Abstract
Formal libraries are treasure troves of detailed mathematical knowledge, but this treasure is usually locked into system- and logic-specific representations that can only be understood by the respective theorem prover system. In this paper we present an ontology for using relational information on mathematical knowledge and a corresponding data set generated from the Isabelle and Coq libraries. We show the utility of the generated data by setting a relational query engine that provides easy access to certain library information that was previously hard or impossible to determine.
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We have reconsidered the name of this class many times: all suggested names can be misunderstood. The current name stems from the intuition that axioms and theorems are the most important named truth-establishing declarations, and statement is a common way to unify them. Arguably more systematic would be proof: anything that establishes truth is formalized as an operator that constructs a proof.
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Versions: Isabelle/9c60fcfdf495, AFP/d50417d0ae64, MMT/e6fa4b852bf9.
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Acknowledgement
The authors were supported by DFG grants RA-18723-1 and KO-2428/13-1 OAF and EU grant Horizon 2020 ERI 676541 OpenDreamKit.
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Condoluci, A., Kohlhase, M., Müller, D., Rabe, F., Sacerdoti Coen, C., Wenzel, M. (2019). Relational Data Across Mathematical Libraries. In: Kaliszyk, C., Brady, E., Kohlhase, A., Sacerdoti Coen, C. (eds) Intelligent Computer Mathematics. CICM 2019. Lecture Notes in Computer Science(), vol 11617. Springer, Cham. https://doi.org/10.1007/978-3-030-23250-4_5
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