Tiling problems and complexity of logics (extended version)

TL;DR

This paper uses domino problems to provide concise proofs of classical predicate logic theorems and establishes lower bounds on the complexity of certain modal predicate logics based on Noetherian orders.

Contribution

It introduces a novel application of domino problems to logic complexity analysis and offers new lower bounds for modal predicate logics with Noetherian frame conditions.

Findings

Short proofs for classical predicate logic theorems

Lower bounds for modal predicate logic complexity

Application of domino problems to logic

Abstract

We apply domino problems to give short proofs for some known theorems for the classical predicate logic and to obtain lower bounds for complexity of modal predicate logics defined by Noetherian orders as Kripke frames.