Licensing contexts

A licensing context is a construction that can host a polarity item. It places a licenser over the item and realizes a function of Haspelmath's implicational map, where it realizes one, and what its licenser carries is a theorem about the operators it denotes. Clausal negation is anti-morphic. Nobody, the restrictor of a universal, without, deny, before, too … to and the clausal comparative are anti-additive and no more, and doubt downward entailing and no more. Few and at most are scalar: downward entailing, and not even that once exhaustified against the stronger no and at most n − 1, the determiner exhaustification Quantifier.Det.exhaustified. Every downward entailing context is so non-trivially. Focus only, adversatives, superlatives, conditional antecedents and temporal since are downward entailing only modulo their presuppositions, the modals, imperatives, generics and free relatives are modal licensers, and questions license by relevance. A study can state the theory of a licenser of its own; the named constructions are the shared inventory that lexical entries cite.

Main declarations

• PolarityItem.LicensingContext: the named constructions.
• PolarityItem.LicensingContext.licenser, PolarityItem.LicensingContext.haspelmath: the operator a construction places over the item and its function on Haspelmath's map.
• Quantifier.Det.exhaustified: a determiner exhaustified against its scale-mates.
• PolarityItem.LicensingContext.holds_negation, holds_nobody_iff, not_isStrawsonUE_nobody, not_holds_exhaustified_few, …: the certificates of each context's licenser.

Implementation notes

• A context is a name, so the lexical entries that list the contexts an item is attested in are computable data with decidable equality, while the licenser, often defined classically, is a function of the name. Distinct constructions can share a licenser: the necessity modal, the imperative, the generic and the free relative are all necessities, and the clausal comparative and too … to both exceed the clause's degrees.
• The inventory is the contexts the library gives a semantics, not an exhaustive list. It realizes six of Haspelmath's nine functions; the irrealis non-specific function, where nonveridical rather than downward-entailing operators license, has no context yet, and neither do many licensers of the downward-entailing literature, such as negative adverbs, neither … nor, the restrictor of no or not every.
• Before is Anscombe's universal reading, before ever. Too … to is the subject's degree exceeding every degree at which the infinitive holds, after Meier. Doubt is not believing and deny asserting the negation, over a doxastic or assertoric accessibility.
• The free relative is read as a necessity over its alternatives, with the modal presupposition of -ever; the generic is a necessity over normal worlds.
• Haspelmath's placements are his book's. Nobody, before-clauses and adversatives sit between direct and indirect negation there, so they realize no function here, nor do the rows outside the map's inventory.

References

• Ladusaw 1979, Polarity Sensitivity as Inherent Scope Relations formalized
• Zwarts 1998, Three Types of Polarity
• van der Wouden 1997, Negative Contexts: Collocation, Polarity and Multiple Negation formalized
• von Fintel 1999, NPI Licensing, Strawson Entailment, and Context Dependency formalized
• Gajewski 2011, Licensing Strong NPIs formalized
• Bylinina & Nouwen 2018, On ‘zero’ and semantic plurality formalized
• Anscombe 1964, Before and After formalized
• Hoeksema 1983, Negative polarity and the comparative formalized
• Meier 2003, The meaning of too, enough, and so...that
• Chierchia 2006, Broaden Your Views: Implicatures of Domain Widening and the “Logicality” of Language formalized
• Kadmon & Landman 1993, Any formalized
• van Rooy 2003, Negative Polarity Items in Questions: Strength as Relevance
• Haspelmath 1997, Indefinite Pronouns formalized