Manuel Enciso

Closure via functional dependence simplification

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.

A Complete Logic for Fuzzy Functional Dependencies over Domains with Similarity Relations

An axiomatic system for fuzzy functional dependencies is introduced. The main novelty of the system is that it is not based on the transitivity rule like all the others, but it is built around a simplification rule which allows the removal of redundancy. The axiomatic system presented here is shown to be sound and complete.

Formalization of UML state machines using temporal logic

The main purpose of this paper is to approach the use of formal methods in computing. In more specific terms, we use a temporal logic to formalize the most fundamental aspects of the semantics of UML state machines. We pay special attention to the dynamic aspects of the different operations associated with states and transitions, as well as the behaviour of transitions related with composite states. This, to the best of our knowledge, has not been done heretofore using temporal logic.Our formalization is based on a temporal logic that combines points, intervals, and dates. Moreover this new temporal logic is built over an innovative and simple topological semantics, which simplifies the metatheory development.

Knowledge discovery in social networks by using a logic-based treatment of implications

This work can be seen as a contribution to the area of social network analysis. By considering Formal Concept Analysis (FCA) as the underlying formalizing tool, we use logic-based techniques in order to offer novel solutions to identify users influence in a social network. We propose the use of the Simplification Logic SL FD for attribute implications as the core of an automated method to build a structure containing the complete set of influences among users.

Negative Attributes and Implications in Formal Concept Analysis

Abstract The mining of negative attributes from datasets has been studied in the last decade to obtain additional and useful information. There exists an exhaustive study around the notion of negative association rules between sets of attributes. However, in Formal Concept Analysis, the needed theory for the management of negative attributes is in an incipient stage. In this work we present an algorithm, based on the NextClosure algorithm, that allows to obtain mixed implications. The proposed algorithm returns a feasible and complete basis of mixed implications by performing a reduced number of requests to the formal context.

A Non-explosive Treatment of Functional Dependencies Using Rewriting Logic

The use of rewriting systems to transform a given expression into a simpler one has promoted the use of rewriting logic in several areas and, particularly, in Software Engineering. Unfortunately, this application has not reached the treatment of Functional Dependencies contained in a given relational database schema. The reason is that the different sound and complete axiomatic systems defined up to now to manage Functional Dependencies are based on the transitivity inference rule. In the literature, several authors illustrate different ways of mapping inference systems into rewriting logics. Nevertheless, the explosive behavior of these inference systems avoids the use of rewriting logics for classical FD logics. In a previous work, we presented a novel logic named SL FD whose axiomatic system did not include the transitivity rule as a primitive rule.

An Efficient Preprocessing Transformation for Functional Dependencies Sets Based on the Substitution Paradigm

Functional Dependency is a fundamental notion of the Relational Model. Since the introduction of this successful theoretical framework in the 70’s, there have been several works focussed on their automated treatment. The pioneer line of this area was the use of Functional Dependencies Logics. Unfortunately, this line has presented several limitations, most of them caused by the crucial role of the transitivity paradigm in the axiomatic system. In [11] we introduce a new Functional Dependencies Logic which does not use the transitivity rule. This logic uses a new substitution rule and the design of its axiomatic system has been guided by the notion of optimality.

Concept lattices with negative information

Classical Formal Concept Analysis (FCA) extracts, represents and manages knowledge from positive information, i.e., its fundamental data model is a binary relation between a set of objects and attributes indicating the presence of a property in an object. However, some applications require to treat the absence of some property in an object as a negative information to be explicitly represented and managed, too. Although mixed (positive and negative) information has been addressed in the past in FCA, such approaches maintain the standard framework, which hides the specific semantics and avoids the further use of direct techniques and methods for mixed information. In this work, the foundations of FCA are extended and, in particular, mixed concept lattices are studied in depth. The main result of this work is a characterization theorem specifying in lattice-theoretic terms which lattices are isomorphic to a mixed concept lattice.

Automated prover for attribute dependencies in data with grades

We present a new axiomatization of logic for dependencies in data with grades, which includes ordinal data and data over domains with similarity relations, and an efficient reasoning method that is based on the axiomatization. The logic has its ordinary-style completeness characterizing the ordinary, bivalent entailment as well as the graded-style completeness characterizing the general, possibly intermediate degrees of entailment. A core of the method is a new inference rule, called the rule of simplification, from which we derive convenient equivalences that allow us to simplify sets of dependencies while retaining semantic closure. The method makes it possible to compute a closure of a given collection of attributes with respect to a collection of dependencies, decide whether a given dependency is entailed by a given collection of dependencies, and more generally, compute the degree to which the dependency is entailed by a collection of dependencies. We also present an experimental evaluation of the presented method. A new axiomatization of logic for dependencies in data with grades is proposed.Introducing an efficient reasoning method based on the logic and anExperimental evaluation of the method.

An efficient reasoning method for dependencies over similarity and ordinal data

We present a new axiomatization of logic for dependencies in data with grades, including ordinal data and data in an extension of Codds model that takes into account similarity relations on domains. The axiomatization makes possible an efficient method for automated reasoning for such dependencies that is presented in the paper. The presented method of automatic reasoning is based on a new simplification equivalence which allows to simplify sets of dependencies while retaining their semantic closures. We include two algorithms for computing closures and checking semantic entailment from sets of dependencies and present experimental comparison showing that the algorithms based on the new axiomatization outperform the algorithms proposed in the past.