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This paper presents novel empirical observations showing that counterfactuals and conditionals involving a contrast between events generate the implicature that their consequent is false, in addition to the well-known implicature that the antecedent is false. I show that existing compositional theories which predict the falsity of the antecedent do not predict the falsity of the consequent, and propose an extension of Starr's unified semantics (Starr, 2014) to capture it. I also examine the effect of this new implicature on minimal model generation for conditionals, providing algorithms for generating minimal models capturing the falsity of the antecedent for counterfactuals, the consistency of presuppositions with the actual world (Ippolito, 2003; Starr, 2014) for indicative and future subjunctive conditionals, and this newly observed falsity of the consequent.
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