580 research outputs found
A Survey on Retrieval of Mathematical Knowledge
We present a short survey of the literature on indexing and retrieval of
mathematical knowledge, with pointers to 72 papers and tentative taxonomies of
both retrieval problems and recurring techniques.Comment: CICM 2015, 20 page
The Mathematical Background of Lomonosov's Contribution
This is a short overview of the influence of mathematicians and their ideas
on the creative contribution of Mikhailo Lomonosov on the occasion of the
tercentenary of his birth
Towards OpenMath Content Dictionaries as Linked Data
"The term 'Linked Data' refers to a set of best practices for publishing and
connecting structured data on the web". Linked Data make the Semantic Web work
practically, which means that information can be retrieved without complicated
lookup mechanisms, that a lightweight semantics enables scalable reasoning, and
that the decentral nature of the Web is respected. OpenMath Content
Dictionaries (CDs) have the same characteristics - in principle, but not yet in
practice. The Linking Open Data movement has made a considerable practical
impact: Governments, broadcasting stations, scientific publishers, and many
more actors are already contributing to the "Web of Data". Queries can be
answered in a distributed way, and services aggregating data from different
sources are replacing hard-coded mashups. However, these services are currently
entirely lacking mathematical functionality. I will discuss real-world
scenarios, where today's RDF-based Linked Data do not quite get their job done,
but where an integration of OpenMath would help - were it not for certain
conceptual and practical restrictions. I will point out conceptual shortcomings
in the OpenMath 2 specification and common bad practices in publishing CDs and
then propose concrete steps to overcome them and to contribute OpenMath CDs to
the Web of Data.Comment: Presented at the OpenMath Workshop 2010, http://cicm2010.cnam.fr/om
Proof Generation from Delta-Decisions
We show how to generate and validate logical proofs of unsatisfiability from
delta-complete decision procedures that rely on error-prone numerical
algorithms. Solving this problem is important for ensuring correctness of the
decision procedures. At the same time, it is a new approach for automated
theorem proving over real numbers. We design a first-order calculus, and
transform the computational steps of constraint solving into logic proofs,
which are then validated using proof-checking algorithms. As an application, we
demonstrate how proofs generated from our solver can establish many nonlinear
lemmas in the the formal proof of the Kepler Conjecture.Comment: Appeared in SYNASC'1
Computing Persistent Homology within Coq/SSReflect
Persistent homology is one of the most active branches of Computational
Algebraic Topology with applications in several contexts such as optical
character recognition or analysis of point cloud data. In this paper, we report
on the formal development of certified programs to compute persistent Betti
numbers, an instrumental tool of persistent homology, using the Coq proof
assistant together with the SSReflect extension. To this aim it has been
necessary to formalize the underlying mathematical theory of these algorithms.
This is another example showing that interactive theorem provers have reached a
point where they are mature enough to tackle the formalization of nontrivial
mathematical theories
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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