  Multi-context systems (MCS) presented by Brewka and Eiter can be considered
as a promising way to interlink decentralized and heterogeneous knowledge
contexts. In this paper, we propose preferential multi-context systems (PMCS),
which provide a framework for incorporating a total preorder relation over
contexts in a multi-context system. In a given PMCS, its contexts are divided
into several parts according to the total preorder relation over them,
moreover, only information flows from a context to ones of the same part or
less preferred parts are allowed to occur. As such, the first $l$ preferred
parts of an PMCS always fully capture the information exchange between contexts
of these parts, and then compose another meaningful PMCS, termed the
$l$-section of that PMCS. We generalize the equilibrium semantics for an MCS to
the (maximal) $l_{\leq}$-equilibrium which represents belief states at least
acceptable for the $l$-section of an PMCS. We also investigate inconsistency
analysis in PMCS and related computational complexity issues.
