Modal Calculus of Illocutionary Logic

TL;DR

This paper introduces a novel many-valued modal calculus for illocutionary logic, formalizing how context influences performative utterances using non-Archimedean valued logic.

Contribution

It presents the first formal many-valued approach to illocutionary logic, modeling illocutionary forces as modal operators with non-Archimedean values.

Findings

Developed a non-Archimedean valued logic for illocutionary acts

Formalized illocutionary forces as modal operators

First formal many-valued approach to illocutionary logic

Abstract

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 many-valued approach to illocutionary logic was offered for the first time.