Abstract
The problem of automated theorem finding is one of 33 basic research problems in automated reasoning which was originally proposed by Wos. The problem is still an open problem until now. To solve the problem, a systematic methodology with forward reasoning based on strong relevant logic has been proposed. This paper presents a case study of automated theorem finding in Tarski’s Geometry to show the generality of the methodology.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Wos L (1988) Automated reasoning: 33 basic research problem. Prentice-Hall, Upper Saddle River
Wos L (1993) The problem of automated theorem finding. J Autom Reasoning 10(1):137–138
Gao H, Goto Y, Cheng J (2014) A systematic methodology for automated theorem finding. Theoret Comput Sci 554:2–21
Gao H, Goto Y, Cheng J (2014) Research on automated theorem finding: current state and future directions. In: Proceedings of the 9th FTRA international conference, FutureTech 2014, LNEE, vol 309. Springer, Heidelberg, pp 105–110
Colton S, Meier A, Sorge V, McCasland R (2004) Automatic generation of classification theorems for finite algebras. In: Automated reasoning, LNCS, vol 3097. Springer, Heidelberg, pp 400–414
McCasland R, Bundy A, Autexier S (2007) Automated discovery of inductive theorems. J Stud Logic Grammar Rhetoric 10(23):135–149
Recio T, Velez MZ (1999) Automatic discovery of theorems in elementary geometry. J Autom Reasoning 23(1):63–82
Tang P, Lin F (2011) Discovering theorems in game theory: two-person games with unique pure nash equilibrium payoffs. Artif Intell 175(14):2010–2020
Cheng J (1994) A relevant logic approach to automated theorem finding. In: The workshop on automated theorem proving attached to international symposium on fifth generation computer systems, pp 8–15
Cheng J (1995) 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, AAAI Press—American Association for Artificial Intelligence, pp 105–110
Cheng J (2000) 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. IOS Press, pp. 136–159
Gao H, Goto Y, Cheng J (2015) Automated theorem finding by forward reasoning based on strong relevant logic: a case study in graph theory. In: Advanced multimedia and ubiquitous engineering—future information technology, LNEE, vol 352. Springer, Heidelberg, pp 23–30
Tarski A, Givant S (1999) Tarski’s system of geometry. Bull Symbolic Logic 5(2):175–214
Quaife A (1992) Automated development of fundamental mathematical theories. Kluwer Academic, Dordrecht
Cheng J, Nara S, Goto Y (2007) FreeEnCal: a forward reasoning engine with general-purpose. In: The 11th international conference on knowledge-based intelligent information and engineering systems, LNCS (LNAI), vol 4693. Springer, Heidelberg, pp 444–452
Cheng J (2007) A semilattice model for the theory grid. In: Proceedings of the 3rd international conference on semantics, knowledge and grid, IEEE Computer Society, pp 152–157
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media Singapore
About this paper
Cite this paper
Gao, H., Cheng, J. (2016). Automated Theorem Finding by Forward Reasoning Based on Strong Relevant Logic: A Case Study in Tarski’s Geometry. In: Park, J., Jin, H., Jeong, YS., Khan, M. (eds) Advanced Multimedia and Ubiquitous Engineering. Lecture Notes in Electrical Engineering, vol 393. Springer, Singapore. https://doi.org/10.1007/978-981-10-1536-6_8
Download citation
DOI: https://doi.org/10.1007/978-981-10-1536-6_8
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-1535-9
Online ISBN: 978-981-10-1536-6
eBook Packages: Computer ScienceComputer Science (R0)