Morphologic for knowledge dynamics: revision, fusion, abduction
This work provides a formal framework for AI tasks involving knowledge dynamics, but it is incremental as it adapts an existing algebraic method to a new context.
The paper tackles the problem of modeling knowledge dynamics, including belief revision, fusion, and abduction, by applying mathematical morphology to propositional logic, resulting in well-defined operators with intuitive interpretations and addressed computational tractability.
Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical morphology in the context of propositional logic, and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based on a semantic approach, that have an intuitive interpretation and that are formally well behaved, to perform revision, fusion and abduction. Computation and tractability are addressed, and simple examples illustrate the typical results that can be obtained.