Compact Representations of Conditional Knowledge and Implementational Aspects: Network Approaches to Ordinal Conditional Functions

Abstract

From the definition of ordinal conditional functions in Section 3.3 we obtained that storing an OCF means to store the ranking value of every possible world, and therefore the space needed to store an OCF is exponentially large in the number of variables. Additionally, generating such an OCF from a conditional knowledge base with the presented inductive approaches of System Z or c-representations has exponential computational time in the size of the propositional alphabet (see Section 3.3.3). Both is unsatisfactory, because both exponential time and space needed for the approaches restricts the problems to which these semantics can be applied in the field, hugely.