scholarly journals Bayesian Optimisation for Premise Selection in Automated Theorem Proving (Student Abstract)

2020 ◽  
Vol 34 (10) ◽  
pp. 13919-13920
Author(s):  
Agnieszka Słowik ◽  
Chaitanya Mangla ◽  
Mateja Jamnik ◽  
Sean B. Holden ◽  
Lawrence C. Paulson
Keyword(s):  
Parameter Space ◽  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Search Space ◽  
Large Set ◽  
Probabilistic Framework ◽  
Formal Proofs ◽  
Dimensional Parameter ◽  
Theorem Provers

Modern theorem provers utilise a wide array of heuristics to control the search space explosion, thereby requiring optimisation of a large set of parameters. An exhaustive search in this multi-dimensional parameter space is intractable in most cases, yet the performance of the provers is highly dependent on the parameter assignment. In this work, we introduce a principled probabilistic framework for heuristic optimisation in theorem provers. We present results using a heuristic for premise selection and the Archive of Formal Proofs (AFP) as a case study.

scholarly journals Bayesian Optimisation for Heuristic Configuration in Automated Theorem Proving

10.29007/q91g ◽  
2020 ◽  
Author(s):  
Agnieszka Słowik ◽  
Chaitanya Mangla ◽  
Mateja Jamnik ◽  
Sean Holden ◽  
Lawrence Paulson
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Probabilistic Framework ◽  
Selection Algorithm ◽  
Formal Proofs ◽  
Proof Search ◽  
Minimum Number ◽  
Selection Algorithms

Modern theorem provers such as Vampire utilise premise selection algorithms to control the proof search explosion. Premise selection heuristics often employ an array of continuous and discrete parameters. The quality of recommended premises varies depending on the parameter assignment. In this work, we introduce a principled probabilistic framework for optimisation of a premise selection algorithm. We present results using Sumo Inference Engine (SInE) and the Archive of Formal Proofs (AFP) as a case study. Our approach can be used to optimise heuristics on large theories in minimum number of steps.

STRATEGY PARALLELISM IN AUTOMATED THEOREM PROVING

1999 ◽  
Vol 13 (02) ◽  
pp. 219-245 ◽  
Author(s):  
ANDREAS WOLF ◽  
REINHOLD LETZ
Keyword(s):  
Theorem Proving ◽  
Experimental Evaluation ◽  
Automated Theorem Proving ◽  
Search Strategies ◽  
Theorem Prover ◽  
Strategy Selection ◽  
Theorem Provers ◽  
Initial Strategy ◽  
Basic Concepts ◽  
Run Time

Automated theorem provers use search strategies. Unfortunately, there is no unique strategy which is uniformly successful on all problems. This motivates us to apply different strategies in parallel, in a competitive manner. In this paper, we discuss properties, problems, and perspectives of strategy parallelism in theorem proving. We develop basic concepts like the complementarity and the overlap value of strategy sets. Some of the problems such as initial strategy selection and run-time strategy exchange are discussed in more detail. The paper also contains the description of an implementation of a strategy parallel theorem prover (p-SETHEO) and an experimental evaluation.

scholarly journals The Thousands of Models for Theorem Provers (TMTP) Model Library - First Steps

10.29007/7dg5 ◽  
2018 ◽  
Author(s):  
Geoff Sutcliffe ◽  
Stephan Schulz
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Theorem Provers ◽  
Model Library ◽  
Problems And Solutions ◽  
Model Finding ◽  
Problem Library

The TPTP World is a well established infrastructure that supports research,development, and deployment of Automated Theorem Proving (ATP) systems forclassical logics.The TPTP world includes the TPTP problem library, the TSTP solution library,standards for writing ATP problems and reporting ATP solutions, and itprovides tools and services for processing ATP problems and solutions.This work describes a new component of the TPTP world - the Thousands ofModels for Theorem Provers (TMTP) Model Library.This is a library of models for identified axiomatizations built fromaxiom sets in the TPTP problem library, along with functions for efficientlyevaluating formulae wrt models, and tools for examining and processingthe models.The TMTP supports the development of semantically guided theorem provingATP systems, provide examples for developers of model finding ATP systems,and provides insights into the semantics of axiomatizations.

