Reason Maintenance - State of the Art

This paper describes state of the art in reason maintenance with a focus on its future usage in the KiWi project. To give a bigger picture of the field, it also mentions closely related issues such as non-monotonic logic and paraconsistency. The paper is organized as follows: first, two motivating scenarios referring to semantic wikis are presented which are then used to introduce the different reason maintenance techniques

Structure identification in relational data

This paper presents several investigations into the prospects for identifying meaningful structures in empirical data, namely, structures permitting effective organization of the data to meet requirements of future queries. We propose a general framework whereby the notion of identifiability is given a precise formal definition similar to that of learnability. Using this framework, we then explore if a tractable procedure exists for deciding whether a given relation is decomposable into a constraint network or a CNF theory with desirable topology and, if the answer is positive, identifying the desired decomposition. Finally, we address the problem of expressing a given relation as a Horn theory and, if this is impossible, finding the best k-Horn approximation to the given relation. We show that both problems can be solved in time polynomial in the length of the data

A logic-based analysis of Dempster-Shafer theory

AbstractDempster-Shafer (DS) theory is formulated in terms of propositional logic, using the implicit notion of provability underlying DS theory. Dempster-Shafer theory can be modeled in terms of propositional logic by the tuple (Σ, ϱ), where Σ is a set of propositional clauses and ϱ is an assignment of mass to each clause Σi ϵ Σ. It is shown that the disjunction of minimal support clauses for a clause Σi with respect to a set Σ of propositional clauses, ξ(Σi, Σ), when represented in terms of symbols for the ϱi 's, corresponds to a symbolic representation of the Dempster-Shafer belief function for δi. The combination of Belief functions using Dempster's rule of combination corresponds to a combination of the corresponding support clauses. The disjointness of the Boolean formulas representing DS Belief functions is shown to be necessary. Methods of computing disjoint formulas using network reliability techniques are discussed.In addition, the computational complexity of deriving DS Belief functions, including that of the logic-based methods which are the focus of this paper, is explored. Because of intractability even for moderately sized problem instances, efficient approximation methods are proposed for such computations. Finally, implementations of DS theory based on domain restrictions of DS theory, hypertree embeddings, and the ATMS, are examined