Inclusion Logic and Fixed Point Logic

TL;DR

This paper explores Inclusion Logic, showing its equivalence to Greatest Fixed Point Logic, and demonstrates its expressive power and game-theoretic properties within the framework of team semantics.

Contribution

It establishes the equivalence of Inclusion Logic to Greatest Fixed Point Logic and characterizes its expressive capabilities and game-theoretic aspects.

Findings

Inclusion Logic is equivalent to Greatest Fixed Point Logic.

All union-closed first-order properties are definable in Inclusion Logic.

An Ehrenfeucht-Fra"issé game for Inclusion Logic is developed.

Abstract

We investigate the properties of Inclusion Logic, that is, First Order Logic with Team Semantics extended with inclusion dependencies. We prove that Inclusion Logic is equivalent to Greatest Fixed Point Logic, and we prove that all union-closed first-order definable properties of relations are definable in it. We also provide an Ehrenfeucht-Fra\"iss\'e game for Inclusion Logic, and give an example illustrating its use.