Concession is one of the trickiest semantic discourse relations appearing in natural language. Many have tried to sub-categorize Concession and to define formal criteria to both distinguish its subtypes as well as for distinguishing Concession from the (similar) semantic relation of Contrast. But there is still a lack of consensus among the different proposals. In this paper, we focus on those approaches, e.g. (Lagerwerf 1998), (Winter & Rimon 1994), and (Korbayova & Webber 2007), assuming that Concession features two primary interpretations, "direct" and "indirect". We argue that this two way classification falls short of accounting for the full range of variants identified in naturally occurring data. Our investigation of one thousand Concession tokens in the Penn Discourse Treebank (PDTB) reveals that the interpretation of concessive relations varies according to the source of expectation. Four sources of expectation are identified. Each is characterized by a different relation holding between the eventuality that raises the expectation and the eventuality describing the expectation. We report a) a reliable inter-annotator agreement on the four types of sources identified in the PDTB data, b) a significant improvement on the annotation of previous disagreements on Concession-Contrast in the PDTB and c) a novel logical account of Concession using basic constructs from Hobbs' (1998) logic. Our proposal offers a uniform framework for the interpretation of Concession while accounting for the different sources of expectation by modifying a single predicate in the proposed formulae.
