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Found 52 papers, 14 papers with code
Learning Guided Automated Reasoning: A Brief Survey
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning.
Translating SUMO-K to Higher-Order Set Theory
We describe a translation from a fragment of SUMO (SUMO-K) into higher-order set theory.
MizAR 60 for Mizar 50
As a present to Mizar on its 50th anniversary, we develop an AI/TP system that automatically proves about 60\% of the Mizar theorems in the hammer setting.
Machine Learning Meets The Herbrand Universe
In particular, we develop a GNN2RNN architecture based on an invariant graph neural network (GNN) that learns from problems and their solutions independently of symbol names (addressing the abundance of skolems), combined with a recurrent neural network (RNN) that proposes for each clause its instantiations.
The Isabelle ENIGMA
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 Program Synthesis for Integer Sequences from Scratch
We present a self-learning approach for synthesizing programs from integer sequences.
Learning Theorem Proving Components
Saturation-style automated theorem provers (ATPs) based on the given clause procedure are today the strongest general reasoners for classical first-order logic.
Fast and Slow Enigmas and Parental Guidance
The second addition is motivated by fast weight-based rejection filters that are currently used in systems like E and Prover9.
The Role of Entropy in Guiding a Connection Prover
This leads us to explore how the entropy of the inference selection implemented via the neural network influences the proof search.
Online Machine Learning Techniques for Coq: A Comparison
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.
Learning Equational Theorem Proving
On these tasks, 3SIL is shown to significantly outperform several established RL and imitation learning methods.
The Tactician (extended version): A Seamless, Interactive Tactic Learner and Prover for Coq
We present Tactician, a tactic learner and prover for the Coq Proof Assistant.
First Neural Conjecturing Datasets and Experiments
We describe several datasets and first experiments with creating conjectures by neural methods.
Prolog Technology Reinforcement Learning Prover
We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus.
Tactic Learning and Proving for the Coq Proof Assistant
Currently, our predictor can identify the correct tactic to be applied to a proof state 23. 4% of the time.
Stateful Premise Selection by Recurrent Neural Networks
In this work, we develop a new learning-based method for selecting facts (premises) when proving new goals over large formal libraries.
ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (system description)
For the neural guidance, we use symbol-independent graph neural networks (GNNs) and their embedding of the terms and clauses.
Exploration of Neural Machine Translation in Autoformalization of Mathematics in Mizar
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.
Property Invariant Embedding for Automated Reasoning
This encoding represents symbols only by nodes in the graph, without giving the network any knowledge of the original labels.
Can Neural Networks Learn Symbolic Rewriting?
This work investigates if the current neural architectures are adequate for learning symbolic rewriting.
Towards Finding Longer Proofs
We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP).
ENIGMAWatch: ProofWatch Meets ENIGMA
In this work we describe a new learning-based proof guidance -- ENIGMAWatch -- for saturation-style first-order theorem provers.
Guiding Inferences in Connection Tableau by Recurrent Neural Networks
We present a dataset and experiments on applying recurrent neural networks (RNNs) for guiding clause selection in the connection tableau proof calculus.
Hammering Mizar by Learning Clause Guidance
We describe a very large improvement of existing hammer-style proof automation over large ITP libraries by combining learning and theorem proving.
ENIGMA-NG: Efficient Neural and Gradient-Boosted Inference Guidance for E
We describe an efficient implementation of clause guidance in saturation-based automated theorem provers extending the ENIGMA approach.
GRUNGE: A Grand Unified ATP Challenge
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
Reinforcement Learning of Theorem Proving
The strongest version of the system is trained on a large corpus of mathematical problems and evaluated on previously unseen problems.
First Experiments with Neural Translation of Informal to Formal Mathematics
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\%.
Learning to Reason with HOL4 tactics
Techniques combining machine learning with translation to automated reasoning have recently become an important component of formal proof assistants.
TacticToe: Learning to Prove with Tactics
We implement a automated tactical prover TacticToe on top of the HOL4 interactive theorem prover.
ProofWatch: Watchlist Guidance for Large Theories in E
Watchlist (also hint list) is a mechanism that allows related proofs to guide a proof search for a new conjecture.
ATPboost: Learning Premise Selection in Binary Setting with ATP Feedback
ATPboost is a system for solving sets of large-theory problems by interleaving ATP runs with state-of-the-art machine learning of premise selection from the proofs.
ENIGMA: Efficient Learning-based Inference Guiding Machine
ENIGMA is a learning-based method for guiding given clause selection in saturation-based theorem provers.
Semantic Parsing of Mathematics by Context-based Learning from Aligned Corpora and Theorem Proving
We study methods for automated parsing of informal mathematical expressions into formal ones, a main prerequisite for deep computer understanding of informal mathematical texts.
BliStrTune: Hierarchical Invention of Theorem Proving Strategies
Inventing targeted proof search strategies for specific problem sets is a difficult task.
Monte Carlo Tableau Proof Search
We study Monte Carlo Tree Search to guide proof search in tableau calculi.
DeepMath - Deep Sequence Models for Premise Selection
We study the effectiveness of neural sequence models for premise selection in automated theorem proving, one of the main bottlenecks in the formalization of mathematics.
Extracting Higher-Order Goals from the Mizar Mathematical Library
Certain constructs allowed in Mizar articles cannot be represented in first-order logic but can be represented in higher-order logic.
Certified Connection Tableaux Proofs for HOL Light and TPTP
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.
Machine Learning of Coq Proof Guidance: First Experiments
We report the results of the first experiments with learning proof dependencies from the formalizations done with the Coq system.
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.
Developing Corpus-based Translation Methods between Informal and Formal Mathematics: Project Description
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 0.4 and 0.5
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.
Learning-assisted Theorem Proving with Millions of Lemmas
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.
MizAR 40 for Mizar 40
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).
Lemma Mining over HOL Light
Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians.
HOL(y)Hammer: Online ATP Service for HOL Light
HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable) mathematics encoded in the HOL Light system.
MaLeS: A Framework for Automatic Tuning of Automated Theorem Provers
MaLeS is an automatic tuning framework for automated theorem provers.
BliStr: The Blind Strategymaker
BliStr is a system that automatically develops strategies for E prover on a large set of problems.
Learning-Assisted Automated Reasoning with Flyspeck
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.
Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs.
