Abstract
The chapter draws on studies of the semantics of modality in the formal semantics tradition. Moving from the need of restricting the domain of quantification in a possible worlds semantics of modality , it presents a relational context-dependent semantics of modality inspired by the theory of Relative Modality. For Relative Modality modal expressions are relational and context-dependent. This approach is immediately applied to the analysis of conditionals and to the modeling of anaphora and rhetorical relations in discourse. The chapter demonstrates the potential of this approach for shedding light on the role of modal constructions as argumentative indicators . The vagueness and ad hoc-ness of modal conversational backgrounds plays an important role in the basic task of determining the propositional commitments of the arguers and for the potential for fallacy inherent in that vagueness. The contextual specification of modal conversational backgrounds is comparable to specifying the domain of quantifiers . Specifying the exact contribution of context dependent modal meanings to propositional content can impact, in turn, further aspects of the reconstruction of an argumentative discussion, notably including the semantic type of the propositions functioning as standpoints, the loci-relations supporting the inference from the premises to the standpoint, and the macrostructure of the argument .
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