This paper is a formal study of a simplified version of Negative Polarity Item (NPI) licensing requirements in two languages, English and Hungarian. In the framework of Model-Theoretic Syntax, using logical formalisms defined over tree-languages, I show that neither pattern can be described with Tier-based Strictly Local (TSL) constraints only, and suggest that they need a more complex logical formula. In particular, Hungarian patterns can be described using a combination of Tier-based Strictly 2-Local constraints over dominance relations and Locally 1-Testable constraints over the left-of relations between nodes. For English, there are no sufficient local constraints, either with or without tiers. As part of the analysis, I give a definition of a generalized tree-language that uses Tier-based 2-Local constraints over dominance relations, while it remains underspecified for left-of relations
