A Self-Reflecting Formal Language

TL;DR

This paper introduces reflectica, a formal language that is both self-reflecting and intensional, enabling it to represent complex natural language features more simply than existing systems.

Contribution

It presents a novel formal theory, reflectica, with a simplified method for constructing intensional logic that incorporates self-reflection and intensional features.

Findings

Reflectica can express propositional attitudes and quotations.

The method simplifies the construction of intensional logics.

Reflectica bridges self-reference and intensionality effectively.

Abstract

We construct a formal theory, which we call reflectica, whose language possesses the following properties of natural language: it is a self-reflecting language and an intensional language. By a self-reflecting language we understand an interpreted language that is a meta-language in relation to itself. By an intensional language we understand a language that has expressive means sufficient to represent intensional features of a natural language, such as statements containing propositional attitude reports, various kinds of quotation, and other types of expressions with an intensional context. At the same time, we present a new method for constructing an intensional logic that allows us to make reflectica an intensional system much simpler than other well-known intensional logics.