Abstract
Automated theorem finding is one of 33 basic research problems in automated reasoning which was originally proposed by Wos in 1988, and it is still an open problem. For the problem, Cheng has proposed a forward deduction approach based on strong relevant logic. To verify the effectiveness of the approach, we tried to rediscover already known theorems in NBG set theory by using the approach, and succeeded in rediscovery of several known theorems. However, the method of the rediscovery is ad hoc, but not systematic. This paper gives an analysis and discussion for our experiment method and results from the viewpoint of the systematic method. The paper also presents some issues and future research directions for a systematic method of automated theorem finding based on Cheng’s approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson, A.R., Belnap Jr., N.D.: Entailment: The Logic of Relevance and Necessity, vol. 1. Princeton University Press (1975)
Anderson, A.R., Belnap Jr., N.D., Dunn, J.M.: Entailment: The Logic of Relevance and Necessity, vol. 2. Princeton University Press (1992)
Cheng, J.: Entailment Calculus as the Logical Basis of Automated Theorem Finding in Scientific Discovery. In: Systematic Methods of Scientific Discovery: Papers from the 1995 Spring Symposium, pp. 105–110. AAAI Press - American Association for Artificial Intelligence (1995)
Cheng, J.: A Strong Relevant Logic Model of Epistemic Processes in Scientific Discovery. In: Information Modelling and Knowledge Bases XI, Frontiers in Artificial Intelligence and Applications, vol. 61, pp. 136–159 (2000)
Cheng, J., Nara, S., Goto, Y.: FreeEnCal: A Forward Reasoning Engine with General-Purpose. In: Apolloni, B., Howlett, R.J., Jain, L. (eds.) KES 2007, Part II. LNCS (LNAI), vol. 4693, pp. 444–452. Springer, Heidelberg (2007)
Fang, W., Takahashi, I., Goto, Y., Cheng, J.: Practical Implementation of EPLAS: An Epistemic Programming Language for All Scientists. In: Proc. 10th International Conference on Machine Learning and Cybernetics. The IEEE Systems, Man, and Cybernetics Society, pp. 608–616 (2011)
Gao, H., Shi, K., Goto, Y., Cheng, J.: Automated Theorem Finding by Forward Deduction Based on Strong Relevant Logic: A Case Study in NBG Set Theory. In: Proc. 11th International Conference on Machine Learning and Cybernetics. The IEEE Systems, Man, and Cybernetics Society, pp. 1859–1865 (2012)
Quaife, A.: Automated Development of Fundamental Mathematical Theories. Kluwer Academic (1992)
Takahashi, I., Nara, S., Goto, Y., Cheng, J.: EPLAS: An Epistemic Programming Language for All Scientists. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2007, Part I. LNCS, vol. 4487, pp. 406–413. Springer, Heidelberg (2007)
Wos, L.: Automated Reasoning: 33 Basic Research Problem. Prentice-Hall (1988)
Wos, L.: The Problem of Automated Theorem Finding. Journal of Automated Reasoning 10(1), 137–138 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gao, H., Shi, K., Goto, Y., Cheng, J. (2013). Finding Theorems in NBG Set Theory by Automated Forward Deduction Based on Strong Relevant Logic. In: Du, DZ., Zhang, G. (eds) Computing and Combinatorics. COCOON 2013. Lecture Notes in Computer Science, vol 7936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38768-5_62
Download citation
DOI: https://doi.org/10.1007/978-3-642-38768-5_62
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38767-8
Online ISBN: 978-3-642-38768-5
eBook Packages: Computer ScienceComputer Science (R0)