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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
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- 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
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- 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.
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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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How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A Deductive Database Approach to Automated Geometry Theorem Proving and Discovering. https://app.cochat.ai/papers/10.1023/a:1006171315513
- The paper
- Chou, S.-C., Gao, X.-S., & Zhang, J.-Z. (2000). A Deductive Database Approach to Automated Geometry Theorem Proving and Discovering. Journal of Automated Reasoning. https://doi.org/10.1023/a%3A1006171315513
