Global Approach to Scalar Implicatures in DRT

It has been disputed whether scalar implicatures (=SIs) arise globally or locally. Basically, SIs should be global because they are calculated by comparing the strengths of whole alternative statements arising from a scalar set. On the other hand, localists claim that local SIs are sometimes favored and they are obtained by applying an operator to part of a statement. In this paper, I show that seemingly local SIs are effects that follow from anaphoric bindings of some variables in global SIs or from the contributiveness constraint. Moreover, some SIs do not correspond to any clause-type syntactic structures. In this paper, I propose an analysis of SIs within the discourse representation theory. The maxim of quantity provides the basic SI, which is the weakest one. The basic SI undergoes some processes in which some variables can be bound or some conditions are eliminated. In these processes, global SIs get the effects of local SIs, and some SIs arise from non-sentential constituents. Then among the resulting meanings, we get the strongest possible meanings, restricted by contributiveness conditions and likelihood.