https://dl.acm.org/doi/10.1109/TC.1976.1674612
PIROTTE A(1974)Automatic Theorem Proving Based on ResolutionComputer Science and Technology and their Application10.1016/B978-0-08-017806-6.50009-2(201-266)Online publication date: 1974
https://doi.org/10.1016/B978-0-08-017806-6.50009-2
Gelperin D(1973)Deletion-directed search in resolution-based proof proceduresProceedings of the 3rd international joint conference on Artificial intelligence10.5555/1624775.1624782(47-50)Online publication date: 20-Aug-1973
https://dl.acm.org/doi/10.5555/1624775.1624782

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An Intuitionistic Completeness Theorem for Classical Predicate Logic