# Iterated reflection principles over full disquotational truth

## TL;DR

This paper demonstrates that in Basic De Morgan Logic, iterated reflection principles can coherently extend a fully disquotational truth theory to a strong compositional truth theory, unlike in classical logic.

## Contribution

It introduces a novel approach to iterated reflection in a weaker logic, enabling coherent extension from disquotational to compositional truth theories.

## Key findings

- In classical logic, such extensions are incoherent.
- In Basic De Morgan Logic, finite iteration yields strong truth theories.
- The approach clarifies the role of reflection principles in truth theory development.

## Abstract

Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection of Tarski-biconditionals and arrive by finitely iterated reflection at strong compositional truth theories. In the context of classical logic it is incoherent to adopt an initial truth theory in which A and 'A is true' are inter-derivable. In this article we show how in the context of a weaker logic, which we call Basic De Morgan Logic, we can coherently start with such a fully disquotational truth theory and arrive at a strong compositional truth theory by applying a natural uniform reflection principle a finite number of times.