# A Non-wellfounded, Labelled Proof System for Propositional Dynamic Logic

## TL;DR

This paper introduces a novel infinitary labelled sequent calculus for propositional dynamic logic (PDL), providing soundness, completeness, and cut-free proof systems, along with proof-search strategies for specific PDL fragments.

## Contribution

It presents a new non-wellfounded, labelled proof system for PDL, including a cyclic system that is finitely representable and proven to be sound and complete.

## Key findings

- Both systems are sound and complete with respect to standard models.
- The cyclic system G3PDL^{} is cut-free complete.
- Proof-search strategies are developed for the fragment of PDL without tests.

## Abstract

We define a infinitary labelled sequent calculus for PDL, G3PDL^{\infty}. A finitarily representable cyclic system, G3PDL^{\omega}, is then given. We show that both are sound and complete with respect to standard models of PDL and, further, that G3PDL^{\infty} is cut-free complete. We additionally investigate proof-search strategies in the cyclic system for the fragment of PDL without tests.