Closed world assumptions having precedence in predicates

1990 ◽  
Vol 8 (3) ◽  
pp. 185-209
Author(s):  
Hirofumi Katsuno
Author(s):  
Magdalena Ortiz

The development of tools and techniques for flexible and reliable data management is a long-standing challenge, ever more pressing in today’s data-rich world. We advocate using domain knowledge expressed in ontologies to tackle it, and summarize some research efforts to this aim that follow two directions. First, we consider the problem of ontology-mediated query answering (OMQA), where queries in a standard database query language are enriched with an ontology expressing background knowledge about the domain of interest, used to retrieve more complete answers when querying incomplete data. We discuss some of our contributions to OMQA, focusing on (i) expressive languages for OMQA, with emphasis on combining the open- and closed-world assumptions to reason about partially complete data; and (ii) OMQA algorithms based on rewriting techniques. The second direction we discuss proposes to use ontologies to manage evolving data. In particular, we use ontologies to model and reason about constraints on datasets, effects of operations that modify data, and the integrity of the data as it evolves.


1994 ◽  
pp. 65-84
Author(s):  
Ian Pratt

1994 ◽  
Vol 122 (1-2) ◽  
pp. 49-68 ◽  
Author(s):  
Luís Moniz Pereira ◽  
JoséJ. Alferes ◽  
Joaquim N. Aparício

1992 ◽  
Vol 7 (3) ◽  
pp. 243-246
Author(s):  
Yidong Shen

1997 ◽  
Vol 32 (2) ◽  
pp. 163-181 ◽  
Author(s):  
Carolina Ruiz ◽  
Jack Minker

2010 ◽  
Author(s):  
Christine E. Valdez ◽  
Michelle M. Lilly

2011 ◽  
Vol 11 (3) ◽  
pp. 272
Author(s):  
Ivan Gavrilyuk ◽  
Boris Khoromskij ◽  
Eugene Tyrtyshnikov

Abstract In the recent years, multidimensional numerical simulations with tensor-structured data formats have been recognized as the basic concept for breaking the "curse of dimensionality". Modern applications of tensor methods include the challenging high-dimensional problems of material sciences, bio-science, stochastic modeling, signal processing, machine learning, and data mining, financial mathematics, etc. The guiding principle of the tensor methods is an approximation of multivariate functions and operators with some separation of variables to keep the computational process in a low parametric tensor-structured manifold. Tensors structures had been wildly used as models of data and discussed in the contexts of differential geometry, mechanics, algebraic geometry, data analysis etc. before tensor methods recently have penetrated into numerical computations. On the one hand, the existing tensor representation formats remained to be of a limited use in many high-dimensional problems because of lack of sufficiently reliable and fast software. On the other hand, for moderate dimensional problems (e.g. in "ab-initio" quantum chemistry) as well as for selected model problems of very high dimensions, the application of traditional canonical and Tucker formats in combination with the ideas of multilevel methods has led to the new efficient algorithms. The recent progress in tensor numerical methods is achieved with new representation formats now known as "tensor-train representations" and "hierarchical Tucker representations". Note that the formats themselves could have been picked up earlier in the literature on the modeling of quantum systems. Until 2009 they lived in a closed world of those quantum theory publications and never trespassed the territory of numerical analysis. The tremendous progress during the very recent years shows the new tensor tools in various applications and in the development of these tools and study of their approximation and algebraic properties. This special issue treats tensors as a base for efficient numerical algorithms in various modern applications and with special emphases on the new representation formats.


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