I wonder if anyone has thought of this. Pre-theoretically, we want to say that 1) "The King of France is bald." "implies" or "pre-supposes" that there is a King of France or that "There is a King of France." is true. Grice offers up a theory where the utterance standardly implicates, but does not *entail*, that there is a King of France or that "There is a King of France." is true. But could we not argue instead that 1) *entails* that probably there is a King of France or that "Probably there is a King of France." is true?
One advantage of looking at things this way is you don't have to invoke any extra-logical notation like `~>'. One supporting line of argument for this way of looking at things is, even assuming the vocabulary of implicature (the wavy arrow and etc.), it is surely the case that we would count a piece of discourse as *Rational* (and therefore, maybe, as truth valued), only if the standard implications of the utterances contained in that piece of discourse were, *mostly* , in place (not cancelled).
Cheers,
M.J.Murphy
The shapes of things are dumb.
-L. Wittgenstein
PS. the site I mentioned http://www.semanticsarchive.net/ went down as soon as I recommended it. However, the site is now operating again and, as I say, they too are looking for papers.
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