Towards having computers understand human users context information, this dissertation proposes a systematic context-sensing implementation methodology that can easily combine sensor outputs with subjective judgments. The feasibility of this idea is demonstrated via a meeting-participants focus-of-attention analysis case study with several simulated sensors using prerecorded experimental data and artificially generated sensor outputs distributed over a LAN network. The methodology advocates a top-down approach: (1) For a given application, a context information structure is defined

Using topos theory I prove that reasoning about probabilities can be formalized with only one simple assumption: given two sets of measures A, B, if B A, then B is less imprecise than A.

A topos of presheaves can be seen as an extension of classical set theory, where sets vary over informational states, therefore it is a powerful and expressive mathematical framework. I introduce a suitable topos of presheaves where imprecise probabilities and imprecise probabilistic reasoning can be represented. In this way we obtain a mathematical definition of imprecise-probabilistic sets. A valid and complete proof system, w.r.t. the intended semantics of imprecise probabilities, is described using the internal language of the topos. Key words: reasoning with uncertainty, topos theory, sheaf theory 1

In this work we propose a general approach for representing uncertainty measures in the framework of t-norm based logics. This approach is extended also to classes of measures like probability, possibility, necessity, lower and upper probability. We show that, under certain conditions, the logical consistency of a theory of uncertainty is tantamount to the coherence of a related assessment of rational values. Finally, we characterize the basic requirements that guarantee the compactness of coherent assessments. Keywords: T-norm based logics, Fuzzy measures, Coherence, Compactness.

The craft of model making: PSPACE bounds for non-iterative modal logics