Enhanced theorem reuse by partial theory inclusions

Authors:
Immanuel Normann
Affiliations:
Computer Science, International University Bremen
Venue:
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Year:
2006

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Abstract

Finding new theorems is essential for the general progress in mathematics. Apart from creating and proving completely new theorems progress can also be achieved by theorem reuse; i.e. by translating theorems from related theories into the target theory and proving its translated premises under which the theorem was proven. This approach is pursued by the ”little theories” and the development graph paradigms. This work suggests an improvement in this direction in two aspects: partial theory inclusions enhances theorem reuse and formula matching to support automated detection of theory inclusions. By representing theory axioms as facts and partial theories (i.e. theorems and their minimal set of premises) as horn clauses, reusable theorems correspond to derived facts such that model generator like KRHyper can be used for this task.