Selection Strategies for Inductive Reasoning From Conditional Belief Bases and for Belief Change Respecting the Principle of Conditional Preservation

Abstract

Given a belief base ∆ consisting of a set of conditionals,
there are many different ways an agent may inductively
complete the knowledge represented by ∆ to a complete
epistemic state; two well-known approaches are given by system
P and system Z, and also each ranking model of ∆ induces a
full inference relation. C-representations are special ranking
models that obey the principle of conditional indifference.
Inductive reasoning using c-representations can be done with
respect to all c-representations, with respect to a subclass of,
e.g., minimal c-representations, or with respect to single
c-representations. In this paper, we present and investigate
selection strategies for determining single c-representations to
be used for inductive reasoning from belief bases. We develop
axioms for specifying characteristics of selection strategies.
We illustrate which desirable properties, like syntax
splitting, are ensured by the axioms, and develop constructions
for obtaining selection strategies satisfying the axioms.
Furthermore, we also present and study the extension of selection
strategies to c-revisions that follow the principle of
conditional preservation and that have been employed successfully
in various belief change settings.