In this work we assume that uncertainty is a multifaceted concept which admits several different measures, and present a system for automated reasoning with multiple representations of uncertainty. Our focus is on problems which present more than one of these facets and therefore in which a multivalued representation of uncertainty and the study of its possibility of computational realisation are important for designing and implementing knowledge-based systems. We present a case study on developing a computational language for reasoning with uncertainty, starting with a semantically sound and computationally tractable language and gradually extending it with specialised syntactic constructs to represent measures of uncertainty, preserving its unambiguous semantic characterisation and computability properties. Our initial language is the language of normal clauses with SLDNF as the inference rule, and we select three facets of uncertainty, which are not exhaustive but cover many situations found in practical problems: vagueness, statistics and degrees of belief. To each of these facets we associate a specific measure: fuzzy measures to vagueness, probabilities on the domain to statistics and probabilities on possible worlds to degrees of belief. The resulting language is semantically sound and computationally tractable, and admits relatively efficient implementations employing ff \Gamma fi pruning and caching. ii Acknowledgements My supervisors were Paul Chung (during the first two years), Jane Hesketh (during the final year) and Dave Robertson (all the way through it). I cannot overstate how important, useful and pleasant their guidance and friendship was to develop this project. Didier Dubois and Henri Prade kindly accepted me as a visiting student at the IRIT - Univ...

In several tasks from different fields, we are encountering sparse events. In order to provide with probabilities for such events, researchers commonly perform a maximum likelihood (ML) estimation. However, it is well-known that the ML estimator is sensitive to extreme values. In other words, configurations with low or high frequencies are respectively underestimated or overestimated and therefore nonreliable. In order to solve this problem and to better evaluate these probability values, we propose a novel approach based on the probabilistic logic (PL) paradigm. For a sake of illustration, we focuss on this paper on events such as word trigrams (w 3 ; w 1 ; w 2 ) or word/pos-tag trigrams ((w 3 ; t 3 ); (w 1 ; t 1 ); (w 2 ; t 2 )). These latter entities are the basic objects used in speech or handwriting recognition. In order to distinguish between for example: "replace the fun" and "replace the floor" an accurate estimation of these two trigrams is needed. The ML estimation is equival...