A split-combination approach to merging knowledge bases in possibilistic logic

In this paper, we propose an adaptive approach to merging possibilistic knowledge bases that deploys multiple operators instead of a single operator in the merging process. The merging approach consists of two steps: one is called the splitting step and the other is called the combination step. The splitting step splits each knowledge base into two subbases and then in the second step, different classes of subbases are combined using different operators. Our approach is applied to knowledge bases which are self-consistent and the result of merging is also a consistent knowledge base. Two operators are proposed based on two different splitting methods. Both operators result in a possibilistic knowledge base which contains more information than that obtained by the t-conorm (such as the maximum) based merging methods. In the flat case, one of the operators provides a good alternative to syntax-based merging operators in classical logic.

Combining multiple prioritized knowledge bases by negotiation.

Recently, several belief negotiation models have been introduced to deal with the problem of belief merging. A negotiation model usually consists of two functions: a negotiation function and a weakening function. A negotiation function is defined to choose the weakest sources and these sources will weaken their point of view using a weakening function. However, the currently available belief negotiation models are based on classical logic, which makes them difficult to define weakening functions. In this paper, we define a prioritized belief negotiation model in the framework of possibilistic logic. The priority between formulae provides us with important information to decide which beliefs should be discarded. The problem of merging uncertain information from different sources is then solved by two steps. First, beliefs in the original knowledge bases will be weakened to resolve inconsistencies among them. This step is based on a prioritized belief negotiation model. Second, the knowledge bases obtained by the first step are combined using a conjunctive operator which may have a reinforcement effect in possibilistic logic.

Merging Knowledge Bases in Possibilistic Logic by Lexicographic Aggregation

Belief merging is an important but difficult problem in Artificial Intelligence, especially when sources of information are pervaded with uncertainty. Many merging operators have been proposed to deal with this problem in possibilistic logic, a weighted logic which is powerful for handling inconsistency and deal-ing with uncertainty. They often result in a possibilistic knowledge base which is a set of weighted formulas. Although possibilistic logic is inconsistency tolerant, it suffers from the well-known "drowning effect". Therefore, we may still want to obtain a consistent possibilistic knowledge base as the result of merging. In such a case, we argue that it is not always necessary to keep weighted information after merging. In this paper, we define a merging operator that maps a set of possibilistic knowledge bases and a formula representing the integrity constraints to a classical knowledge base by using lexicographic ordering. We show that it satisfies nine postulates that generalize basic postulates for propositional merging given in [11]. These postulates capture the principle of minimal change in some sense. We then provide an algorithm for generating the resulting knowledge base of our merging operator. Finally, we discuss the compatibility of our merging operator with propositional merging and establish the advantage of our merging operator over existing semantic merging operators in the propositional case.

Polynomials on Banach spaces with unconditional bases

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of the domain.