Angel Mora

SLFD Logic: Elimination of Data Redundancy in Knowledge Representation

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.

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.

An ATP of a Relational Proof System for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance

We introduce an Automatic Theorem Prover (ATP) of a dual tableau system for a relational logic for order of magnitude qualitative reasoning, which allows us to deal with relations such as negligibility, non-closeness and distance. Dual tableau systems are validity checkers that can serve as a tool for verification of a variety of tasks in order of magnitude reasoning, such as the use of qualitative sum of some classes of numbers. In the design of our ATP, we have introduced some heuristics, such as the so called phantom variables , which improve the efficiency of the selection of variables used un the proof.

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.

Implementing a relational theorem prover for modal logic [image omitted]

An automatic theorem prover for a proof system in the style of dual tableaux for the relational logic associated with modal logic has been introduced. Although there are many well-known implementations of provers for modal logic, as far as we know, it is the first implementation of a specific relational prover for a standard modal logic. There are two main contributions in this paper. First, the implementation of new rules, called ( ) and ( ), which substitute the classical relational rules for composition and negation of composition in order to guarantee not only that every proof tree is finite but also to decrease the number of applied rules in dual tableaux. Second, the implementation of an order of application of the rules which ensures that the proof tree obtained is unique. As a consequence, we have implemented a decision procedure for modal logic . Moreover, this work would be the basis for successive extensions of this logic, such as , and .

An implementation of a dual tableaux system for order-of-magnitude qualitative reasoning

Logic programming has been used as a natural framework to automate deduction in the logic of order-of-magnitude reasoning. Specifically, we introduce a Prolog implementation of the Rasiowa–Sikorski proof system associated with the relational translation Re(OM) of the multi-modal logic of order-of-magnitude qualitative reasoning OM.

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.