13,503 research outputs found
Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar
This paper presents a combination of several automated reasoning and proof
presentation tools with the Mizar system for formalization of mathematics. The
combination forms an online service called MizAR, similar to the SystemOnTPTP
service for first-order automated reasoning. The main differences to
SystemOnTPTP are the use of the Mizar language that is oriented towards human
mathematicians (rather than the pure first-order logic used in SystemOnTPTP),
and setting the service in the context of the large Mizar Mathematical Library
of previous theorems,definitions, and proofs (rather than the isolated problems
that are solved in SystemOnTPTP). These differences poses new challenges and
new opportunities for automated reasoning and for proof presentation tools.
This paper describes the overall structure of MizAR, and presents the automated
reasoning systems and proof presentation tools that are combined to make MizAR
a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial
Intelligence and Symbolic Computation AISC 201
Performance Royalties for Sound Recordings on Terrestrial Radio: A Private Solution to a Public Problem
US copyright law provides for a digital performance right in sound recordings but does not provide for a performance right in sound recordings when broadcast over terrestrial radio. Proponents of this asymmetry posit that the difference relates to the promotional value of terrestrial radio to record labels, but this rationale has eroded in recent years. The recording industry experienced a drastic decline at the turn of the millennium, and record labels have attempted many creative approaches to bridging the profit gap. Major labels and radio conglomerates of late have begun negotiating private contracts that effectively extend the benefits of a performance right to sound recordings broadcast over terrestrial radio. This Note argues that Congress should allow these private parties to continue experimenting with these agreements. As it stands, the government\u27s regulation of digital performance of sound recordings is creating negative consequences, and Congress should only intervene in the terrestrial radio arena if a holdout problem arises
Pairing correlations of cold fermionic gases at overflow from a narrow to a wide harmonic trap
Within the context of Hartree-Fock-Bogoliubov theory, we study the behavior
of superfluid Fermi systems when they pass from a small to a large container.
Such systems can be now realized thanks to recent progress in experimental
techniques. It will allow to better understand pairing properties at overflow
and in general in rapidly varying external potentials
The Shears Mechanism in 142Gd in the Skyrme-Hartree-Fock Method with the Tilted-Axis Cranking
We report on the first Skyrme-Hartree-Fock calculations with the tilted-axis
cranking in the context of magnetic rotation. The mean field symmetries,
differences between phenomenological and self-consistent methods and the
generation of shears-like structures in the mean field are discussed.
Significant role of the time-odd spin-spin effective interaction is pointed
out. We reproduce the shears mechanism, but quantitative agreement with
experiment is rather poor. It may have to do with too large core polarization,
lack of pairing correlations or properties of the Skyrme force.Comment: Presented at the XXVII Mazurian Lakes School of Physics, September
2-9 2001, Krzyze, Poland, Submitted to Acta Physica Polonic
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
Eliciting implicit assumptions of proofs in the MIZAR Mathematical Library by property omission
When formalizing proofs with interactive theorem provers, it often happens
that extra background knowledge (declarative or procedural) about mathematical
concepts is employed without the formalizer explicitly invoking it, to help the
formalizer focus on the relevant details of the proof. In the contexts of
producing and studying a formalized mathematical argument, such mechanisms are
clearly valuable. But we may not always wish to suppress background knowledge.
For certain purposes, it is important to know, as far as possible, precisely
what background knowledge was implicitly employed in a formal proof. In this
note we describe an experiment conducted on the MIZAR Mathematical Library of
formal mathematical proofs to elicit one such class of implicitly employed
background knowledge: properties of functions and relations (e.g.,
commutativity, asymmetry, etc.).Comment: 11 pages, 3 tables. Preliminary version presented at the 3rd Workshop
on Modules and Libraries for Proof Assistants (MLPA-11), affiliated with the
2nd Conference on Interactive Theorem Proving (ITP-2011), Nijmegen, the
Netherland
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