Speech act theory broadly explains these utterances as having three parts or aspects: locutionary, illocutionary and perlocutionary acts. Locutionary acts are simply the speech acts that have taken place. Illocutionary acts are the real actions which are performed by the utterance, where saying equals doing, as in betting, plighting one's troth, welcoming and warning. Perlocutionary acts are the effects of the utterance on the listener, who accepts the bet or pledge of marriage, is welcomed or warned.
Some linguists have attempted to classify illocutionary acts into a number of categories or types. David Crystal, quoting J.R. Searle, gives five such categories: representatives, directives, commissives, expressives and declarations. (Perhaps he would have preferred declaratives, but this term was already taken as a description of a kind of sentence that expresses a statement.)
The conversational implicature is a message that is not found in the plain sense of the sentence. The speaker implies it. The hearer is able to infer (work out, read between the lines) this message in the utterance, by appealing to the rules governing successful conversational interaction.
In analyzing utterances and searching for relevance we can use a hierarchy of propositions - those that might be asserted, presupposed, entailed or inferred from any utterance.
Assertion: what is asserted is the obvious, plain or surface meaning of the utterance (though many utterances are not assertions of anything).
Presupposition: what is taken for granted in the utterance. “I saw the Mona Lisa in the Louvre” presupposes that the Mona Lisa is in the Louvre.
Entailments: logical or necessary corollaries of an utterance, thus, the above example entails: I saw something in the Louvre.
Inferences: these are interpretations that other people draw from the utterance, for which we cannot always directly account.