When we speak, we often convey more than what we literally say, enriching our message with implicit content. We also provide cues to our listeners or readers to derive inferences from what we say. To exemplify, consider the conversation in (1), in which a teacher asks their students about their homework, which comprised exercises on pages 41 and 43: (1) Teacher: Did you do your homework? a. Student A replies: I did some of the exercises . b. Student B replies: I did the exercises on page 41 . c. Student C replies: I had a terrible headache yesterday . From the students' responses, the teacher will infer that none of the students completed their homework, and, in particular, the Conversational Implicatures in (2) will be derived: (2) a. Student A completed some but not all of the assignments. b. Student B completed only page 41, not page 43 . c. Student C did none of the exercises. How? Conversational Implicatures arise in discourse by virtue of the mutual agreement between speakers and hearers to be cooperative and obey some maxims (Grice, 1975). These maxims urge us to make our contributions maximally informative (Quantity); to say something which is true and reliable (Quality); to be relevant (Relevance) and clear, brief, orderly, and unambiguous (Manner). Assuming that participants in a conversation are cooperative and eager to provide a contribution that is qualitatively and quantitatively appropriate to the purposes of the exchange, the student's answers in (1a-c) can be judged informative and cooperative answers only if they are evaluated with respect to what is relevant in the exchange, or in contrast with what the students could have said instead but didn't. For example, students A and B could have uttered the alternative (and more informative) statements in (3) (1a-b): (3) a. I did all the exercises . b. I completed page 41 and 43 . The fact that they did not constitute a cue for their teacher to derive the implicatures in (2). Such implicatures, albeit conveying the same message, are distinct on a theoretical basis. The inference in (2a) is called a scalar implicature , given that it is based on an ordered scale in which the elements (in this case, the quantifiers some and all) are ordered with respect to the information they convey (Horn, 1972). All , which is the most informative quantifier in the scale, implies some : if someone made all the exercises, they also made some of the exercises, by virtue of logical entailment between all and some . Mentioning the weaker scalar alternative (in this case, some , as in (1a)) triggers the scalar inference in (2a) that the most informative alternative (in this case, all , as in (3a)) is not true. The inference in (2b) is called ad hoc implicature , and it is based on alternatives that are contextually, not linguistically, triggered. In this case, mentioning only one of the available alternatives in the discourse (as in (1b)) will trigger the ad hoc inference that the other alternatives (as in (3b)) are not true. In both cases, the use of a weaker utterance in a situation in which the more informative alternative holds constitutes a violation of the maxim of Quantity, resulting in an utterance that is said to be “underinformative.”