A Short Note on Two-Variable Logic with a Linear Order Successor and a Preorder Successor

TL;DR

This paper proves that the finite satisfiability problem for two-variable logic extended with both a linear order successor and a preorder successor is undecidable, highlighting limitations in logical expressiveness.

Contribution

It establishes the undecidability of finite satisfiability for this extended logic, a novel result in the study of two-variable logic with additional order relations.

Findings

Finite satisfiability problem is undecidable with these extensions.

Undecidability holds for logic with both linear order and preorder successors.

Results impact the understanding of logical expressiveness with order relations.

Abstract

The finite satisfiability problem of two-variable logic extended by a linear order successor and a preorder successor is shown to be undecidable.