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Adaptive Merging of Prioritized Knowledge Bases

Liu W., Qi G., Bell D.A.

Fundamenta Informaticae

2006

Vol. 73, nr 3

389-407

In this paper, we propose an adaptive algorithm for merging n (n ł 2) prioritized knowledge bases which takes into account the degrees of conflict and agreement among these knowledge bases. The algorithm first selects largely partially maximal consistent subsets (LPMCS) of sources by assessing how (partially) consistent the information in the subset is. Then within each of these created subsets, a maximal consistent subset is further selected and knowledge bases in it are merged with a suitable conjunctive operator based on the degree of agreement among them. This result is then merged with the remaining knowledge bases in the corresponding LPMCS in the second step through the relaxation of the minimum operator. Finally, the knowledge bases obtained from the second step are merged by a maximum operator. In comparison with other merging methods, our approach is more context dependent and is especially useful when most sources of information are in conflict.

Incidence Calculus on Łukasiewicz's Three-valued Logic

Qi G., Milligan P., Sage P.

Fundamenta Informaticae

2005

Vol. 68, nr 4

357--378

Incidence calculus is a probabilistic logic which possesses both numerical and symbolic approaches. However, Liu in [5] pointed out that the original incidence calculus had some drawbacks and she established a generalized incidence calculus theory (GICT) based on ukasiewicz's three-valued logic to improve it. In a GICT, an incidence function is defined to relate each proposition f in the axioms of the theory to a set of possible worlds in which f has truth value true. But the incidence function only represents those absolute true states of propositions, so it can not deal with the uncertain states. In this paper, we use two incidence functions i* and i* to relate the axioms to the sets of possible worlds. For an axiom f, i*(f) is to be thought of as the set of possible worlds in which f has truth value true, while i*(f) is the set of possible worlds in which f is true or undeterminable. Since i* can represent the undeterminable state, our newly defined theory is more efficient to handle vague information than GICT.