Management of Uncertainty Orderings through ASP

Traditionally, most of the proposed probabilistic models of decision under uncertainty rely on numerical measures and representations. Alternative proposals call for qualitative (non-numerical) treatment of uncertainty, based on preference relations and belief orders. The automation of both numerical and non-numerical frameworks surely represents a preliminary step in the development of inference engines of intelligent agents, expert systems, and decision-support tools. In this paper we exploit Answer Set Programming to formalize and reason about uncertainty expressed by belief orders. The availability of ASP-solvers supports the design of automated tools to handle such formalizations. Our proposal reveals particularly suitable whenever the domain of discernment is \emph{partial}, i.e. it does not represent a closed world but just the relevant part of a problem. We first illustrate how to automatically ``classify'', according to the most well-known uncertainty frameworks, any given partial qualitative uncertainty assessment. Then, we show how to compute the enlargement of an assessment to any other new inference target, with respect to a fixed (admissible) qualitative framework.