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Precision of Probabilistic Deduction under Taxonomic Knowledge

Thomas Lukasiewicz

Precision of Probabilistic Deduction under Taxonomic Knowledge

Dissertation, University of Augsburg.
1st Examiner: Prof. Dr. W. Kießling
2nd Examiner: Prof. Dr. W. Dosch
erschienen 07/1996


Abstract

The deduction of probabilistic knowledge can be performed in a global approach by solving linear programming problems and in a local approach by the iterative application of inference rules. We analyze deeply the advantages and disadvantages of both approaches. We show that the local approach generally cannot compete with the global one. We clearly specify the very restricted class of knowledge-bases in which the local approach has advantages over the global one.

We focus on a framework in which probabilistic deductions are to be performed from knowledge-bases containing taxonomic and probabilistic knowledge. We show that taxonomic knowledge can naturally be exploited in the local approach to probabilistic deduction. It assures the local precision of inference rules and provides a very efficient representation of probabilistic knowledge.

We provide precise inference rules for local probabilistic deductions under taxonomic knowledge. The soundness and the local precision of the presented inference rules are systematically proved by linear and nonlinear optimizations. This approach gives a deep theoretical insight into local probabilistic deductions. It shows a proof-theoretic elegance unknown in the literature so far.

We show that the presented local approach to probabilistic deduction can efficiently be implemented within the framework of concept lattices. Concept lattices allow a very efficient representation of taxonomic and probabilistic knowledge. They also provide a useful framework for comparisons between the local and the global approach to probabilistic deduction.

We elaborate techniques for probabilistic deductions in correlation trees. We show that precise probabilistic deductions in a restricted class of correlation trees can be achieved by local computations only. This result is comparable to the well-known results for Bayesian networks. We show that precise probabilistic deductions in a broader class of correlation trees can be done by solving certain linear programming problems, which have a number of variables that is linear in the size of the probabilistic knowledge-base.