We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways.
Learning complex programs through inductive logic programming (ILP) remains a formidable challenge.
The heterogeneous nature of the logical foundations used in different interactive proof assistant libraries has rendered discovery of similar mathematical concepts among them difficult.
Learning happens in an online manner, meaning that Tactician's machine learning model is updated immediately every time the user performs a step in an interactive proof.
We propose the task of disambiguating symbolic expressions in informal STEM documents in the form of LaTeX files - that is, determining their precise semantics and abstract syntax tree - as a neural machine translation task.
Applying machine learning to mathematical terms and formulas requires a suitable representation of formulas that is adequate for AI methods.
In our context informal mathematics refers to human-written mathematical sentences in the LaTeX format; and formal mathematics refers to statements in the Mizar language.
This encoding represents symbols only by nodes in the graph, without giving the network any knowledge of the original labels.
This work investigates if the current neural architectures are adequate for learning symbolic rewriting.
We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP).
This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms.
Logic in Computer Science
The strongest version of the system is trained on a large corpus of mathematical problems and evaluated on previously unseen problems.
Our experiments show that our best performing model configurations are able to generate correct Mizar statements on 65. 73\% of the inference data, with the union of all models covering 79. 17\%.
Techniques combining machine learning with translation to automated reasoning have recently become an important component of formal proof assistants.
We propose various machine learning tasks that can be performed on this dataset, and discuss their significance for theorem proving.
Ranked #3 on Automated Theorem Proving on HolStep (Unconditional)
Here we suggest deep learning based guidance in the proof search of the theorem prover E. We train and compare several deep neural network models on the traces of existing ATP proofs of Mizar statements and use them to select processed clauses during proof search.
We study methods for automated parsing of informal mathematical expressions into formal ones, a main prerequisite for deep computer understanding of informal mathematical texts.
This volume of EPTCS contains the proceedings of the First Workshop on Hammers for Type Theories (HaTT 2016), held on 1 July 2016 as part of the International Joint Conference on Automated Reasoning (IJCAR 2016) in Coimbra, Portugal.
We discuss the differences between our direct implementation using an explicit Prolog stack, to the continuation passing implementation of MESON present in HOLLight and compare their performance on all core HOLLight goals.
The goal of this project is to (i) accumulate annotated informal/formal mathematical corpora suitable for training semi-automated translation between informal and formal mathematics by statistical machine-translation methods, (ii) to develop such methods oriented at the formalization task, and in particular (iii) to combine such methods with learning-assisted automated reasoning that will serve as a strong semantic component.
Machine Learner for Automated Reasoning (MaLARea) is a learning and reasoning system for proving in large formal libraries where thousands of theorems are available when attacking a new conjecture, and a large number of related problems and proofs can be used to learn specific theorem-proving knowledge.
We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs.
As a present to Mizar on its 40th anniversary, we develop an AI/ATP system that in 30 seconds of real time on a 14-CPU machine automatically proves 40% of the theorems in the latest official version of the Mizar Mathematical Library (MML).
The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the proofs, producing an AI system capable of answering a wide range of mathematical queries automatically.