scholarly journals Automated Theorem Proving using the TPTP Process Instruction Language

10.29007/f997 ◽  
2018 ◽  
Author(s):  
Muhammad Nassar ◽  
Geoff Sutcliffe
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Input Output ◽  
Theorem Provers ◽  
And Control

The TPTP (Thousands of Problems for Theorem Provers) World is a well established infrastructure for Automated Theorem Proving (ATP). In the context of the TPTP World, the TPTP Process Instruction (TPI) language provides capabilities to input, output and organize logical formulae, and control the execution of ATP systems. This paper reviews the TPI language, describes a shell interpreter for the language, and demonstrates their use in theorem proving.

scholarly journals Proof simplification and automated theorem proving

2019 ◽  
Vol 377 (2140) ◽  
pp. 20180034 ◽  
Author(s):  
Michael Kinyon
Keyword(s):  
Theorem Proving ◽  
Simple Proof ◽  
Automated Theorem Proving ◽  
Theme Issue ◽  
Theorem Provers ◽  
Open Question

The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper, I describe a technique for simplifying automated proofs. Hopefully, this discussion will stimulate interest in the larger, still open, question of what reasonable measures of proof simplicity might be. This article is part of the theme issue ‘The notion of ‘simple proof’ - Hilbert's 24th problem’.

scholarly journals Improving the Fine-Tuning of Metaheuristics: An Approach Combining Design of Experiments and Racing Algorithms

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Eduardo Batista de Moraes Barbosa ◽  
Edson Luiz França Senne
Keyword(s):  
Heuristic Method ◽  
Search Space ◽  
Computational Effort ◽  
Traveling Salesman ◽  
The Other ◽  
Fine Tuning ◽  
Large Set ◽  
Promising Alternative ◽  
Tuning Process

Usually, metaheuristic algorithms are adapted to a large set of problems by applying few modifications on parameters for each specific case. However, this flexibility demands a huge effort to correctly tune such parameters. Therefore, the tuning of metaheuristics arises as one of the most important challenges in the context of research of these algorithms. Thus, this paper aims to present a methodology combining Statistical and Artificial Intelligence methods in the fine-tuning of metaheuristics. The key idea is a heuristic method, called Heuristic Oriented Racing Algorithm (HORA), which explores a search space of parameters looking for candidate configurations close to a promising alternative. To confirm the validity of this approach, we present a case study for fine-tuning two distinct metaheuristics: Simulated Annealing (SA) and Genetic Algorithm (GA), in order to solve the classical traveling salesman problem. The results are compared considering the same metaheuristics tuned through a racing method. Broadly, the proposed approach proved to be effective in terms of the overall time of the tuning process. Our results reveal that metaheuristics tuned by means of HORA achieve, with much less computational effort, similar results compared to the case when they are tuned by the other fine-tuning approach.

scholarly journals Rewriting and Well-Definedness within a Proof System

10.29007/b7wc ◽  
2018 ◽  
Author(s):  
Issam Maamria ◽  
Michael Butler
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Term Rewriting ◽  
Proof System ◽  
Proof Technique ◽  
Partial Functions ◽  
Deductive Proof ◽  
Theorem Provers ◽  
Theoretical Foundations

Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving between deduction and computation (i.e., rewriting) steps. If the logic of reasoning supports partial functions, it is necessary that rewriting copes with potentially ill-defined terms. In this paper, we provide a basis for integrating rewriting with a deductive proof system that deals with well-definedness. The definitions and theorems presented in this paper are the theoretical foundations for an extensible rewriting-based prover that has been implemented for the set theoretical formalism Event-B.

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