Lattice-Based Graded Logic: a Multimodal Approach
This work addresses the challenge of managing uncertain and incomplete knowledge in expert systems, though it appears incremental as it builds on existing qualitative and multimodal logic frameworks.
The paper tackles the problem of experts' discomfort with precise numerical certainty estimations by introducing a qualitative approach that attaches partially ordered symbolic grades to logical formulas, resulting in a sound and complete axiomatization for a multimodal logic with parameterized modal operators.
Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical formulas. Uncertain information is expressed by means of parameterized modal operators. We propose a semantics for this multimodal logic and give a sound and complete axiomatization. We study the links with related approaches and suggest how this framework might be used to manage both uncertain and incomplere knowledge.