Logic and Implicature According to Grice [Hui Yang]

I agree with Grice on there is implicature when people say something, and sometimes the implication is different from what the sentence seems to indicate logically. A simple sentence, depending on how it is said and in what conversational context, it can have two or more, sometimes totally opposite, meanings. 

It is more about me questioning instead of disagreeing with Grice: although sometimes just by what the sentence looks like we cannot tell what the speaker exactly means, surely we know what the speaker does not mean. For example, “he is a nice person” can surely express different meanings like "he IS a nice person" or "he IS NOT a nice person", but I highly doubt that it can imply as far as anything like "his ex-girlfriend works in a hospital.” In other words, by basic logic, we can still know what the speaker DOES NOT mean by the sentences he/she says.

I doubt though when people mean something different from what they said (e.g. sarcasm or joking) they usually indicate that by their tone of voice (I believe that is how we can tell it is sarcasm or jokes), and the tone of voice is usually part of language, so shouldn’t we take that into our logical variation? Then everything can be perfectly explained by logic, and we do not need to bring in the idea of “implicature” to the discussion (e.g. *the sarcastic tone of voice*= negative, so “he is a nice person” with a sarcastic tone of voice = “he is not a nice person”).