Magri (2014): An Account for the Homogeneity Effect Triggered by Plural Definites and Conjunction #

This file formalizes the double-strengthening account of homogeneity of [Mag14]. A plural definite has the plain existential meaning of the indefinite, and its universal reading is an implicature of an implicature: the indefinite triggers the only some inference, and the definite triggers the inference that this inference is false, by the iterated exhaustification (19) of [Spe07a] over the exhaustivity operator (18). The paper's abstract configuration (§5.2) is three items, the item displaying homogeneity and the weak and strong poles of the scale it patterns with (Item), with a non-transitive Horn-mateness that pairs the item with one pole only. In the primal theory (52) the item means the weak pole and is a Horn-mate of it (primal, primalMates), so the inner exhaustification excludes nothing for the item while the outer one, denying the strengthened meaning of the weak pole, yields the strong one, (53b) (strengthened_primal_mystery_eq_strong); in a downward-entailing environment the negated meanings are already strongest and nothing is strengthened, (53a) (strengthened_primal_not_mystery). The dual theory (54), (55) turns this upside down by swapping the poles (dual, dualMates), and its computations are the primal ones relabeled (strengthened_comp_equiv). In a scenario where the weak pole holds without the strong both the positive and the negated sentence are false after strengthening, the homogeneity gap (primal_gap, dual_gap).

Plural definites and plural morphology instantiate the primal theory with cardinality thresholds over the extension of the predicate, (32) (atLeast, the_eq_all), and the same computation in the non-monotonic scope of exactly one student gives universal force in its upward and existential force in its downward component, (37) (exactlyOne_the). Unfocused conjunction instantiates the dual theory (§5.3), so under negation it behaves as disjunction, (61) (not_andUnF_eq_not_or); with the appendix's enriched alternatives, the atomic conjuncts (69), the same result comes out of [Fox07]'s innocent exclusion, (71) and (72) (strengthened_not_andUnF). Questions, which license no strengthening, would tell the theories apart, (62) and (63), and the paper conjectures (§4) that a matrix definite has universal force exactly when the indefinite triggers its implicature, which yields the sloppy existential reading of the classroom example of [Gaj05]; neither is modeled.

Implementation notes #

Meanings are sets of worlds over a finite world type; exhaustification is the substrate's innocent exclusion, so the excludable alternatives of (18) are those of the appendix's (70) throughout, which agrees with the paper's simpler definition on every computation it performs.
Each item carries its own Horn-mates, which is how the non-transitivity of (52b), (54b) and (69b) is encoded; the prejacent is not among its own alternatives.
The consistency hypotheses of the general computations, that the weak pole can hold without the strong and that the strong pole is satisfiable, are the conditions under which Fox's exclusion denies an alternative.

TODO #

The appendix's computations for conjunction under exactly one girl, (74) to (76), need three girls for the strengthened meaning to be satisfiable and are not formalized.

Magri (2014): An Account for the Homogeneity Effect Triggered by Plural Definites and Conjunction #

Implementation notes #

TODO #

References #

Iterated exhaustification over Horn-mates (§3.1, §3.2) #

The primal and the dual theory (§5.2) #

Plural definites and plural morphology (§3.3, §3.4) #

Non-monotonic environments (§3.4) #

Unfocused conjunction (§5.3, Appendix) #