Docs / Semantics / Exhaustification / Disjunctive

Exhaustifying a disjunction against its closure under disjunction

import Linglib.Semantics.Exhaustification.Disjunctive · namespace Exhaustification

Source

A disjunction ⋃ i ∈ I, p i whose alternatives lie in its closure under disjunction, supClosure (p '' I), the disjunctions over the nonempty subsets of I with no conjunctions, strengthens under exhIEII to their conjunction, provided some world verifies each disjunct alone and some world verifies all of them: nothing is innocently excludable, since a single-disjunct world is minimal, and everything is innocently includable, since the cell is consistent. With the whole closure the result is the conjunction of the disjuncts; with only the disjunctions over subsets of size m it is that at least |I| + 1 - m disjuncts hold. This is the generalization behind free choice without a conjunctive alternative and behind the implicature account of homogeneity, where the disjuncts are the atoms of a plurality and pruning to the size-m alternatives gives the non-maximal readings.

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