Modal Calculus of Illocutionary Logic

The aim of illocutionary logic is to explain how context can affect the meaning of certain special kinds of performative utterances. Recall that performative utterances are understood as follows: a speaker performs the illocutionary act (e.g. act of assertion, of conjecture, of promise) with the illocutionary force (resp. assertion, conjecture, promise) named by an appropriate performative verb in the way of representing himself as performing that act. In the paper I proposed many-valued interpretation of illocutionary forces understood as modal operators. As a result, I built up a non-Archimedean valued logic for formalizing illocutionary acts. A formal manyvalued approach to illocutionary logic was offered for the first time. 1. A non-Fregean formal analysis of illocutionary acts Conventional logics including the most non-classical logics like fuzzy logics, paraconsistent logics, etc. satisfy the so-called Fregean approach according to that the meaning of a well-formed expression (for instance, the meaning of a propositional formula) should depend on meanings of its components (respectively, on meanings of propositional variables), i.e. the meaning of a composite expression should be a function defined inductively on meanings of atoms. This feature distinguishes the most formal languages from the natural one. In the speech living practice we could exemplify a lot that the meaning of a composite speech act may be not a function defined inductively on meanings of elementary speech acts included in that composite expression. This means that a logic of speech acts cannot satisfy the Fregean approach in general. Now let us consider the structure of speech acts and their compositions. We are trying to show how compositions in natural language (i.e. in speech acts) differ from compositions defined inductively within the conventional formal logic. Speech acts from the logical point of view are said to be illocutionary acts. We know that whenever a speaker utters a sentence in an appropriate context with certain intentions, he performs one or more illocutionary acts. We will denote the simple illocutionary act by F(Φ).