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October 20, 2025Open Access

Strongly First Order Disjunctive Embedded Dependencies in Team Semantics

Key Points

First order team semantics extends traditional logic by introducing new atoms, allowing for richer expressions.
The study identifies which disjunctive embedded dependencies do not enhance the expressive capacity of first order team semantics.
Database theory significantly influences the types of dependencies examined within team semantics.
Characterizing these dependencies can guide practical implementations in databases and logic.

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.

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