Conditionals and Modality

The Limit Assumption

“…Now on to the equivalent conditions on frames. One of them, here dubbed (KLA), is due to Schwager (2005) and Kaufmann & Kaufmann (2015). It lends itself well to an intuitive paraphrase in terms of paths through the modal background, which I mentioned in Section 1.3 above: it states that from every world in the modal background there is a path to a minimal world; or equivalently, that every nonmaximal chain can be extended to a maximal chain with a least element.…”

“…Since none of the definitions of necessity refers to worlds outside of the modal background, I take the version that quantifies over all non-empty subsets of the modal background as representative of this variant, which I dub the Powerset Limit Assumption (PLA). Finally, we will see below that the version of Schwager (2005) and Kaufmann & Kaufmann (2015) differs from both (SLA) and (PLA).…”

“…The set R f w of worlds accessible from w (i.e., at which all propositions in f (w) are true) plays an important role in Kratzer's semantics, yet there is no established name for it. I follow Cariani et al (2013), Kaufmann & Kaufmann (2015) and call it the modal background. I also assume, following Kratzer, that the value of the modal base is generally a consistent set of propositions (i.e., R f w is non-empty for all f , w).…”

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

“…The limit assumption says that we can single out a set of 'best' worlds starting from any world in the modal base. Formally (and following the formulation in Kaufmann & Kaufmann 2015):…”