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A Deductive Database Approach to Automated Geometry Theorem Proving and Discovering
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In the citing paper
“Previous methods to generate them are based on hand-crafted templates and domain-specific heuristics8–12, and are, therefore, limited by a subset of human experiences expressible in hard-coded rules.”
From Solving olympiad geometry without human demonstrations (2024) · cites this paper as [10]
In the citing paper
“In geometry, the symbolic deduction engine is deductive database (refs. 10,17), with the ability to efficiently deduce new statements from the premises by means of geometric rules.”
From Solving olympiad geometry without human demonstrations (2024) · cites this paper as [10]
In the citing paper
“Current approaches to geometry, therefore, still primarily rely on symbolic methods and human-designed, hard-coded search heuristics10–14.”
From Solving olympiad geometry without human demonstrations (2024) · cites this paper as [10]
In the citing paper
“| Search (human-like) | Deductive database (DD)10 | 7 |”
From Solving olympiad geometry without human demonstrations (2024) · cites this paper as [10]
In the citing paper
“Geometry theorem proving of today, however, is still relying on human-designed heuristics for auxiliary constructions10–14.”
From Solving olympiad geometry without human demonstrations (2024) · cites this paper as [10]
In the citing paper
“We use the method of structured DD10,17 for this purpose as it can find the deduction closure in just seconds on standard non-accelerator hardware.”
From Solving olympiad geometry without human demonstrations (2024) · cites this paper as [10]
In the citing paper
“With the introduction of DD10,17, area methods61 and full-angle methods30, geometry solvers use higher-level deduction rules than Tarski’s or Hilbert’s axioms and are able to prove a larger number of more complex theorems than those operating in formal languages.”
From Solving olympiad geometry without human demonstrations (2024) · cites this paper as [10]
Citations
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Research works printed but not linked: 25
- Bancilhon, F. and Ramakrishnan, R.: An amateur's introduction to recursive query processing strategies, in C. Zanioilo (ed.), Proc. of ACM SIGMOD Conference, 1986, pp. 16-52. · DOI
- Buntine, W.: Generalized subsumption and its application to induction and redundancy, Artif. Intell. 36(2) (1988), 149-179. · DOI · Paper page
- Chou, S. C.: Mechanical Geometry Theorem Proving, D. Reidel Publishing Company, Dordrecht, Netherlands, 1988.
- Chou, S. C. and Gao, X. S.: Mechanical formula derivation in elementary geometries, in Proc. ISSAC-90, ACM, New York, 1990, pp. 265-270.
- Chou, S. C., Gao, X. S. and Zhang, J. Z.: Machine Proofs in Geometry, World Scientific, 1994. · DOI · Paper page
- Chou, S. C., Gao, X. S. and Zhang, J. Z.: Automated generation of readable proofs with geometric invariants, I: Multiple and shortest proof generation, J. Automated Reasoning 17(3) (1996), 325-347. · DOI
- Chou, S. C., Gao, X. S. and Zhang, J. Z.: Automated generation of readable proofs with geometric invariants, II: Proving theorems with full-angles, WSUCS-94-3, CS Dept, Wichita State University, March 1994, J. Automated Reasoning 17(3) (1996), 349-370. · DOI · Paper page
- Coelho, H. and Pereira, L.M.: Automated reasoning in geometry theorem proving with prolog, J. Automated Reasoning 2 (1986), 329-390. · DOI
- Bulmer, M. and Fearnley-Sander, D.: The kinds of truth of geometry theorems, Preprint.
- Gallaire, H., Minker, J. and Nicola, J. M.: Logic and databases: A deductive approach, ACM Comput. Surveys 16(2) (1984), 153-185. · DOI
- Gerlentner, H., Hanson, J. R. and Loveland, D. W.: Empirical explorations of the geometry-theorem proving machine, in Proc. West. Joint Computer Conf., 1960, pp. 143-147. · DOI
- Havel, T.: The use of distance as coordinates in computer-aided proofs of theorems in Euclidean geometry, IMA Preprint, No. 389, University of Minnesota, 1988.
