Three Types of Existential Entailments in a Multi-domain Semantics

In this article, we argue for the distinction of three different types of predicates: existence entailing, (existence) neutral, and nonexistence entailing predicates. We provide linguistic tests as well as examples to motivate this distinction. After motivating our views on predicates, we show how our theory is able to deal with a multitude of problematic data both known from the literature as well as new. Then, we develop a multi-domain predicate logic inspired by certain versions of free logics in order to represent these entailments in a formal way.