Observations on the Minimality of Ranking Functions for Qualitative Conditional Knowledge Bases and Their Computation

Ordinal conditional functions (OCFs) provide a semantic domain for qualitative conditionals of the form “if A, then (normally) B” by ordering worlds according to their degree of surprise. Transferring the idea of maximum entropy to a more qualitative domain, c-representations of a knowledge base R consisting of a set of conditionals have been defined as OCFs satisfying in particular the property of conditional indifference. While c-representations for R can be specified as the solutions of a constraint satisfaction problem CR(R), it has been an open problem whether there may be different minimal c-representations induced by minimal solutions of CR(R). Another open question has been whether particular inequations in CR(R) may be sharpened by transforming them into equations without loosing any minimal solutions, taking different notions of minimality into account. In this paper, we answer both questions and discuss further aspects of OCF minimality.