- Helm, R.: On the elimination of redundant derivations during execution, in Proc. of 1990 North American Conference on Logic Programming, The MIT Press, 1990, pp. 551-568.
- Kapur, D.: Geometry theorem proving using Hilbert's nullstellensatz, in Proc. SYMSAC'86, Waterloo, 1986, pp. 202-208. · DOI
- Koedinger, K. R. and Anderson, J. R.: Abstract planning and perceptual chunks: Elements of expertise in geometry, Cognitive Science 14 (1990), 511-550. · DOI
- Hong-Bo, Li and Minteh, Cheng: Clifford algebraic reduction method for automated theorem proving in differential geometry, J. Automated Reasoning 21(1) (1998), 1-21. · DOI
- Nevins, A. J.: Plane geometry theorem proving using forward chaining, Artif. Intell. 6 (1975), 1-23. 18._ Recio, T. and Velex-Melon, M. P.: Automatic discovery of theorems in elementary geometry, Preprint, 1997. · DOI
- Reiter, R.: A semantically guided deductive system for automatic theorem proving, IEEE Trans. on Computers C-25(4) (1976), 328-334. · DOI
- Reiter, R.: On the closed world data bases, in H. Gallaire and J. Minker (eds), Logic and Data Bases, Plenum Press, New York, 1978, pp. 55-76. · DOI
- Robinson, A.: Proving a theorem (as done by Man, Logician, or Machine), in J. Siekmann and G. Wrightson (eds), Automation of Reasoning, Springer-Verlag, 1983, pp. 74-78. · DOI
- Sagiv, Y.: Optimizing datalog programs, in J. Minker (ed.), Foundations of Deductive Databases and Logic Programming, Morgan Kauffmann, 1988, pp. 659-698. · DOI
- Wang, D. M.: Reasoning about geometric problems using an elimination method, in J. Pfalzgraf and D. M. Wang (eds), Automated Practical Reasoning, Springer-Verlag, 1995, pp. 148-185. · DOI
- White, N. L. and Mcmillan, T.: Cayley factorization, in Proc. ISSAC'88, ACM Press, 1988, pp. 4-8.
- Wos, L.: Automated Reasoning: 33 Basic Research Problems, Prentice-Hall, Englewood Cliffs, New Jersey, 1988.
- Wu Wen-tsün: Basic Principles of Mechanical Theorem Proving in Geometries, Volume I: Part of Elementary Geometries, Science Press, Beijing (in Chinese), 1984. English version, Springer-Verlag, 1993.
Cited by
Sorted by citations
Solving olympiad geometry without human demonstrations
Trinh, T. H., Wu, Y., Le, Q. V., He, H., & Luong, T. (2024) · Nature · doi:10.1038/s41586-023-06747-5 · Cited by 311
Metadata
- Authors
- Chou, S.-C., Gao, X.-S., & Zhang, J.-Z.
- Affiliations
- Wichita State University (US)
- ORCID
- Gao, Xiao-Shan
- Venue
- Journal of Automated Reasoning
- Published
- 2000-10
- Volume
- 25
- Issue
- 3
- Pages
- 219-246
- ISSN
- 0168-7433 (ISSN-L)
- 1573-0670
- OpenAlex
- W2120243289
- Cited by
- 89
- References
- 0
- Citations by year
- 2026: 8 · 2025: 3 · 2024: 9 · 2023: 3 · 2022: 3 · 2021: 8 · 2020: 3 · 2019: 2 · 2018: 4 · 2017: 2 · 2015: 3 · 2014: 5 · 2013: 1 · 2012: 2
- FWCI
- 2.42
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- Journal of Automated Reasoning (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Mathematics and Applications
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Polynomial and algebraic computation
- Physical Sciences › Computer Science › Artificial Intelligence › Logic, Reasoning, and Knowledge
- Keywords
- deductive databases, geometry theorem proving, fixpoint computation, geometric configuration, database size reduction, forward chaining, auxiliary points
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