A proof-theoretic approach to hierarchical math library organization

Authors:
Kamal Aboul-Hosn;Terese Damhøj Andersen
Affiliations:
Department of Computer Science, Cornell University, Ithaca, New York;Department of Computer Science, Cornell University, Ithaca, New York
Venue:
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
Year:
2005

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Abstract

The relationship between theorems and lemmas in mathematical reasoning is often vague. No system exists that formalizes the structure of theorems in a mathematical library. Nevertheless, the decisions we make in creating lemmas provide an inherent hierarchical structure to the statements we prove. In this paper, we develop a formal system that organizes theorems based on scope. Lemmas are simply theorems with a local scope. We develop a representation of proofs that captures scope and present a set of proof rules to create and reorganize the scopes of theorems and lemmas. The representation and rules allow systems for formalized mathematics to more accurately reflect the natural structure of mathematical knowledge.