Possibilistic logic bases and possibilistic graphs
This work addresses knowledge representation issues in AI, but it appears incremental as it focuses on translating between existing frameworks without introducing new paradigms.
The paper tackles the problem of representing knowledge using possibilistic logic bases and possibilistic graphs, showing their semantic equivalence and providing translation methods between them based on different conditioning types in possibility theory.
Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) according to their level of certainty, while the latter exhibits relationships between variables. The two types of representations are semantically equivalent when they lead to the same possibility distribution (which rank-orders the possible interpretations). A possibility distribution can be decomposed using a chain rule which may be based on two different kinds of conditioning which exist in possibility theory (one based on product in a numerical setting, one based on minimum operation in a qualitative setting). These two types of conditioning induce two kinds of possibilistic graphs. In both cases, a translation of these graphs into possibilistic bases is provided. The converse translation from a possibilistic knowledge base into a min-based graph is also described.