Pragmatic Interpretations of Vague Expressions: Strongest Meaning and Nonmonotonic Consequence

Recent experiments have shown that naive speakers find borderline contradictions involving vague predicates acceptable. In Cobreros et al (2012a) we proposed a pragmatic explanation of the acceptability of borderline contradictions, building on a three-valued semantics. In a reply, Alxatib, Pagin & Sauerland (2013) show, however, that the pragmatic account predicts the wrong interpretations for some examples involving disjunction, and propose as a remedy a semantic analysis instead, based on fuzzy logic. In this paper we provide an explicit global pragmatic interpretation rule, based on a somewhat richer semantics, and show that with its help the problem can be overcome in pragmatics after all. Furthermore, we use this pragmatic interpretation rule to define a new (nonmonotonic) consequence-relation and discuss some of its properties.