Given a belief base ∆ consisting of a set of conditionals,there are many different ways an agent may inductivelycomplete the knowledge represented by ∆ to a completeepistemic state; two well-known approaches are given by systemP and system Z, and also each ranking model of ∆ induces afull inference relation. C-representations are special rankingmodels that obey the principle of conditional indifference.Inductive reasoning using c-representations can be done withrespect to all c-representations, with respect to a subclass of,e.g., minimal c-representations, or with respect to singlec-representations. In this paper, we present and investigateselection strategies for determining single c-representations tobe used for inductive reasoning from belief bases. We developaxioms for specifying characteristics of selection strategies.We illustrate which desirable properties, like syntaxsplitting, are ensured by the axioms, and develop constructionsfor obtaining selection strategies satisfying the axioms.Furthermore, we also present and study the extension of selectionstrategies to c-revisions that follow the principle ofconditional preservation and that have been employed successfullyin various belief change settings.
System Z for Conditional Belief Bases with Positive and Negative Information
