Inmaculada Perez de Guzmán

A Tableau Calculus for Equilibrium Entailment

We apply tableau methods to the problem of computing entailment in the nonmonotonic system of equilibrium logic, a generalisation of the inference relation associated with the stable model and answer set semantics for logic programs. We describe tableau calculi for the nonclassical logics underlying equilibrium entailment, namely here-and-there with strong negation and its strengthening classical logic with strong negation. A further tableau calculus is then presented for computing equilibrium entailment. This makes use of a new method for reducing the complexity of the tableau expansion rules, which we call signing-up.

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.

Computing Equilibrium Models Using Signed Formulas

We discuss equilibrium logic, first presented in Pearce (1997), as a system of nonmonotonic reasoning based on the nonclassical logic N5 of here-and-there with strong negation. Equilibrium logic is a conservative extension of answer set inference, not only for extended, disjunctive logic programs, but also for significant extensions such as the programs with nested expressions described by Lifschitz, Tang and Turner (forthcoming). It provides a theoretical basis for extending the paradigm of answer set programming beyond current systems such as smodels and dlv. The paper provides proof systems for N5 and for model-checking in equilibrium logic. The reduction of the latter problem to an unsatisfiability problem of classical logic yields complexity results for the various decision problems concerning equilibrium entailment. The reduction also yields a basis for the practical implementation of an automated reasoning tool.

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.

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.

Lnint: A Temporal Logic That Combines Points And Intervals And The Absolute And Relative Approaches

The introduction of the temporal analysis in Logic has stimulated diierent approaches, some of them artiicially opposed, such as to consider an absolute or relative nature of time, to consider points or intervals or to consider diierent time flows. .. In this paper we develop a temporal logic that combines these approaches to have a logic with a good computational behaviour. This logic, which we call LNint, is a modal logic that combines the treatment of points and intervals and declarations about dates and dated intervals like temporal logics with temporal arguments, or like reiied logics and consequently, we obtain a mixture of the absolute and relative approaches to the treatment of time. LNint subsumes the US logic 12] and allows us not only to treat intervals with the operators of the logic proposed by Halpern and Shoham 14], but to deene naturally operators like the chop presented by Moszkowski in 19] Moreover, the semantics of LNint can be extended, in a natural way, to continuous time flows by employing RLN logic introduced in 9].

Specification and inference of fuzzy attributes

In this work, an extension of the database relational model which incorporates vague or imprecise data is presented. Specifically, we extend the concept of functional dependency to Fuzzy Attributes Tables. This extension is based on the use of a residuated lattice as a truthfulness value set. For this goal, the domains are enriched with fuzzy similarity relations, the atomic values of the tables become fuzzy, and the functional dependencies are also fuzzy and based on the similarity relations. Moreover, we introduce a sound and complete axiomatic system to manipulate these dependencies, named Simplification Logic for fuzzy functional dependencies.

MAT logic: a temporal×modal logic with non-deterministic operators to deal with interactive systems in communication technologies

In this paper, the Multi-flow Asynchronous Temporal Logic, called MAT Logic, is presented. MAT Logic is a new temporal×modal logic with non-deterministic operators among time flows as accessibility relations. The main goal of this work has been the design and description of a logic that could be capable of managing communications among systems with not necessarily synchronizable time flows. In order to better understand the design of the logic, an example in the field of communications is given.