Scalar implicatures of embedded disjunction

Abstract

Sentences with disjunction in the scope of a universal quantifier, Every A is P or Q, tend to give rise to distributive inferences that each of the disjuncts holds of at least one individual in the domain of the quantifier, Some A is P & Some A is Q. These inferences are standardly derived as an entailment of the meaning of the sentence together with the scalar implicature that it is not the case that either disjunct holds of every individual in the domain of the quantifier, ¬Every A is P & ¬Every A is Q (plain negated inferences). As we show, this derivation faces a challenge in that distributive inferences may obtain in the absence of plain negated inferences. We address this challenge by showing that on particular assumptions about alternatives, a derivation of distributive inferences as scalar implicatures can be maintained without in fact necessitating plain negated inferences. These assumptions accord naturally with the grammatical approach to scalar implicatures. We also present experimental data that suggest that plain negated inferences are not only unnecessary for deriving distributive inferences, but might in fact be unavailable.

Deriving the positive polarity behavior of plain disjunction

“…The first step in the analysis will be to render the SI optional in the case of plain disjunctions. In this spirit, I follow previous authors (Fox & Katzir (2011), Crnič, Chemla & Fox (2015) who have argued that alternatives can be pruned, namely that exhaustification can proceed with respect to a subset of the set of innocently excludable alternatives. I will adopt this assumption and propose that plain disjunction may prune the scalar alternative from its alternative set, whereas complex disjunction may not.…”

Any: Logic, likelihood, and context (Pt. 1)

“…The excludable alternatives can be further restricted in the application of exh to include only relevant alternatives, which is captured by equipping exh with a resource domain, in (23). What alternatives may count as not relevant is tightly constrained (see, e.g., Bar‐Lev, ; Crnič et al, ; Fox & Katzir, ; Katzir, for discussion).…”

Probability and implicatures: A unified account of the scalar effects of disjunction under modals

“…There is broad (though not universal) agreement that a Boolean analysis of disjunction (and classical modal semantics) are essentially correct, and that the scalar effects we described should be captured as implicatures that arise on top of literal meaning (Kratzer & Shimoyama 2002, Simons 2005, Fox 2007, Klinedinst 2007, Chemla 2008, van Rooij 2010, Franke 2011, Alonso Ovalle 2005, Chierchia 2013, Crnič et al 2015. 3 The main argument for this approach is that the problematic effects disappear in downward entailing contexts -a signature of scalar implicatures in general.…”

“…See also footnote 8 below, where we point to arguments from Crnič et al (2015), which call into question whether we should treat at least the case of all in the same way.…”