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An interval-valued fuzzy answer set programming paradigm is proposed fornonmonotonic reasoning with vague and uncertain information. The set ofsub-intervals of $[0,1]$ is considered as truth-space. The intervals areordered using preorder-based truth and knowledge ordering. The preorder basedordering is an enhanced version of bilattice-based ordering. The system canrepresent and reason with prioritized rules, rules with exceptions. Aniterative method for answer set computation is proposed. The sufficientconditions for termination of iterations are identified for a class of logicprograms using the notion of difference equations.

A Unified Framework for Nonmonotonic Reasoning with Vagueness and Uncertainty