- Avoid obscurity of expression.
- Avoid ambiguity.
- Be brief (avoid unnecessary prolixity).
- Be orderly.
It is obvious that the observance of some of these maxims is a matter of less urgency than is the observance of others; a man has expressed himself with undue prolixity would, in general, be open to milder comment than would a man who has said something he believes to be false. Indeed, it might be felt that the importance of at least the first maxim of Quality is such that it should not be included in a scheme of the kind Grice was constructing; other maxims come into operation only on the assumption that this maxim of Quality is satisfied. While this may be correct, so far as generation of implicatures is concerned it seems to play a role not totally different from the other maxims, and it will be convenient, for the present at least, to treat it as a member of the list of maxims.
There are all sorts of other maxims (aesthetic, social, or moral in character), such as Be polite, that are also generate nonconventional implicatures. The conversational maxims, however, and the conversational implicatures connected with them, are specially connected with the particular purpose that talk (and so, talk exchange) is adapted to serve and is primarily employed to serve. When Grice stated his maxims, the main purpose were a maximally effective exchange of information; this specification is too narrow, and the scheme needs to be generalized to allow for such general purpose as influencing or directing the actions of others.
These maxims may be better understood as describing the assumptions listeners normally make about the way speakers will talk, rather than prescriptions for how one ought to talk. Philosopher Kent Bach writes:...We need first to get clear on the character of Grices maxims. They are not sociological generalizations about speech, nor they are moral prescriptions or proscriptions on what to say or communicate. Although Grice presented them in the form of guidelines for how to communicate successfully, I think they are better construed as presumptions about utterances, presumptions that we as listeners rely on and as speakers exploit.
Gricean Maxims generate implicatures. If the overt, surface meaning of a sentence does not seem to be consistent with the Gricean maxims, and yet the circumstances lead us to think that the speaker is nonetheless obeying the cooperative principle, we tend to look for other meanings that could be implicated by the sentence.
Grice did not, however, assume that all people should constantly follow these maxims. Instead, he found it interesting when these were not respected, namely either "flouted" (with the listener being expected to be able to understand the message) or "violated" (with the listener being expected to not note this). Flouting would imply some other, hidden meaning. The importance was in what was not said. For example: Answering It's raining to someone who has suggested a game of tennis only disrepects the maxim of relation on the surface, the reasoning behind this 'fragment' sentence is normally clear to the interlocutor (the maxim is just "flouted").
Grices theory is often disputed with the argument that cooperative conversation, as with most social behavior, is culturally determined. Therefore, the Gricean Maxims and the Cooperative Principle cannot be universally applied due to intercultural differences. The Malagasy, for example, follow a completely opposite Cooperative Principle in order to achieve conversational cooperation. In their culture, speakers are reluctant to share information and flout the Maxim of Quantity by evading direct questions and replying on incomplete answers because of the risk of losing face by committing oneself to the truth of the information, as well as the fact that having information is a form of prestige.
Another criticism is that the Gricean Maxims can easily be misinterpreted to be a guideline for etiquette, instructing speakers on how to be moral, polite conversationalists. However, the Gricean Maxims, despite their wording, are only meant to describe the commonly accepted traits of successful cooperative communication. Geoffrey Leech created the Politeness maxims: tact, generosity, approbation, modesty, agreement, and sympathy.
1.2.2 Conversation implicatures
An implicature is something meant, implied, or suggested distinct from what is said. Implicatures can be part of sentence meaning or dependent on conversational context, and can be conventional or unconventional. Conversational implicatures have become one of the principal subjects of pragmatics. Figures of speech provide familiar examples. An important conceptual and methodological issue in semantics is how to distinguish senses and entailments from conventional implicatures. Implicature has been invoked for a variety of purposes, from defending controversial semantic claims in philosophy to explaining lexical gaps in linguistics. H. P. Grice, who coined the term “implicature,” and classified the phenomenon, developed an influential theory to explain and predict conversational implicatures, and describe how they are understood. The “Cooperative Principle” and associated “Maxims” play a central role. Other authors have focused on principles of politeness and communicative efficiency. Questions have been raised as to how well these principle-based theories account for the intentionality of speaker implicature and conventionality of sentence implicature. Critics observe that speakers often have goals other than the cooperative and efficient exchange of information, and that conventions are always arbitrary to some extent.
Grice characterizes the notion of conversational implicature in such a way: A man who, by (in, when) saying (or making as if to say) that p has implicated q, may be said to have conversationally implicated that q, provided that (1) he is to presumed to be observing the conversational maxims, or at least the cooperative principle; (2) the supposition that he is aware that, or thinks that, q is required in order to make his saying or making as if to say p (or doing so in those terms) consistent with the presumption; and (3) the speaker thinks (and would expect the hearer th think that the speaker thinks) that it is within the competence of the hearer to work out, or grasp intuitively, that the supposition mentioned in 2 is required.
The presence of a conversational implicature must be capable of being worked out; for even it can in fact be intuitively grasped, unless the intuition is replaceable by any argument, the implicature (if present at all) will not count as a conversational implicature; it will be a conventional implicature. To work out a particular conversational implicature is present, the hearer will replay on the following data: (1) the conventional meaning of the words used, together with the identity of any references that may be involved; (2) the CP and its maxims; (3) the context, linguistic or otherwise, of the utterance; (4) other items of background knowledge; and (5) the fact (or supposed fact) that all relevant items falling under the previous headings are available to both participants know or assume this to be the case. 
So H.P. Grice coined the term implicature for communicated non-truth-conditional meaning:
a conventional implicature is non-truth-conditional meaning associated with a particular linguistic expression E.g.: Even John couldnt eat the quince and locust fritters.
a conversational implicature is not intrinsically associated with any expression; it is inferred from the use of some utterance in context
(1) Johns been making a lot of trips to Paphos lately.
What is said: Johns been making a lot of trips to Paphos lately
What is implicated: The speaker believes that John may have a girlfriend in Paphos
According to Grice , another form of conversational implicature is also known as a scalar implicature. This concerns the conventional uses of words like "all" or "some" in conversation. E.g. I ate some of the pie.
This sentence implies "I did not eat all of the pie." While the statement "I ate some pie" is still true if the entire pie was eaten, the conventional meaning of the word "some" and the implicature generated by the statement is "not all".
The implicatures are:
(2) A: Has John got a girlfriend? / Has John started his Christmas shopping yet?
B: Hes been making a lot of trips to Paphos lately.
(3) A: Ive run out of petrol. / Damn; its midnight already and Im starving.
B: Theres a garage just round the corner.
b) Cancelable (or defeasible):
(4) A: Has John got a girlfriend?
B: Hes been making a lot of trips to Paphos lately.
That usually means hes on the pull, so I dont suppose he has a girlfriend.
(5) Ive read some of those books.
In fact, unlike you, Ive read them all.
(6) A: Ive run out of petrol.
B: Theres a garage just round the corner.
Theyve run out of petrol, but might be able to call someone who could help.
c) Non-detachable (usually), i.e. you dont lose the implicature by substituting synonyms:
(7) A: Has John got a girlfriend?
B: Hes been a regular visitor to the east of the Akamas peninsula recently.
(8) Ive completed a number of those tomes.
(9) A: Ive run out of petrol.
B: Youll find a filling station just beyond that bend.
but some certain implicatures are deta