  The logic of hybrid MKNF (minimal knowledge and negation as failure) is a
powerful knowledge representation language that elegantly pairs ASP (answer set
programming) with ontologies. Disjunctive rules are a desirable extension to
normal rule-based reasoning and typically semantic frameworks designed for
normal knowledge bases need substantial restructuring to support disjunctive
rules. Alternatively, one may lift characterizations of normal rules to support
disjunctive rules by inducing a collection of normal knowledge bases, each with
the same body and a single atom in its head. In this work, we refer to a set of
such normal knowledge bases as a head-cut of a disjunctive knowledge base. The
question arises as to whether the semantics of disjunctive hybrid MKNF
knowledge bases can be characterized using fixpoint constructions with
head-cuts. Earlier, we have shown that head-cuts can be paired with fixpoint
operators to capture the two-valued MKNF models of disjunctive hybrid MKNF
knowledge bases. Three-valued semantics extends two-valued semantics with the
ability to express partial information. In this work, we present a fixpoint
construction that leverages head-cuts using an operator that iteratively
captures three-valued models of hybrid MKNF knowledge bases with disjunctive
rules. This characterization also captures partial stable models of disjunctive
logic programs since a program can be expressed as a disjunctive hybrid MKNF
knowledge base with an empty ontology. We elaborate on a relationship between
this characterization and approximators in AFT (approximation fixpoint theory)
for normal hybrid MKNF knowledge bases.
