Minimal change: Relevance and recovery revisited

The operation of contraction (referring to the removal of knowledge from a knowledge
base) has been extensively studied in the research field of belief change, and different
postulates (e.g., the AGM postulates with recovery, or relevance) have been proposed, as
well as several constructions (e.g., partial meet) that allow the definition of contraction
operators satisfying said postulates. Most of the related work has focused on classical
logics, i.e., logics that satisfy certain intuitive assumptions; in such logics, several nice
properties and equivalences related to the above postulates and constructions have been
shown to hold. Unfortunately, previous work has shown that the postulates’ applicability
and the related results generally fail for non-classical logics. Motivated by the fact that nonclassical
logics (like Description Logics or Horn logic) are increasingly being used in various
applications, we study contraction for all monotonic logics, classical or not. In particular,
we identify several sufficient conditions for the various postulates to be applicable, and
show that, in practice, relevance is a more suitable (i.e., applicable) minimality criterion
than recovery for non-classical logics. In addition, we revisit some important related results
from the classical belief change literature and study conditions sufficient for them to hold
for non-classical logics; the corresponding results for classical logics emerge as corollaries
of our more general results. Our work is another step towards the aim of exploiting the
rich belief change literature for addressing the evolution problem in a larger class of logics.