The subject matter of the study is communicative implications as one of the forms of implementation of speech acts. The starting point is the well-known theory of H. P. Grice, in which pragmatic implications are based on the principle of cooperation. The author shows the limitations of Grice’s theory, which presents the communicative conditions of implications, but does not present the communicative consequences. As an alternative, the author proposes the concept of pragmatic implications, taking into account the premises and consequences of indirect speech acts. Considering implication as a two-place relation between antecedent and consequent, the author identifies three types of implications that differ in the type of information in the antecedent and consequent parts: 1) semantic antecedent > pragmatic consequent; 2) pragmatic antecedent > pragmatic consequent; 3) pragmatic antecedent > semantic consequent. This approach makes it possible to present indirect communication to the fullest extent, and also to explain many communicative phenomena in terms of the interaction between semantics and pragmatics. Implications are interpreted as the result of mental processing of conditionally categorical syllogisms, in which the first premise is an element of the cultural worldview. Thus, the author shows the relative nature of the opposition of conventional and communicative implications. The article uses the material of the modern Russian language, borrowed from various sources: journalism, fiction, the Internet, urban folklore and colloquial speech. The leading research method was pragmatic, namely, illocutionary, analysis with elements of discourse content analysis.