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Lexical presuppositions depend on the specific meaning of words used. Example: 'John stopped smoking' presupposes that John used to smoke.

Conventional implicature is an implication that is attached to specific words or phrases and is part of their conventional meaning. Example: 'He is poor but happy' implicates that poverty usually doesn't go with happiness.

Scalar implicature is an implication that comes from the use of a word which suggests a position on a scale, such as 'some', 'all', or 'often'. Example: Saying 'Some of the guests have arrived' implicates that not all have arrived.

Negative face refers to the desire to be autonomous and not imposed upon. Politeness strategies can be employed to avoid presupposing an intrusion. Example: 'If you have time, could you look at this?'

Irony is a figure of speech in which the intended meaning is opposite to the literal meaning. It often implies an evaluative stance and can flout the Maxim of Quality. Example: Saying 'What a beautiful day!' when it is raining heavily.

Implicature refers to what is suggested in an utterance, even though neither expressed nor explicitly stated. Example: Saying 'It's cold in here' may serve as an indirect way to ask someone to close the window.

Existential presuppositions are assumptions that something exists. Example: The sentence 'Did Jane pick up her dry cleaning?' presupposes that Jane has some clothing at the dry cleaners.

Flouting a maxim involves deliberately violating one of Grice's Maxims to create an implicature. Example: Answering a question with an apparently unrelated response can flout the Maxim of Relation to imply a message without stating it.

Speech Act Theory posits that saying something can be an act in itself, and such acts carry implicature based on illocutionary force. Example: The utterance 'I do' in a wedding context is not just a statement, but an action performing the marriage.

Structural presuppositions are determined by the linguistic structure of the sentence. Example: The question 'Who is drinking wine?' presupposes that there is someone drinking wine.

The Maxim of Quality states that one should not convey information that is false or for which there is no adequate evidence. Example: If someone says 'I have seen aliens', it would violate this maxim if they haven’t actually seen aliens.

Positive face refers to the desire to be approved of in certain respects. Politeness can involve implicatures that affirm the interlocutor's positive attributes. Example: 'It's amazing how you can handle this much work!'

Counterfactual presuppositions involve situations contrary to fact. Example: 'If Peter had won the race, he would have thrown a party' presupposes that Peter did not win the race.

The Maxim of Quantity suggests that one should be as informative as required, but not more informative than necessary. Example: When asked 'What time is it?', responding with just the current time follows this maxim.

A metaphor is a figure of speech where a word or phrase is applied to an object or action to which it is not literally applicable. It can flout the Maxim of Quality. Example: 'He drowned in a sea of grief' does not mean an actual sea.

Politeness theory involves maintaining face in social interaction, which can affect the use of implicature and presupposition. Example: Indirectly refusing an offer by saying 'I'm not sure I can' is often a strategy to save the offerer's face.

Conversational implicature is an implication derived from conversational context and the principle of cooperation. Example: If A says 'Can you pass the salt?' and B passes the salt, B's action relies on the implicature that A was not asking about B’s ability but making a request.

The Maxim of Relation, or Relevance, suggests that contributions should be relevant to the conversation. Example: In a conversation about the weather, suddenly talking about sports without any link would violate this maxim.

Presupposition is an implicit assumption about the world or background belief relating to an utterance whose truth is taken for granted in discourse. Example: The statement 'John's sister is intelligent' presupposes that John has a sister.

Factive presuppositions are triggered by factive verbs which assume the truth of their complement clause. Example: 'I regret that I was rude' presupposes that the speaker was indeed rude.

The Maxim of Manner advises to be clear, avoid ambiguity, and be brief and orderly. Example: Avoiding jargon when talking to someone outside your field adheres to this maxim.