# The Fluted Fragment with Transitivity

## TL;DR

This paper investigates the satisfiability problem for the fluted fragment extended with transitive relations, showing decidability with one relation and undecidability with three relations.

## Contribution

It establishes the finite model property for the one-transitive relation case and proves undecidability for the three-transitive relations case.

## Key findings

- Finite model property with one transitive relation
- Undecidability with three transitive relations
- Complexity varies with the number of transitive relations

## Abstract

We study the satisfiability problem for the fluted fragment extended with transitive relations. We show that the logic enjoys the finite model property when only one transitive relation is available. On the other hand we show that the satisfiability problem is undecidable already for the two-variable fragment of the logic in the presence of three transitive relations.