M. Enciso

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.

Ideal non-deterministic operators as a formal framework to reduce the key finding problem

A formal development in the framework of the lattice theory for functional dependencies and minimal keys is presented. Beyond this theoretical study, a technique to prune the key finding problem, named scheme pruning transformation, is proposed in this work. This transformation is founded on theoretical results and has linear cost in the worst case. Moreover, this approach has provided a better size reduction than the usual techniques existing in the literature.

Non-deterministic ideal operators: An adequate tool for formalization in Data Bases

In this paper, we propose the application of formal methods to Software Engineering. The most used data model is the relational model and we present, within the general framework of lattice theory, this analysis of functional dependencies. For this reason, we characterize the concept of f-family by means of a new concept which we call non-deterministic ideal operator (nd.ideal-o). The study of nd.ideal-o.s allows us to obtain results about functional dependencies as trivial particularizations, to clarify the semantics of the functional dependencies and to progress in their efficient use, and to extend the concept of schema. Moreover, the algebraic characterization of the concept of Key of a schema allows us to propose new formal definitions in the lattice framework for classical normal forms in relation schemata. We give a formal definition of the normal forms for functional dependencies more frequently used in the bibliography: the second normal form (2FN), the third normal form(3FN) and Boyce-Codds normal form (FNBC).

Temporal Reasoning over Linear Discrete Time

In this work we present a new Automated Theorem Prover, called TAS-FNext, applied to temporal logic. This is part of a broader project developed by our research group GIMAC. It is an extension of works [4], [5] and [6] concerns classical logic and [9] Minimal Temporal Logic.

Bases for closed sets of implicants and implicates in temporal logic

Abstract. Prime implicates and implicants are used in several areas of Artificial Intelligence. However, their calculation is not always an easy task. Nevertheless, it is important to remark the distinction between (i) computing the prime implicates and implicants and (ii) using the information they contain.In this paper, we present a way in which (ii) can be done without actually doing (i) by limiting prime implicants and implicates management to unitary implicants and implicates. Besides, we outline how the use of this technique is particularly relevant in the field of automated deduction in temporal logics. The information contained in temporal implicates and implicants can be used to design transformations of temporal formulae able to increase the power of automated deduction techniques for temporal logics. Particularly, we have developed a theory for unitary temporal implicates and implicants that can be more efficiently computed than prime implicants, while still providing the information needed to design this kind of transformations.The theory we have developed in this paper is easily extensible to cover different types of temporal logics, and is integrable in different automated deduction methods for these temporal logics.

An efficient algorithm for reasoning about fuzzy functional dependencies

A sound and complete Automated Prover for the Fuzzy Simplification Logic (FSL logic) is introduced and based on it a method for efficiently reasoning about fuzzy functional dependencies over domains with similarity relations. The complexity of the algorithm is the same as that of equivalent algorithms for crisp functional dependencies that appear in the literature.

Structure Theorems for Closed Sets of Implicates/ Implicants in Temporal Logic

Implicants and implicates has proven to be powerful tools to improve the deduction capabilities of automated theorem provers. In this work, we focussed on the propositional temporal logic and we propose a new theoretical framework to capture maximum information about implicants and implicates. Concretely, we study the structure of the sets of unitary implicates and implicants and present the concept of base as the smallest finite set that generates them. As we shall show, using bases it is possible to handle efficiently the sets of implicants and implicates. For this, we introduce a set of operators having linear cost.

Reducing the search space by closure and simplification paradigms

In this paper, we present an innovative method to solve the minimal keys problem strongly based on the Simplification Logic for Functional Dependencies. This novel method improves previous logic-based methods by reducing, in a significant degree, the size of the search space this problem deals with. Furthermore, the new method has been designed to easily fit within a parallel implementation, thereby increasing the boundaries current methods can reach.

Minimal generators, an affordable approach by means of massive computation

Closed sets and minimal generators are fundamental elements to build a complete knowledge representation in formal concept analysis. The enumeration of all the closed sets and their minimal generators from a set of rules or implications constitutes a complex problem, drawing an exponential cost. Even for small datasets, such representation can demand an exhaustive management of the information stored as attribute implications. In this work, we tackle this problem by merging two strategies. On the one hand, we design a pruning, strongly based on logic properties, to drastically reduce the search space of the method. On the other hand, we consider a parallelization of the problem leading to a massive computation by means of a map-reduce like paradigm. In this study we have characterized the type of search space reductions suitable for parallelization. Also, we have analyzed different situations to provide an orientation of the resources (number of cores) needed for both the parallel architecture and the size of the problem in the splitting stage to take advantage in the map stage.