It is generally accepted that a discourse connective expresses a semantic and/or pragmatic relation between its matrix sentence or clause and something in the previous discourse. Usually the sense of this relation is expressed as a label, often within a hierarchy of sense labels. But the meaning of these labels may vary from system to system, and the same connective may be assigned different labels in different systems. Given this, we might learn more and make better predictions if (ⅰ) sense labels were associated with (some of) their entailments and (ⅱ) connectives were characterized in terms of both their formal properties and their use conditions. I'll give examples of both.
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