A Complete Map of Conditional Knowledge Bases in Different Normal Forms and Their Induced System P Inference Relations Over Small Signatures - Christoph Beierle; Jonas Haldimann; Steven Kutsch (Proceedings of the International Florida Artificial Intelligence Research Society Conference)
Conditional knowledge bases consisting of qualitative conditionals play a predominant role in knowledge representation and reasoning. In this paper, we develop a full map of all consistent conditional knowledge bases over a small signature in different normal forms. We introduce two new normal forms that take the induced system P inference relation into account, the system P normal form (SPNF) and the renaming SPNF (ρSPNF) considering additionally renamings of the underlying signature. For a two-element signature, we systematically generate and compare all consistent knowledge bases in ANF, RANF, SPNF, and their renaming counterparts, as well as all complete system P inference relations induced by conditional knowledge bases.