NPIs, Intervention, and Collectivity

This file models the Revised NPI Licensing Condition (LicensingCondition): a negative polarity item is acceptable only in a sentence that is downward entailing with respect to it and that none of its scalar alternatives entails, so that the sentence is a strongest of its alternatives. The condition is stated over a constituent with its alternatives (WithAlternatives), not over the operators above the item, and some constituent containing the item must meet it. In the models the clause below negation is upward entailing with respect to the item, so the condition falls on the negated sentence. Under negation it asks that the positive sentence be a weakest of its alternatives (licensingCondition_compl_iff), the sentence-level counterpart of a scalar term at the bottom of its scale.

With and between any NP and another plurality, the or-alternative entails the sentence whenever the predicate holds of the parts of any plurality it holds of, so conjoined any requires a predicate that is not divisive, while a collective predicate meets the condition. A numeral above one intervenes with a divisive predicate for the same reason, and a universal quantifier over a nonempty domain intervenes with any predicate of individuals, since it entails its existential alternative.

Under doubt, the sentence is a strongest of its alternatives exactly when Chierchia's Strong Application gives it no implicature. Strong Application negates only the alternatives that asymmetrically entail a sentence, so a collective conjunction stays downward entailing with respect to any, while exhaustification against every alternative the sentence does not entail destroys that downward entailment. The condition the substrate places on the environment of a weak item, downward and not upward entailment, is the first clause of the revised condition without the second, and holds of an environment that the revised condition rejects.

Implementation notes

• Pluralities form a join semilattice with a bottom, conjunction is the join, and the indefinite ranges over the nonzero parts of its restrictor; the models take the finite sets of individuals. A predicate of pluralities is divisive at a world when it holds of the parts of what it holds of (Mereology.DIV), which is antitonicity (antitone_iff_forall_div).
• Downward entailment with respect to the item is checked under strengthening of its restrictor. The scalar alternatives come with the sentence, so restricting them to local ones is the caller's choice, and an alternative equivalent to the sentence does not entail it in the sense of the condition.
• The constituents containing the item are the domains of a path (PolarityItem.Path), whose layers apply to the alternatives of the clause. Each model's clause is upward entailing in the restrictor and empty at its bottom, so no clause without the negation meets the condition.
• The condition is necessary for acceptability; the paper also reasons from its satisfaction to acceptability, and rows_licensing pairs it with the judgments in both directions.
• Negation is complementation. A numeral sentence asserts a plurality of exactly that many, and a numeral's alternatives are the numerals from one up. The universal and existential determiners are the substrate's.
• The models instantiate the conjunctions of plural DPs; a judged row is read only when its sentence is one the models instantiate.

Errata

• The interfering implicature of a collective conjunction is presented as following from Chierchia's (2004) core idea. It follows from the exhaustification the paper attributes to Chierchia (2013), not from the 2004 scalar assertion, which negates only the weakest alternative that asymmetrically entails the sentence; the paper's own observation is that the or-alternative of a collective conjunction does not, so on the 2004 definitions the implicature does not arise (strongApply_andNode_wroteTogether).

TODO

• The operator-based Revised Additional Restriction and its undergeneration and overgeneration under boolean, non-boolean and ambiguous conjunction; conjunctions of singular and mass DPs, whose or-alternative may be ill-formed; collective universal quantification; always; mixed predicates disambiguated to the collective reading; the movement-based accounts; the pruning constraints.

References

• Buccola & Crnič 2021, NPIs, Intervention, and Collectivity
• Linebarger 1987, Negative polarity and grammatical representation
• Chierchia 2004, Scalar Implicatures, Polarity Phenomena, and the Syntax/Pragmatics Interface formalized
• Chierchia 2013, Logic in Grammar: Polarity, Free Choice, and Intervention formalized
• Gajewski 2011, Licensing Strong NPIs formalized