657 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
On Krawtchouk Transforms
Krawtchouk polynomials appear in a variety of contexts, most notably as
orthogonal polynomials and in coding theory via the Krawtchouk transform. We
present an operator calculus formulation of the Krawtchouk transform that is
suitable for computer implementation. A positivity result for the Krawtchouk
transform is shown. Then our approach is compared with the use of the
Krawtchouk transform in coding theory where it appears in MacWilliams' and
Delsarte's theorems on weight enumerators. We conclude with a construction of
Krawtchouk polynomials in an arbitrary finite number of variables, orthogonal
with respect to the multinomial distribution.Comment: 13 pages, presented at 10th International Conference on Artificial
Intelligence and Symbolic Computation, AISC 2010, Paris, France, 5-6 July
201
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
Conformant Planning as a Case Study of Incremental QBF Solving
We consider planning with uncertainty in the initial state as a case study of
incremental quantified Boolean formula (QBF) solving. We report on experiments
with a workflow to incrementally encode a planning instance into a sequence of
QBFs. To solve this sequence of incrementally constructed QBFs, we use our
general-purpose incremental QBF solver DepQBF. Since the generated QBFs have
many clauses and variables in common, our approach avoids redundancy both in
the encoding phase and in the solving phase. Experimental results show that
incremental QBF solving outperforms non-incremental QBF solving. Our results
are the first empirical study of incremental QBF solving in the context of
planning and motivate its use in other application domains.Comment: added reference to extended journal article; revision (camera-ready,
to appear in the proceedings of AISC 2014, volume 8884 of LNAI, Springer
AIoT for Smart territories
Artificial Intelligence revived in the last decade. The need for progress, the growing processing capacity and the low cost of the Cloud have facilitated the development of new, powerful algorithms. The efficiency of these algorithms in Big Data processing, Deep Learning and Convolutional Networks is transforming the way we work and is opening new horizons. Thanks to them, we can now analyse data and obtain unimaginable solutions to today’s problems. Nevertheless, our success is not entirely based on algorithms, it also comes from our ability to follow our “gut” when choosing the best combination of algorithms for an intelligent artefact. It's about approaching engineering with a lot of knowledge and tact. This involves the use of both connectionist and symbolic systems, and of having a full understanding of the algorithms used. Moreover, to address today’s problems we must work with both historical and real-time data
DeepTech – AI-IoT in smart cities
In this keynote, the evolution of intelligent computer systems will be examined. The need for human capital will be emphasised, as well as the need to follow one’s “gut instinct” in problem-solving. We will look at the benefits of combining information and knowledge to solve complex problems and will examine how knowledge engineering facilitates the integration of different algorithms. Furthermore, we will analyse the importance of complementary technologies such as IoT and Blockchain in the development of intelligent systems. It will be shown how tools like "Deep Intelligence" make it possible to create computer systems efficiently and effectively. "Smart" infrastructures need to incorporate all added-value resources so they can offer useful services to the society, while reducing costs, ensuring reliability and improving the quality of life of the citizens. The combination of AI with IoT and with blockchain offers a world of possibilities and opportunities
Making Math Searchable in Wikipedia
Wikipedia, the world largest encyclopedia contains a lot of knowledge that is
expressed as formulae exclusively. Unfortunately, this knowledge is currently
not fully accessible by intelligent information retrieval systems. This immense
body of knowledge is hidden form value-added services, such as search. In this
paper, we present our MathSearch implementation for Wikipedia that enables
users to perform a combined text and fully unlock the potential benefits.Comment: 7 pages, 2 figures, Conference on Intelligent Computer Mathematics,
July 9-14 2012, Bremen, Germany. To be published in Lecture Notes, Artificial
Intelligence, Springe
Accurate and efficient explicit approximations of the Colebrook flow friction equation based on the Wright omega-function
The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor, f. To date, the captured flow friction factor, f, can be extracted from the logarithmic form analytically only in the term of the Lambert W-function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W-function also known as the Wright omega-function. The Wright omega-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term, y = W (e(x)), of the Lambert W-function to series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert W-function is identical to the original expression in terms of accuracy, a further evaluation of the Lambert W-function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contain only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with a relative error of no more than 0.0096%. The presented approximations are in a form suitable for everyday engineering use, and are both accurate and computationally efficient.Web of Science71art. no. 3
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