Strongly First Order Disjunctive Embedded Dependencies in Team Semantics

TL;DR

This paper characterizes certain disjunctive embedded dependencies in Team Semantics that do not enhance the expressive power of First-Order Logic, clarifying their limitations in database-related logic extensions.

Contribution

It provides a characterization of disjunctive embedded dependencies that do not increase expressiveness in First-Order Team Semantics.

Findings

Identifies dependencies that do not extend expressive power

Clarifies limitations of disjunctive embedded dependencies

Enhances understanding of Team Semantics in databases

Abstract

First Order Team Semantics is a generalization of Tarskian Semantics in which formulas are satisfied with respect to sets of assignments. In Team Semantics, it is possible to extend First Order Logic via new types of atoms that describe dependencies between variables; some of these extensions are strictly more expressive than First Order Logic, while others are reducible to it. Many of the atoms studied in Team Semantics are inspired by Database Theory and belong in particular to the class of Disjunctive Embedded Dependencies, a very general family of dependencies that contains most of the dependencies of practical interest in the study of databases. In this work, I provide a characterization for the (domain-independent) Disjunctive Embedded Dependencies that fail to increase the expressive power of First-Order Team Semantics when added to it.