 Implicature is important even in truth conditional semantics. For example, logicians customarily take sentences of the form “p or q” to be true provided “p” or “q” or both are true. Thus “It is not the case that cats meow or purr” would be counted as false. But there are also cases in which speakers use “p or q” to mean that “p” or “q” is true but not both. This would be the natural way to interpret someone who said “John is going to invite Mary or Jane to the prom”. Some maintain that “or” is ambiguous in English, with an inclusive and an exclusive sense. But another possibility is that the exclusive interpretation is a generalized conversational implicature. One piece of evidence supporting the implicature hypothesis is that the exclusive interpretation seems cancelable. Thus “Jane will visit France or Germany this summer; indeed, she will drive through both on her way to Poland” has no contradictory interpretation. A methodological issue is to describe the evidence necessary to decide whether a particular interpretation is a sense or a generalized conversational implicature. A foundational issue to is describe exactly what the difference consists in.