Abstract
Methods based on resolution have been widely used for theorem proving since it was proposed. This paper presents a new method for theorem proving that uses the inverse of resolution and employs the inclusion-exclusion principle to circumvent the problem of space complexity. We prove its soundness and completeness. The concept of complementary factor is introduced to estimate its complexity. We also show that our method outperforms resolution-based methods in some cases. Thus it is potentially a complementary method to resolution-based methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
del Val, A.: On some tractable classes in deduction and abduction, Artificial Intelligence 116 (2000), 297-313.
Hooker, J. N., Rago, G., Chandru, V. and Shrivastava, A.: Partial instantiation methods for inference in first-order logic, J. Automated Reasoning 28(4) (2002), 371-396.
Selman, B. and Kautz, H. A.: Knowledge compilation using Horn approximation, in Proc. of AAAI-1991, 1991, pp. 904-909.
Dechter, R. and Rish, I.: Directional resolution: The Davis-Putnam procedure, revisited, in Proc. of the 4th International Conference on Principles of KR&R, 1994, pp. 134-145.
del Val, A.: Tractable classes for directional resolution, in AAAI'2000, Proc. 17th Nat. Conf. on Artificial Intelligence, 2000, pp. 343-348.
Rish, I. and Dechter, R.: Resolution versus search: Two strategies for SAT, in Frontiers in Ariificial Intelligence and Applications, IOS Press, 2000, pp. 215-259.
Dechter, R.: Bucket elimination: A unifying framework for structure-driven inference, in Learning and Inference in Graphical Models, 1998.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hai, L., Jigui, S. & Yimin, Z. Theorem Proving Based on the Extension Rule. Journal of Automated Reasoning 31, 11–21 (2003). https://doi.org/10.1023/A:1027339205632
Issue Date:
DOI: https://doi.org/10.1023/A:1027339205632