Skip to main content
Log in

CLIN-E - Smallest Instance First Hyper-Linking

  • Published:
Journal of Automated Reasoning Aims and scope Submit manuscript

Abstract

Hyper-linking is an instance-based automated theorem proving strategy that uses unification to generate instances of the input clauses. Lee implemented hyper-linking in the automated theorem prover CLIN, which uses a breadth-first strategy for generating instances of clauses via the hyper-link operation. In attempting to add equality support to CLIN, a number of inefficiencies with Lee's breadth-first strategy for generating instances were encountered. An alternative depth-first strategy, referred to as smallest-instance-first hyper-linking, for generating instances via the hyper-link operation was developed to address these inefficiencies. Smallest-instance-first hyper-linking is implemented in the automated theorem prover CLIN-E.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alexander, G. D.: Proving First-Order Equality Theorems with Hyper-Linking, PhD Dissertation, University of North Carolina at Chapel Hill, 1995. Available from the Department of Computer Science as Technical Report TR96-019.

  2. Alexander, G. D. and Plaisted, D. A.: Proving equality theorems with hyper-linking, in Deepak Kapur (ed.), Proceedings of the 11th International Conference on Automated Deduction, Lecture Notes in Artificial Intelligence 607, Springer-Verlag, Saratoga Springs, New York, 15-18 June 1992, pp. 706–710. System abstract.

  3. Brand, D.: Proving theorems with the modification method, SIAM J. Comput. 4(4) (1975), 412–430.

    Google Scholar 

  4. Gilmore, P. C.: A proof method for quantification theory: Its justification and realization, IBM J. Res. Dev. 4(1) (1960), 28–35.

    Google Scholar 

  5. Herbrand, J.: Recherches sur la Théorie de la Démonstration, Thesis, University of Paris, 1930. English translation in Herbrand [6].

  6. Herbrand, J.: Jacques Herbrand: Logical Writings, Harvard University Press, Cambridge, Massachusetts, 1971. Edited by Warren D. Goldfarb.

    Google Scholar 

  7. Lee, Sh-J.: CLIN: An Automated Reasoning System Using Clause Linking, PhD Dissertation, University of North Carolina at Chapel Hill, 1990. Available from the Department of Computer Science as Technical Report TR90-029.

  8. Lee, Sh-J. and Plaisted, D. A.: Eliminating duplication with the hyper-linking strategy, J. Automated Reasoning 9 (1992), 25–42.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alexander, G.D. CLIN-E - Smallest Instance First Hyper-Linking. Journal of Automated Reasoning 18, 177–182 (1997). https://doi.org/10.1023/A:1005818927764

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1005818927764

Navigation