Probability-Possibility Transformations: Application to Credal Networks

IEEE Trans. Fuzzy Syst.

2022

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We address the problem of handling inconsistency in uncertain knowledge bases that are specified in the lightweight fragments of Description Logics DL-Lite. More specifically, we assume that the TBox component is coherent, stable and fully reliable. However, the ABox component may be inconsistent with respect to the TBox, partially preordered and uncertain. Uncertainty is encoded in the framework of possibility theory. In this context, we propose an extension of standard possibilistic DL-Lite. We represent the ABox as a symbolic weighted base, where the weights attached to the assertions are ordered according to a strict partial order. We define a tractable method for computing a single possibilistic repair for a partially preordered weighted ABox. The idea is to consider the possibilistic compatible bases of such an ABox, which intuitively encode all the possible extensions of a partial order, and compute the possibilistic repair of each compatible base. We then compute the intersection of all these possibilistic repairs to obtain a single repair for the initial ABox. We also provide an equivalent characterization by introducing the notion of π-accepted assertions. This ensures that the computation of the partially preordered possibilistic repair can be achieved in polynomial time in DL-Lite.

Section: Possibility Distributionsmentioning

confidence: 99%

Computing a Possibility Theory Repair for Partially Preordered Inconsistent Ontologies

Belabbès¹,

IEEE Trans. Fuzzy Syst.

2022

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“…PNs could be seen as approximate models of some imprecise probabilistic models. In [Benferhat et al, 2015b], an approach based on probability-possibility transformations is proposed to perform approximate MAP inference in credal networks where MAP inference is very hard [Mauá et al, 2014].…”

Section: Fig 8 Example Of a Possibilistic Networkmentioning

confidence: 99%

Belief Graphical Models for Uncertainty Representation and Reasoning

A Guided Tour of Artificial Intelligence Research

Leray

Tabia

2020

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Many real world problems and applications require to exploit incomplete, complex and uncertain information. Belief graphical models encompass a wide range of graphical formalisms for representing and reasoning with uncertain and complex information. They generally involve a graphical component which can be directed or undirected and a numerical one depending on the considered uncertainty setting. The graphical component encodes a set of independence statements while the numerical one quantifies the uncertainty regarding variables. The main use of belief graphical models is knowledge representation, reasoning and decision making for multivariate problems. Belief graphical models can be built either by eliciting the uncertain knowledge of an expert or automatically learnt from data using machine learning techniques. Many types of inference algorithms exist and many platforms are now available allowing modeling and reasoning with belief graphical models in many application areas such as diagnosis, forecasting, decision making and classification. This chapter provides an overview of the most common belief graphical models. In particular, it gives an overview on various aspects related to graphical models for uncertainty: representation, inference, learning and finally applications.

“…Possibilistic networks could also be used to approximate inference models of some imprecise probabilistic models. For instance, in [3], an approach based on probability-possibility transformations is proposed to perform approximate MAP inference in credal networks where MAP inference is very hard [15]. Clearly, modeling and reasoning with complex problems involving many variables will not be tractable unless strong assumption are made regarding the structure of the network.…”

Section: High Computational Complexitymentioning

confidence: 99%

Possibilistic Networks: Computational Analysis of MAP and MPE Inference

Levray

Int. J. Artif. Intell. Tools

Tabia

2020

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Possibilistic graphical models are powerful modeling and reasoning tools for uncertain information based on possibility theory. In this paper, we provide an analysis of computational complexity of MAP and MPE queries for possibilistic networks. MAP queries stand for maximum a posteriori explanation while MPE ones stand for most plausible explanation. We show that the decision problems of answering MAP and MPE queries in both min-based and product-based possibilistic networks is NP-complete. Definitely, such results represent an advantage of possibilistic graphical models over probabilistic ones since MAP queries are NPPP -complete in Bayesian networks. Our proofs for querying min-based possibilistic networks make use of reductions from the 3SAT problem to querying possibilistic networks decision problem. Moreover, the provided reductions may be useful for the implementation of MAP and MPE inference engines based on the satisfiability problem solvers. As for product-based networks, the provided proofs are incremental and make use of reductions from SAT and its weighted variant WMAXSAT.