Undecidability of a Very Simple Modal Logic with Binding

TL;DR

This paper proves that the satisfiability problem for a very simple modal logic with binding is undecidable, extending the understanding of undecidability in modal logics with binders.

Contribution

It demonstrates the undecidability of the simplest non-Boolean modal logic with implicit binding, advancing the theoretical landscape of modal logic complexity.

Findings

Satisfiability problem is undecidable for this logic.

Extends previous undecidability results to simpler modal logics with binders.

Highlights limits of decidability in modal logic with implicit binding.

Abstract

We show undecidability of the satisfiability problem of what is arguably the simplest non-sub-Boolean modal logic with an implicit notion of binding. This work enriches the series of existing results of undecidability of modal logics with binders, which started with Hybrid Logics and continued with Memory Logics.