Tractable approximate deduction for OWL

Acknowledgements This work has been partially supported by the European project Marrying Ontologies and Software Technologies (EU ICT2008-216691), the European project Knowledge Driven Data Exploitation (EU FP7/IAPP2011-286348), the UK EPSRC project WhatIf (EP/J014354/1). The authors thank Prof. Ian Horrocks and Dr. Giorgos Stoilos for their helpful discussion on role subsumptions. The authors thank Rafael S. Gonçalves et al. for providing their hotspots ontologies. The authors also thank BoC-group for providing their ADOxx Metamodelling ontologies.Peer reviewedPostprin

Rough matroids based on coverings

The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving them are usually greedy. Matroid, as a generalization of linear independence in vector spaces, it has a variety of applications in many fields such as algorithm design and combinatorial optimization. An excellent introduction to the topic of rough matroids is due to Zhu and Wang. On the basis of their work, we study the rough matroids based on coverings in this paper. First, we investigate some properties of the definable sets with respect to a covering. Specifically, it is interesting that the set of all definable sets with respect to a covering, equipped with the binary relation of inclusion $\subseteq$, constructs a lattice. Second, we propose the rough matroids based on coverings, which are a generalization of the rough matroids based on relations. Finally, some properties of rough matroids based on coverings are explored. Moreover, an equivalent formulation of rough matroids based on coverings is presented. These interesting and important results exhibit many potential connections between rough sets and matroids.Comment: 15page

Decision-Making with Belief Functions: a Review

Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A distinction is made between methods that construct a complete preference relation among acts, and those that allow incomparability of some acts due to lack of information. Methods developed in the imprecise probability framework are applicable in the Dempster-Shafer context and are also reviewed. Shafer's constructive decision theory, which substitutes the notion of goal for that of utility, is described and contrasted with other approaches. The paper ends by pointing out the need to carry out deeper investigation of fundamental issues related to decision-making with belief functions and to assess the descriptive, normative and prescriptive values of the different approaches

Continuous Improvement Through Knowledge-Guided Analysis in Experience Feedback

Continuous improvement in industrial processes is increasingly a key element of competitiveness for industrial systems. The management of experience feedback in this framework is designed to build, analyze and facilitate the knowledge sharing among problem solving practitioners of an organization in order to improve processes and products achievement. During Problem Solving Processes, the intellectual investment of experts is often considerable and the opportunities for expert knowledge exploitation are numerous: decision making, problem solving under uncertainty, and expert configuration. In this paper, our contribution relates to the structuring of a cognitive experience feedback framework, which allows a flexible exploitation of expert knowledge during Problem Solving Processes and a reuse such collected experience. To that purpose, the proposed approach uses the general principles of root cause analysis for identifying the root causes of problems or events, the conceptual graphs formalism for the semantic conceptualization of the domain vocabulary and the Transferable Belief Model for the fusion of information from different sources. The underlying formal reasoning mechanisms (logic-based semantics) in conceptual graphs enable intelligent information retrieval for the effective exploitation of lessons learned from past projects. An example will illustrate the application of the proposed approach of experience feedback processes formalization in the transport industry sector

Parametric matroid of rough set

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set family, with any subset of a universe as its parameter, to connect rough sets and matroids. On the one hand, for a universe and an equivalence relation on the universe, a parametric set family is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore it can generate a matroid, called a parametric matroid of the rough set. Three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, since partition-circuit matroids were well studied through the lower approximation number, we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.Comment: 15 page

Complementary Lipschitz continuity results for the distribution of intersections or unions of independent random sets in finite discrete spaces

We prove that intersections and unions of independent random sets in finite spaces achieve a form of Lipschitz continuity. More precisely, given the distribution of a random set $\Xi$, the function mapping any random set distribution to the distribution of its intersection (under independence assumption) with $\Xi$ is Lipschitz continuous with unit Lipschitz constant if the space of random set distributions is endowed with a metric defined as the $L_k$ norm distance between inclusion functionals also known as commonalities. Moreover, the function mapping any random set distribution to the distribution of its union (under independence assumption) with $\Xi$ is Lipschitz continuous with unit Lipschitz constant if the space of random set distributions is endowed with a metric defined as the $L_k$ norm distance between hitting functionals also known as plausibilities. Using the epistemic random set interpretation of belief functions, we also discuss the ability of these distances to yield conflict measures. All the proofs in this paper are derived in the framework of Dempster-Shafer belief functions. Let alone the discussion on conflict measures, it is straightforward to transcribe the proofs into the general (non necessarily epistemic) random set terminology