Zied Bouraoui

Possibilistic DL-Lite

DL-Lite is one of the most important fragment of description logics that allows a flexible representation of knowledge with a low computational complexity of the reasoning process. This paper investigates an extension of DL-Lite to deal with uncertainty associated with objects, concepts or relations using a possibility theory framework. Possibility theory offers a natural framework for representing uncertain and incomplete information. It is particularly useful for handling inconsistent knowledge. We first provide foundations of possibilistic DL-Lite, denoted by π-DL-Lite, where we present its syntax and its semantics. We then study the reasoning tasks and show how to measure the inconsistency degree of a knowledge base using query evaluations. An important result of the paper is that the extension of the expressive power of DL-Lite is done without additional extra computational costs.

Min-based Assertional Merging Approach for Prioritized DL-Lite Knowledge Bases

DL-Lite is a powerful and tractable family of description logics specifically tailored for applications that use huge volumes of data. In many real world applications, data are often provided by several and potentially conflicting sources of information having different levels of priority. Possibility theory offers a very natural framework to deal with ordinal and qualitative uncertain beliefs or prioritized preferences. Thus, to encode prioritized assertional facts, a possibility DL-Lite logic is more suited. We propose in this paper a min-based assertional merging operator for possibilistic DL-Lite knowledge bases. We investigate in particular the situation where the sources share the same terminological base. We present a syntactic method based on conflict resolution which has a meaningful semantic counterpart when merging possibility distributions. We finally provide an analysis in the light of a new set of postulates dedicated to uncertain DL-Lite merging.

Min-Based Fusion of Possibilistic DL-Lite Knowledge Bases

DL-Lite is one of the most important tractable fragment of DLs that provides a powerful framework to compactly encode available knowledge with a low computational complexity of the reasoning process. In semantic web area, merging different and often conflicting sources of information, has been recognized as an important problem. Pieces of information to be combined are provided with uncertainty due for instance to the reliability of sources. Possibility theory offers an important tool for representing and reasoning with uncertain, partial and inconsistent pieces of information. This paper first presents possibilistic DL-Lite, denoted by π-DL-Lite as an extension of DL-Lite within a possibility theory setting. It then focuses on the use of a minimum-based (min-based) operator, well known as idempotent conjunctive operator to combine π-DLLite possibility distributions and it shows that the semantic fusion of π-DL-Lite possibility distributions has a natural syntactic counterpart when dealing with π-DL-Lite knowledge bases. The min-based fusion operator is recommended when distinct sources that provide information are dependent.

Inconsistency-Tolerant Query Answering: Rationality Properties and Computational Complexity Analysis

Generalising the state of the art, an inconsistency-tolerant semantics can be seen as a couple composed of a modifier operator and an inference strategy. In this paper we deepen the analysis of such general setting and focus on two aspects. First, we investigate the rationality properties of such semantics for existential rule knowledge bases. Second, we unfold the broad landscape of complexity results of inconsistency-tolerant semantics under a specific (yet expressive) subclass of existential rules.

On the Revision of Prioritized DL-Lite Knowledge Bases

DL-Lite is a tractable family of description logics particularly suitable for query answering. One of the fundamental issues in this area is the dynamics of the knowledge base which is a problem closely related to the belief revision one. This paper investigates revision of prioritized DL-Lite knowledge bases when a new input piece of information, possibly conflicting or uncertain, becomes available. To encode the prioritized knowledge, we use a possibility theory-based DL-Lite logic. We first study revision at the semantic level consisting in directly conditioning possibility distributions. In particular, we show that such conditioning provides in some situations some counterintuitive results compared with the ones of conditioning directly the knowledge base syntactically. We then study revision at the syntactic level of possibilistic DL-Lite knowledge bases. Finally, we show that such revision process has a meaningful semantic counterpart.

A Polynomial Algorithm for Merging Lightweight Ontologies in Possibility Theory Under Incommensurability Assumption.

The context of this paper is the one of merging lightweight ontologies with prioritized or uncertain assertional bases issued from different sources. This is especially required when the assertions are provided by multiple and often conflicting sources having different reliability levels. We focus on the so-called egalitarian merging problem which aims to minimize the dissatisfaction degree of each individual source. The question addressed in this paper is how to merge prioritized assertional bases, in a possibility theory framework, when the uncertainty scales are not commensurable, namely when the sources do not share the same meaning of uncertainty scales. Using the notion of compatible scale, we provide a safe way to perform merging. The main result of the paper is that the egalitarian merging of prioritized assertional bases can be achieved in a polynomial time even if the uncertainty scales are not commensurable.

MEmbER: Max-Margin Based Embeddings for Entity Retrieval

We propose a new class of methods for learning vector space embeddings of entities. While most existing methods focus on modelling similarity, our primary aim is to learn embeddings that are interpretable, in the sense that query terms have a direct geometric representation in the vector space. Intuitively, we want all entities that have some property (i.e. for which a given term is relevant) to be located in some well-defined region of the space. This is achieved by imposing max-margin constraints that are derived from a bag-of-words representation of the entities. The resulting vector spaces provide us with a natural vehicle for identifying entities that have a given property (or ranking them according to how much they have the property), and conversely, to describe what a given set of entities have in common. As we show in our experiments, our models lead to a substantially better performance in a range of entity-oriented search tasks, such as list completion and entity ranking.

Learning Conceptual Space Representations of Interrelated Concepts

Several recently proposed methods aim to learn conceptual space representations from large text collections. These learned representations asso- ciate each object from a given domain of interest with a point in a high-dimensional Euclidean space, but they do not model the concepts from this do- main, and can thus not directly be used for catego- rization and related cognitive tasks. A natural solu- tion is to represent concepts as Gaussians, learned from the representations of their instances, but this can only be reliably done if sufficiently many in- stances are given, which is often not the case. In this paper, we introduce a Bayesian model which addresses this problem by constructing informative priors from background knowledge about how the concepts of interest are interrelated with each other. We show that this leads to substantially better pre- dictions in a knowledge base completion task.

Qualitative-Based Possibilistic \(\mathcal {EL}\) Ontology

In different situations, information coming from different sources are often affected with uncertainty and imprecision. Representing such information generally gives rise to a prioritized (i.e. stratified) knowledge base. To reason with such prioritized knowledge in a principled way, we propose an extension of \(\mathcal {EL}\) description logics within possibility theory, which provides a very natural framework to deal with ordinal, qualitative uncertainty, preferences and priorities. We first introduce the syntax and semantics of possibilistic \(\mathcal {EL}\), and then provide the main related reasoning tasks. We show in particular that these tasks remain tractable in possibilistic \(\mathcal {EL}\).

Polynomial Algorithms for Computing a Single Preferred Assertional-Based Repair

This paper investigates different approaches for handling inconsistent DL-Lite knowledge bases in the case where the assertional base is prioritized and inconsistent with the terminological base. The inconsistency problem often happens when the assertions are provided by multiple conflicting sources having different reliability levels. We propose different inference strategies based on the selection of one consistent assertional base, called a preferred repair. For each strategy, a polynomial algorithm for computing the associated single preferred repair is proposed. Selecting a unique repair is important since it allows an efficient handling of queries. We provide experimental studies showing (from a computational point of view) the benefits of selecting one repair when reasoning under inconsistency in lightweight knowledge bases.