We provide non-deterministic semantics for some content inclusion logics standing between the first-degree entailment fragments of Parry’s logic \({\textrm{PAI}}\) and Angell’s logic of analytic implication \({\textrm{AC}}\) . Our semantics is inspired by two-address semantics developed following ideas introduced by Herzberger and Woodruff, suggesting to independently evaluate formulas on their alethic and topical status. Building on this, we explore the results of allowing negation to be non-deterministic on either of these independent aspects. For this purpose, we emulate the presence of truth-value gaps and gluts by letting negation work non-deterministically on the alethic coordinate. At the same time, we emulate the presence of topic-transformed negated formulas by letting negation work non-deterministically on the topical coordinate. The outcome is a unifying framework for classical logic and a vast collection of non-classical systems that characterize them according to how negation and the set of designated values are defined.
