Restriction in doubly-modal disjunctions

Abstract

Within a disjunction ⌜φ or ψ⌝, the right disjunct ψ is typically evaluated on the supposition of ¬φ. This observation is central to recent dynamic and information-sensitive analyses of disjunction. However, in doubly-modal disjunctions (DMDs) – expressions of the form ⌜△₁φ or △₂ψ⌝ where △₁,△₂ ∈ {♢,□}, the second disjunct is often (though not always) interpreted relative to the negation of the left modal’s prejacent, i.e., ¬φ, instead of ¬△₁φ. In this paper, we critically evaluate two extant accounts of prejacent restriction in DMDs due to Klinedinst & Rothschild (2012) and Meyer (2015), arguing that neither account is predictive. Drawing on Singh’s (2007, 2008) approach to the proviso problem, we then argue that prejacent restriction in DMDs arises from speakers locally updating with the negation of a formal alternative to the left disjunct. The alternatives available for update are, we argue, constrained both by structural similarity and relevance.