5,664 research outputs found
The Vampire and the FOOL
This paper presents new features recently implemented in the theorem prover
Vampire, namely support for first-order logic with a first class boolean sort
(FOOL) and polymorphic arrays. In addition to having a first class boolean
sort, FOOL also contains if-then-else and let-in expressions. We argue that
presented extensions facilitate reasoning-based program analysis, both by
increasing the expressivity of first-order reasoners and by gains in
efficiency
Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
Smart premise selection is essential when using automated reasoning as a tool
for large-theory formal proof development. A good method for premise selection
in complex mathematical libraries is the application of machine learning to
large corpora of proofs. This work develops learning-based premise selection in
two ways. First, a newly available minimal dependency analysis of existing
high-level formal mathematical proofs is used to build a large knowledge base
of proof dependencies, providing precise data for ATP-based re-verification and
for training premise selection algorithms. Second, a new machine learning
algorithm for premise selection based on kernel methods is proposed and
implemented. To evaluate the impact of both techniques, a benchmark consisting
of 2078 large-theory mathematical problems is constructed,extending the older
MPTP Challenge benchmark. The combined effect of the techniques results in a
50% improvement on the benchmark over the Vampire/SInE state-of-the-art system
for automated reasoning in large theories.Comment: 26 page
ATP and Presentation Service for Mizar Formalizations
This paper describes the Automated Reasoning for Mizar (MizAR) service, which
integrates several automated reasoning, artificial intelligence, and
presentation tools with Mizar and its authoring environment. The service
provides ATP assistance to Mizar authors in finding and explaining proofs, and
offers generation of Mizar problems as challenges to ATP systems. The service
is based on a sound translation from the Mizar language to that of first-order
ATP systems, and relies on the recent progress in application of ATP systems in
large theories containing tens of thousands of available facts. We present the
main features of MizAR services, followed by an account of initial experiments
in finding proofs with the ATP assistance. Our initial experience indicates
that the tool offers substantial help in exploring the Mizar library and in
preparing new Mizar articles
Development of a new running gear for the Spectrum intermodal vehicle
The European Union (EU) Seventh Framework Programme (FP7) project Spectrum [12] set out to develop a freight vehicle which would facilitate the exploitation of the low density, high value (LDHV) goods market. Key to the performance criteria for the vehicle were: increased speed to enable mixed running with passenger services; improved ride quality to avoid damage to the LDHV goods; and reduced track damage for longevity and sustainability on increasingly stressed infrastructure. This paper presents aspects of the development of a novel running gear arrangement for the Spectrum vehicle, focussing on the dynamic performance of a Vampire vehicle model and the steps to realising stable running. Finally, the estimated performance of the Spectrum vehicle concept is compared against calculations for a conventional freight wagon with respect to curving, vertical track forces and potential savings in track access charges through implementation of Network Rail’s Variable Track Access Charge Calculator. It was found that the novel Spectrum concept could offer savings in Variable Usage Charges of between 8% and 16% compared to the conventional equivalent
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. The
performance of this architecture is evaluated in a bootstrapping scenario
emulating the development of Flyspeck from axioms to the last theorem, each
time using only the previous theorems and proofs. It is shown that 39% of the
14185 theorems could be proved in a push-button mode (without any high-level
advice and user interaction) in 30 seconds of real time on a fourteen-CPU
workstation. The necessary work involves: (i) an implementation of sound
translations of the HOL Light logic to ATP formalisms: untyped first-order,
polymorphic typed first-order, and typed higher-order, (ii) export of the
dependency information from HOL Light and ATP proofs for the machine learners,
and (iii) choice of suitable representations and methods for learning from
previous proofs, and their integration as advisors with HOL Light. This work is
described and discussed here, and an initial analysis of the body of proofs
that were found fully automatically is provided
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. The service allows its users to
upload and automatically process an arbitrary formal development (project)
based on HOL Light, and to attack arbitrary conjectures that use the concepts
defined in some of the uploaded projects. For that, the service uses several
automated reasoning systems combined with several premise selection methods
trained on all the project proofs. The projects that are readily available on
the server for such query answering include the recent versions of the
Flyspeck, Multivariate Analysis and Complex Analysis libraries. The service
runs on a 48-CPU server, currently employing in parallel for each task 7 AI/ATP
combinations and 4 decision procedures that contribute to its overall
performance. The system is also available for local installation by interested
users, who can customize it for their own proof development. An Emacs interface
allowing parallel asynchronous queries to the service is also provided. The
overall structure of the service is outlined, problems that arise and their
solutions are discussed, and an initial account of using the system is given
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