AbstractThis article offers a unified theory of the licensing of Negative and Positive Polarity Items (PIs), focusing on the acceptability conditions of PPIs of the some-type, and NPIs of the any-type. It argues that licensing has both a syntactic and a semantic component. On the syntactic side, the acceptability of PIs is checked in constituents; in fact, for any given PI, only some constituents, referred to as `domains', are eligible for the evaluation of that PI. The semantic dimension of licensing consists in the sensitivity of PIs to the monotonicity properties of the syntactic environments they find themselves in. Two pieces of evidence support the semantic dimension of what I call the ‘environment-based’ approach defended here: (i.) PIs are subject to flip-flop and (ii.) certain inferences affect their acceptability by modifying the monotonicity of their environment. A third property, called ‘entanglement’ and so far unnoticed, is described: the acceptability of PIs depends on the acceptability of other PIs in the same syntactic environment. The latter property is exploited to determine what semantic property some is sensitive to: it turns out that, contrary to the consensus among researchers, some is acceptable in the complement of the set of environments in which any is acceptable, and vice versa.