A Complete Map of Conditional Knowledge Bases in Different Normal Forms and Their Induced System P Inference Relations Over Small Signatures

Abstract

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.