The paper considers new logical semantics for the classic propositional logic which states that a propositional formula refers to a special structure – “the tree of messages”. This tree of message determines the truth values for the elements of the propositional formula. The source of inspiration for creating a concept of such semantics is a philosophical-linguistic program advanced by H.P. Grice. Grice made a hypothesis according to which the meaning of the speech act is defined more by speaker’s intention than by the “conventional” meaning of utterances. A speaker may have hidden intentions towards his speech act – he is manipulating his audience for political or economic aims, for example. Thus, the true meaning of the utterance the speaker uses may even contradict the “conventional” meanings of those expressions. As a consequence, to understand the true meaning of those utterances you should take the speaker's true intentions into consideration. A message is a textual expression of such intentions. In general, messages can express different meta-rules which specify the context for the propositional formula which refers to the “tree”.
Messages can cooperate between each other as well as with the messages from different trees creating specific kinds of “algebras”. By specifying these “algebras” the variety of different alternative propositional logics based on this semantics can be created. By interpreting messages and accordingly modifying the truth values of propositional formulas the situation described by Grice can be emulated. However, it should be admitted that the idea of such logical semantics is wider than just an emulation of the particular linguistic theory.
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