When people communicate, we often face situations where decisions have to be made, regardless of silence of one of the interlocutors. That is, we have to decide from incomplete information, guessing the intentions of the silent person. Implicatures allow to make inferences from what is said, but we can also infer from omission, or specifically from intentional silence in a conversation. In some contexts, not saying p generates a conversational implicature: that the speaker did not have sufficient reason, all things considered, to say p. This behaviour has been studied by several disciplines but barely touched in logic or artificial intelligence. After reviewing some previous studies of intentional silence and implicature, we formulate a semantics with five different interpretations of omissive implicature, in terms of the Says() predicate, and focus on puzzles involving assertions or testimonies, to analyze their implications. Several conclusions are derived from the different possibilities that were opened for analysis after taking into account silence. Finally, we develop a general strategy for the use of the proposed semantics in cases involving some kind of silence.
