31 research outputs found
Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
Smart premise selection is essential when using automated reasoning as a tool
for large-theory formal proof development. A good method for premise selection
in complex mathematical libraries is the application of machine learning to
large corpora of proofs. This work develops learning-based premise selection in
two ways. First, a newly available minimal dependency analysis of existing
high-level formal mathematical proofs is used to build a large knowledge base
of proof dependencies, providing precise data for ATP-based re-verification and
for training premise selection algorithms. Second, a new machine learning
algorithm for premise selection based on kernel methods is proposed and
implemented. To evaluate the impact of both techniques, a benchmark consisting
of 2078 large-theory mathematical problems is constructed,extending the older
MPTP Challenge benchmark. The combined effect of the techniques results in a
50% improvement on the benchmark over the Vampire/SInE state-of-the-art system
for automated reasoning in large theories.Comment: 26 page
mizar-items: Exploring fine-grained dependencies in the Mizar Mathematical Library
The Mizar Mathematical Library (MML) is a rich database of formalized
mathematical proofs (see http://mizar.org). Owing to its large size (it
contains more than 1100 "articles" summing to nearly 2.5 million lines of text,
expressing more than 50000 theorems and 10000 definitions using more than 7000
symbols), the nature of its contents (the MML is slanted toward pure
mathematics), and its classical foundations (first-order logic, set theory,
natural deduction), the MML is an especially attractive target for research on
foundations of mathematics. We have implemented a system, mizar-items, on which
a variety of such foundational experiements can be based. The heart of
mizar-items is a method for decomposing the contents of the MML into
fine-grained "items" (e.g., theorem, definition, notation, etc.) and computing
dependency relations among these items. mizar-items also comes equipped with a
website for exploring these dependencies and interacting with them.Comment: Accepted at CICM 2011: Conferences in Intelligent Computer
Mathematics, Track C: Systems and Project
Initial Experiments with TPTP-style Automated Theorem Provers on ACL2 Problems
This paper reports our initial experiments with using external ATP on some
corpora built with the ACL2 system. This is intended to provide the first
estimate about the usefulness of such external reasoning and AI systems for
solving ACL2 problems.Comment: In Proceedings ACL2 2014, arXiv:1406.123