What's on a machine's mind? Models for reasoning with incomplete and uncertain knowledge
Nico Roos · Research Repository (Delft University of Technology) · 1991
In this thesis, which consists of two parts, two different subjects are discussed. In the first part of the thesis a logic for reasoning with inconsistent knowledge will be described. The second part of the thesis contains a proposal for to view a reasoning process as a process of constructing a partial model of the world we are reasoning about. The purpose of the logic described in the first part of this thesis is to be able to derive useful conclusions from inconsistent knowledge. Knowledge can be inconsistent for several reasons. Firstly, knowledge sources do not have to be completly reliable. For example, even experts do not always agree. Secondly, default reasoning can be viewed as a special case of reasoning with inconsistent knowledge. To be able to reason with inconsistent knowledge, premisses cannot be viewed as being true statements about the world. Therefore, in the logic described premisses will be view as assumptions about the world. The premisses are assumed to be true statements about the world unless proven otherwise. By applying this view on the premisses, a logic for reasoning with inconsistent knowledge is being developed. The semantics of this logic is based on the ideas of Shoham. This semantics turns out to be a preferential semantics according to the definition of Kraus, Lehmann and Magidor. This implies that the logic is a logic of system P. Therefore, it possesses all the properties an ideal non-monotonic logic should possess. The second part of the thesis contains a proposal to view a reasoning process as a process of constructing a partial model of the world we are reasoning about. This view on a reasoning process has some important advantages over the traditional view on a reasoning process. Firstly, constructing a partial model of the world is more intuitive than generating propositions by combining already derived propositions. Secondly, constructing a partial model is more efficient than searching for a proof of some fact. Thirdly, in a partial model the consistency problem is decidable. This makes it possible to guarantee the correctness of the conclusions derived, when defaults rules are being used. For the conclusions based on a partial model two certainty measures can be defined, viz. a probability and a unlikelihood measure. The former will be used for conclusions expressing an expectation and the latter for conclusions expressing an explanation. For the probability measure we can show that it satisfies the laws of the probability theory and Gardenfors's postulates for the dynamical behaviour of probabilistic models. It turns out that the probability measure can be used to solve the problem of pre-emption and multiple inheritance in inheritance networks. The unlikelihood measure can be used to realize an every efficient heuristic diagnostic reasoning process.