Skip to main content
SpringerLink
Log in

Determination of the Class of Validity of Logical Formulas by Directed Exhaustive Search

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

An algorithm is described for the proof of satisfiability, general validity, and inconsistency of logical formulas. The algorithm is based on the method of directed exhaustive search for variants of truth values of variables.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. S. Yu. Maslov, “An inverse method of determination of deducibility in the classical predicate calculus,” Dokl. Akad. Nauk SSSR, Vol. 159, No. 1, 17-20 (1964).

    Google Scholar 

  2. N. A. Shanin, G. V. Davydov, S. Yu. Maslov, et al., An Algorithm of Machine Search for Natural Logical Inference in Propositional Calculus [in Russian], Nauka, Moscow-Leningrad (1965).

    Google Scholar 

  3. J. A. Robinson, “A machine-oriented logic based on the resolution principle,” J. ACM, 12, 25-41 (1965).

    Google Scholar 

  4. J. R. Slagle, “Automatic theorem proving with renaming and semantic resolution,” J. Assoc. Comput. Machinery, 14, No. 4, 687-697 (1967).

    Google Scholar 

  5. D. W. Loveland, “A linear format for resolution,” in: Proc. IRIA Symp. Automatic Demonstration, Springer, New York (1970), pp. 147-162.

    Google Scholar 

  6. R. Kowalski and D. Kuehner, “Linear resolution with selection function,” Artificial Intelligence, 2, 227-260 (1971).

    Google Scholar 

  7. V. N. Vagin, Deduction and Generalization in Decision-Making Systems [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  8. C. Chang and R. Lee, Mathematical Logic and Automatic Theorem Proving [Russian translation], Nauka, Moscow (1983).

    Google Scholar 

  9. H. Papadimitriu and K. Steiglitz, Combinatorial Optimization, Algorithms, and Complexity [Russian translation], Mir, Moscow (1985).

    Google Scholar 

  10. I. P. Pavlov, A. B. Litvinov, Ye. B. Misyura, et al., Constructive Polynomial Algorithms of Solution of Concrete NP-Complete Problems [in Russian], Tekhnika, Kiev (1993).

    Google Scholar 

  11. A. Ye. Litvinenko, “Method of solution of extremal combinatorial problems with nonlinear structure,” Kibernetika, No. 5, 83-85 (1983).

Download references

Author information

Authors and Affiliations

  1. National Aviation University, Kiev, Ukraine

    A. E. Litvinenko

Authors
  1. A. E. Litvinenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Litvinenko, A.E. Determination of the Class of Validity of Logical Formulas by Directed Exhaustive Search. Cybernetics and Systems Analysis 36, 652–658 (2000). https://doi.org/10.1023/A:1009468520734

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009468520734

Search

Navigation