  We introduce a variant of free logic (i.e., a logic admitting terms with
nonexistent referents) that accommodates truth-value gluts as well as gaps.
Employing a suitable expansion of the Belnap-Dunn four-valued logic, we specify
a dual-domain semantics for free logic, in which propositions containing
non-denoting terms can be true, false, neither true nor false, or both true and
false. In each model, the dual domain semantics separates existing and
non-existing objects into two subdomains, making it possible to quantify either
over all objects or existing objects only. We also outline a fuzzy variant of
the dual-domain semantics, accommodating non-denoting terms in fuzzy contexts
that can be partially indeterminate or inconsistent.
