There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

What is modal logic

Fuzzy Relational Systems: Foundations and Principles

On soft equality

This chapter provides an introduction to using the Object Constraint Language (OCL) in composing UML models. Our goal in this chapter is to gain an introductory understanding of how to use the OCL.

The Object Constraint Language (OCL)

In this paper, a method for computing the closure of a set of attributes according to a specification of functional dependencies of the relational model is described. The main feature of this method is that it computes the closure using solely the inference system of the SL FD logic. For the first time, logic is used in the design of automated deduction methods to solve the closure problem. The strong link between the SL FD logic and the closure algorithm is presented and an SL FD simplification paradigm emerges as the key element of our method. In addition, the soundness and completeness of the closure algorithm are shown. Our method has linear complexity, as the classical closure algorithms, and it has all the advantages provided by the use of logic. We have empirically compared our algorithm with the Diederich and Milton classical algorithm. This experiment reveals the best behaviour of our method which shows a significant improvement in the average speed.

Closure via functional dependence simplification

In this paper, we propose the use of formal techniques on Software Engineering in two directions: 1)We present, within the general framework of lattice theory, the analysis of relational databases. To do that, we characterize the concept of f-family (Armstrong relations) by means of a new concept which we call non-deterministic ideal operator. This characterization allows us to formalize database redundancy in a more significant way than it was thought of in the literature. 2) We introduce the Substitution Logic SLFD for functional dependencies that will allows us the design of automatic transformations of data models to remove redundancy.

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SLFD Logic: Elimination of Data Redundancy in Knowledge Representation

After recalling the different interpretations usually assigned to the term Galois connection, both in the crisp and in the fuzzy case, we survey on several of their applications in Computer Science and specifically, in Soft Computing.

On galois connections and soft computing

In the design of mathematical methods for a medical problem, one of the kernel issues is the identification of symptoms and measures that could help in the diagnosis. Discovering connections among them constitute a big challenge because it allows to reduce the number of parameters to be considered in the mathematical model. In this work, we focus on formal concept analysis as a very promising technique to address this problem. In previous works, we have studied the use of formal concept analysis to manage attribute implications. In this work, we propose to extend the knowledge that we can extract from every context using positive and negative information, which constitutes an open problem.



Based on the main classical algorithms, we propose new methods to generate the lattice concept with positive and negative information to be used as a kind of map of attribute connections. We also compare them in an experiment built with datasets from the UCI repository for machine learning. We finally apply the mining techniques to extract the knowledge contained in a real data set containing information about patients suffering breast cancer. The result obtained have been contrasted with medical scientists to illustrate the benefits of our proposal. Copyright © 2016 John Wiley & Sons, Ltd.

Pablo Cordero

Papers

Closure via functional dependence simplification

SLFD Logic: Elimination of Data Redundancy in Knowledge Representation

On galois connections and soft computing

Data mining algorithms to compute mixed concepts with negative attributes: an application to breast cancer data analysis

Concept lattices with negative information