Abstract
Geometry theorem proofs like propositions in Euclid’s geometry elements contain fruitful geometry knowledge, and the statements of geometry proofs are almost structural mathematics language. Hence, it is possible to let computer understand geometry theorem proofs. Based on the process ontology, a novel geometry knowledge base (GKB) in this paper is built by letting computer learn from theorem proofs. The resulting process ontology is automatically constructed by extracting abstract and instance models (IMS) from proofs. The abstract model displays the causal relations of conditions with conclusions, and the instance model (IM) holds the formal relationship of abstract model so that the deduction can be reused. Thus, two kinds of models completely describe the proving process of geometry theorem. Furthermore, GKB based on the process ontology can be gradually extended by learning from more and more proofs. Finally, GKB learning from about 200 examples is implemented, and an application in automated theorem proving is given.
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Acknowledgments
The work in this paper was supported by National Natural Science Foundation of China (No. 61073099 and No. 61202257) and the Sichuan Provincial Science and Technology Department (No. 2012FZ0120).
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Fu, H., Zhong, X., Li, Q., Xia, H., Li, J. (2014). Geometry Knowledge Base Learning from Theorem Proofs. In: Wen, Z., Li, T. (eds) Knowledge Engineering and Management. Advances in Intelligent Systems and Computing, vol 278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54930-4_3
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DOI: https://doi.org/10.1007/978-3-642-54930-4_3
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