84 research outputs found
Prolog Technology Reinforcement Learning Prover: (System Description)
We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus. The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP builds on the leanCoP Prolog implementation and adds learning-guided Monte-Carlo Tree Search as done in the rlCoP system. Other components include a Python interface to plCoP and machine learners, and an external proof checker that verifies the validity of plCoP proofs. The toolkit is evaluated on two benchmarks and we demonstrate its extendability by two additions: (1) guidance is extended to reduction steps and (2) the standard leanCoP calculus is extended with rewrite steps and their learned guidance. We argue that the Prolog setting is suitable for combining statistical and symbolic learning methods. The complete toolkit is publicly released. © 2020, Springer Nature Switzerland AG
Lemmas: Generation, Selection, Application
Noting that lemmas are a key feature of mathematics, we engage in an
investigation of the role of lemmas in automated theorem proving. The paper
describes experiments with a combined system involving learning technology that
generates useful lemmas for automated theorem provers, demonstrating
improvement for several representative systems and solving a hard problem not
solved by any system for twenty years. By focusing on condensed detachment
problems we simplify the setting considerably, allowing us to get at the
essence of lemmas and their role in proof search
Proceedings of the Automated Reasoning Workshop (ARW 2019)
Preface
This volume contains the proceedings of ARW 2019, the twenty sixths Workshop on Automated Rea-
soning (2nd{3d September 2019) hosted by the Department of Computer Science, Middlesex University,
England (UK). Traditionally, this annual workshop which brings together, for a two-day intensive pro-
gramme, researchers from different areas of automated reasoning, covers both traditional and emerging
topics, disseminates achieved results or work in progress. During informal discussions at workshop ses-
sions, the attendees, whether they are established in the Automated Reasoning community or are only at
their early stages of their research career, gain invaluable feedback from colleagues. ARW always looks
at the ways of strengthening links between academia, industry and government; between theoretical and
practical advances. The 26th ARW is affiliated with TABLEAUX 2019 conference.
These proceedings contain forteen extended abstracts contributed by the participants of the workshop
and assembled in order of their presentations at the workshop. The abstracts cover a wide range of topics
including the development of reasoning techniques for Agents, Model-Checking, Proof Search for classical
and non-classical logics, Description Logics, development of Intelligent Prediction Models, application of
Machine Learning to theorem proving, applications of AR in Cloud Computing and Networking.
I would like to thank the members of the ARW Organising Committee for their advice and assis-
tance. I would also like to thank the organisers of TABLEAUX/FroCoS 2019, and Andrei Popescu, the
TABLEAUX Conference Chair, in particular, for the enormous work related to the organisation of this
affiliation. I would also like to thank Natalia Yerashenia for helping in preparing these proceedings.
London Alexander Bolotov
September 201
A Deep Reinforcement Learning Approach to First-Order Logic Theorem Proving
Automated theorem provers have traditionally relied on manually tuned
heuristics to guide how they perform proof search. Deep reinforcement learning
has been proposed as a way to obviate the need for such heuristics, however,
its deployment in automated theorem proving remains a challenge. In this paper
we introduce TRAIL, a system that applies deep reinforcement learning to
saturation-based theorem proving. TRAIL leverages (a) a novel neural
representation of the state of a theorem prover and (b) a novel
characterization of the inference selection process in terms of an
attention-based action policy. We show through systematic analysis that these
mechanisms allow TRAIL to significantly outperform previous
reinforcement-learning-based theorem provers on two benchmark datasets for
first-order logic automated theorem proving (proving around 15% more theorems)
Ludii -- The Ludemic General Game System
While current General Game Playing (GGP) systems facilitate useful research
in Artificial Intelligence (AI) for game-playing, they are often somewhat
specialised and computationally inefficient. In this paper, we describe the
"ludemic" general game system Ludii, which has the potential to provide an
efficient tool for AI researchers as well as game designers, historians,
educators and practitioners in related fields. Ludii defines games as
structures of ludemes -- high-level, easily understandable game concepts --
which allows for concise and human-understandable game descriptions. We
formally describe Ludii and outline its main benefits: generality,
extensibility, understandability and efficiency. Experimentally, Ludii
outperforms one of the most efficient Game Description Language (GDL)
reasoners, based on a propositional network, in all games available in the
Tiltyard GGP repository. Moreover, Ludii is also competitive in terms of
performance with the more recently proposed Regular Boardgames (RBG) system,
and has various advantages in qualitative aspects such as generality.Comment: Accepted at ECAI 202
The Role of Entropy in Guiding a Connection Prover
In this work we study how to learn good algorithms for selecting reasoning
steps in theorem proving. We explore this in the connection tableau calculus
implemented by leanCoP where the partial tableau provides a clean and compact
notion of a state to which a limited number of inferences can be applied. We
start by incorporating a state-of-the-art learning algorithm -- a graph neural
network (GNN) -- into the plCoP theorem prover. Then we use it to observe the
system's behaviour in a reinforcement learning setting, i.e., when learning
inference guidance from successful Monte-Carlo tree searches on many problems.
Despite its better pattern matching capability, the GNN initially performs
worse than a simpler previously used learning algorithm. We observe that the
simpler algorithm is less confident, i.e., its recommendations have higher
entropy. This leads us to explore how the entropy of the inference selection
implemented via the neural network influences the proof search. This is related
to research in human decision-making under uncertainty, and in particular the
probability matching theory. Our main result shows that a proper entropy
regularisation, i.e., training the GNN not to be overconfident, greatly
improves plCoP's performance on a large mathematical corpus
Preprints of Proceedings of GWAI-92
This is a preprint of the proceedings of the German Workshop on Artificial Intelligence (GWAI) 1992. The final version will appear in the Lecture Notes in Artificial Intelligence
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