Automated Reasoning with Uncertainties

In this work we assume that uncertainty is a multifaceted concept and present a system for automated reasoning with multiple representations of uncertainty.

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, while preserving its unambiguous semantic characterization and computability properties. Our initial language is the language of normal clauses with SLDNF as the inference rule, and we select three specific facets of uncertainty for our study: vagueness, statistics and degrees of belief.

The resulting language is semantically sound and computationally tracable. It also admits relatively efficient implementations employing α⋅β pruning and caching.