Parentheticality, assertion strength, and polarity

Sentences with slifting parentheticals (such as The dean greeted the secretary, Jill said; Ross, in: Gross, Schutzenberger (eds) The formal analysis of natural language, Mouton, The Hague, 1973) grammaticalize an intriguing interaction between truth-conditional meaning and speech act function. In such sentences, the assertion strength of the slifted clause (the non-parenthetical part of the sentence) is modulated by the parenthetical, which provides evidential support (Urmson in Mind 61(244):480-496, 1952; Asher in J Semant 17:31-50, 2000; Rooryck in Glot Int 5(4):125-133, 2001; Jayez and Rossari in: Corblin, de Swart (eds) Handbook of French semantics, CSLI, Stanford, 2004; Davis et al. in Proc Semant Linguist Theory 17:71-88, 2007; Simons in Lingua 117:1034-1056, 2007; Murray in Semant Pragmat 7(2):1-53, 2014; Maier and Bary in: Brochhagen et al. (eds) Proceedings of the 20th Amsterdam colloquium, 2015; AnderBois in Semant Pragmat 9(19):1-55, 2016; Hunter in Dialogue Discourse 7(4):1-35, 2016). Starting with the idea that assertability comes in degrees (Lewis in Philos Rev 85:297-315, 1976; Davis et al. in Proc Semant Linguist Theory 17:71-88, 2007), this paper develops a probabilistic updatemodel that captures the role of parentheticality as a language tool for qualifying commitments. A crucial role here is played by the rule of Jeffrey conditionalization (Jeffrey in The logic of decision, The University of Chicago Press, Chicago, 1990), which factors in the uncertainty of the parenthetical information itself. The model also derives certain effects of parenthetical modification not found in regular embedding constructions, including the fact that slifting parentheticals are limited to creating upward-entailing environments.