Modelos de representación de imprecisión e incertidumbre en fusión de alto nivel

Actas de: XVII Congreso Español sobre Tecnologías y Lógica Fuzzy (ESTYLF 2014). Zaragoza, 5-7 de febrero de 2014.Las técnicas de fusión de datos e información procedente de redes de sensores necesitan manejar información incierta e imprecisa, puesto que es habitual enfrentarse a problemas en los que el conocimiento disponible es vago o insuficiente y/o los aparatos de medición están sujetos a fallos. Con el reciente auge de la denominada "fusión de alto nivel", que tiene como objetivo reconocer la situación observada e identificar posibles riesgos, este problema se ha acentuado, ya que los formalismos que se utilizan habitualmente para construir un modelo simbólico del escenario, como la lógica de primer orden y las ontologías, no proporcionan soporte para este tipo de conocimiento. En este trabajo repasamos varias propuestas recientes para representación y razonamiento con información incierta e imprecisa en fusión de alto nivel. Nos centramos en dos tipos: (a) las que incorporan estos mecanismos en los propios modelos de representación, como las ontologías probabilísticas y difusas y las redes lógicas de Markov; (b) las que extienden el proceso de fusión con una capa de gestión de incertidumbre adicional, como las basadas en argumentación probabilística.Este trabajo ha sido financiado por la Junta de Andalucía (P11-TIC-7460), la Comunidad de Madrid (S2009/TIC- 1485) y el Ministerio de Economía y Competitividad de España (TEC2012-37832-C02-01, TEC2011-28626-C02- 02, TIN2012-30939).Publicad

Fuzzy ontology representation using OWL 2

AbstractThe need to deal with vague information in Semantic Web languages is rising in importance and, thus, calls for a standard way to represent such information. We may address this issue by either extending current Semantic Web languages to cope with vagueness, or by providing a procedure to represent such information within current standard languages and tools. In this work, we follow the latter approach, by identifying the syntactic differences that a fuzzy ontology language has to cope with, and by proposing a concrete methodology to represent fuzzy ontologies using OWL 2 annotation properties. We also report on some prototypical implementations: a plug-in to edit fuzzy ontologies using OWL 2 annotations and some parsers that translate fuzzy ontologies represented using our methodology into the languages supported by some reasoners

On similarity in fuzzy description logics

This paper is a contribution to the study of similarity relations between objects represented as attribute-value pairs in Fuzzy Description Logics . For this purpose we use concrete domains in the fuzzy description logic IALCEF(D)IALCEF(D) associated either with a left-continuous or with a finite t-norm. We propose to expand this fuzzy description logic by adding a Similarity Box (SBox) including axioms expressing properties of fuzzy equalities. We also define a global similarity between objects from similarities between the values of each object attribute (local similarities) and we prove that the global similarity defined using a t-norm inherits the usual properties of the local similarities (reflexivity, symmetry or transitivity). We also prove a result relative to global similarities expressing that, in the context of the logic MTL∀, similar objects have similar properties, being these properties expressed by predicate formulas evaluated in these object

Fuzzy description logics with general t-norms and datatypes

Fuzzy description logics (DLs) are a family of logics which allow the representation of (and the reasoning within) structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, current fuzzy DLs still present several limitations. In this work we face two problems: the common restriction to Zadeh and Łukasiewicz fuzzy logics and the inability to deal with datatypes different from fuzzy sets. In particular, we propose a semantics based on the use of a general left-continuous t-norm and an involutive negation (specially focused on Product logic) and, furthermore, we show how to handle functional concrete roles relating individuals of the domain and strings, real or integer numbers

Fuzzy Description Logics with General Concept Inclusions

Description logics (DLs) are used to represent knowledge of an application domain and provide standard reasoning services to infer consequences of this knowledge. However, classical DLs are not suited to represent vagueness in the description of the knowledge. We consider a combination of DLs and Fuzzy Logics to address this task. In particular, we consider the t-norm-based semantics for fuzzy DLs introduced by Hájek in 2005. Since then, many tableau algorithms have been developed for reasoning in fuzzy DLs. Another popular approach is to reduce fuzzy ontologies to classical ones and use existing highly optimized classical reasoners to deal with them. However, a systematic study of the computational complexity of the different reasoning problems is so far missing from the literature on fuzzy DLs. Recently, some of the developed tableau algorithms have been shown to be incorrect in the presence of general concept inclusion axioms (GCIs). In some fuzzy DLs, reasoning with GCIs has even turned out to be undecidable. This work provides a rigorous analysis of the boundary between decidable and undecidable reasoning problems in t-norm-based fuzzy DLs, in particular for GCIs. Existing undecidability proofs are extended to cover large classes of fuzzy DLs, and decidability is shown for most of the remaining logics considered here. Additionally, the computational complexity of reasoning in fuzzy DLs with semantics based on finite lattices is analyzed. For most decidability results, tight complexity bounds can be derived

Learning Terminological Knowledge with High Confidence from Erroneous Data

Description logics knowledge bases are a popular approach to represent terminological and assertional knowledge suitable for computers to work with. Despite that, the practicality of description logics is impaired by the difficulties one has to overcome to construct such knowledge bases. Previous work has addressed this issue by providing methods to learn valid terminological knowledge from data, making use of ideas from formal concept analysis. A basic assumption here is that the data is free of errors, an assumption that can in general not be made for practical applications. This thesis presents extensions of these results that allow to handle errors in the data. For this, knowledge that is "almost valid" in the data is retrieved, where the notion of "almost valid" is formalized using the notion of confidence from data mining. This thesis presents two algorithms which achieve this retrieval. The first algorithm just extracts all almost valid knowledge from the data, while the second algorithm utilizes expert interaction to distinguish errors from rare but valid counterexamples

Temporalised Description Logics for Monitoring Partially Observable Events

Inevitably, it becomes more and more important to verify that the systems surrounding us have certain properties. This is indeed unavoidable for safety-critical systems such as power plants and intensive-care units. We refer to the term system in a broad sense: it may be man-made (e.g. a computer system) or natural (e.g. a patient in an intensive-care unit). Whereas in Model Checking it is assumed that one has complete knowledge about the functioning of the system, we consider an open-world scenario and assume that we can only observe the behaviour of the actual running system by sensors. Such an abstract sensor could sense e.g. the blood pressure of a patient or the air traffic observed by radar. Then the observed data are preprocessed appropriately and stored in a fact base. Based on the data available in the fact base, situation-awareness tools are supposed to help the user to detect certain situations that require intervention by an expert. Such situations could be that the heart-rate of a patient is rather high while the blood pressure is low, or that a collision of two aeroplanes is about to happen. Moreover, the information in the fact base can be used by monitors to verify that the system has certain properties. It is not realistic, however, to assume that the sensors always yield a complete description of the current state of the observed system. Thus, it makes sense to assume that information that is not present in the fact base is unknown rather than false. Moreover, very often one has some knowledge about the functioning of the system. This background knowledge can be used to draw conclusions about the possible future behaviour of the system. Employing description logics (DLs) is one way to deal with these requirements. In this thesis, we tackle the sketched problem in three different contexts: (i) runtime verification using a temporalised DL, (ii) temporalised query entailment, and (iii) verification in DL-based action formalisms