Overview and evaluation of premise selection techniques for large theory mathematics

Authors:
Daniel Kühlwein;Twan van Laarhoven;Evgeni Tsivtsivadze;Josef Urban;Tom Heskes
Affiliations:
Radboud University, Nijmegen, Netherlands;Radboud University, Nijmegen, Netherlands;Radboud University, Nijmegen, Netherlands;Radboud University, Nijmegen, Netherlands;Radboud University, Nijmegen, Netherlands
Venue:
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Year:
2012

Citing 19
Cited 3

Random projection in dimensionality reduction: applications to image and text data

Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
leanCoP: lean connection-based theorem proving

Journal of Symbolic Computation - Special issue: First order theorem proving
Kernel Methods for Pattern Analysis

Kernel Methods for Pattern Analysis
The design and implementation of VAMPIRE

AI Communications - CASC
E - a brainiac theorem prover

AI Communications - CASC
SRASS - A Semantic Relevance Axiom Selection System

CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
MaLARea SG1 - Machine Learner for Automated Reasoning with Semantic Guidance

IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Personalized recommendation on dynamic content using predictive bilinear models

Proceedings of the 18th international conference on World wide web
SPASS Version 3.5

CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Divvy: An ATP Meta-system Based on Axiom Relevance Ordering

CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
seL4: formal verification of an operating-system kernel

Communications of the ACM
Z3: an efficient SMT solver

TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Evaluation of automated theorem proving on the Mizar mathematical library

ICMS'10 Proceedings of the Third international congress conference on Mathematical software
The naproche project controlled natural language proof checking of mathematical texts

CNL'09 Proceedings of the 2009 conference on Controlled natural language
MaLeCoP: machine learning connection prover

TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Sine Qua non for large theory reasoning

CADE'11 Proceedings of the 23rd international conference on Automated deduction
Advances in the formalization of the odd order theorem

ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Automatic proof and disproof in Isabelle/HOL

FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Automated and human proofs in general mathematics: an initial comparison

LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning

MaSh: machine learning for sledgehammer

ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Automated reasoning service for HOL light

CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
The 6th IJCAR automated theorem proving system competition --CASC-J6

AI Communications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, an overview of state-of-the-art techniques for premise selection in large theory mathematics is provided, and new premise selection techniques are introduced. Several evaluation metrics are introduced, compared and their appropriateness is discussed in the context of automated reasoning in large theory mathematics. The methods are evaluated on the MPTP2078 benchmark, a subset of the Mizar library, and a 10% improvement is obtained over the best method so far.