Parameterized Complexity of Weighted Team Definability

TL;DR

This paper investigates the parameterized complexity of weighted team definability in team semantics logics, relating it to known complexity classes and providing complexity results for various team-based logics.

Contribution

It introduces the complexity analysis of weighted team definability for fixed formulas in team semantics, connecting it to the W-hierarchy and paraNP classes.

Findings

Complexity results for dependence, independence, and inclusion logic formulas.

Relations established between weighted team definability and W-hierarchy classes.

Insights into the parameterized complexity landscape of team semantics logics.

Abstract

In this article, we study the complexity of weighted team definability for logics with team semantics. This problem is a natural analogue of one of the most studied problems in parameterized complexity, the notion of weighted Fagin-definability, which is formulated in terms of satisfaction of first-order formulas with free relation variables. We focus on the parameterized complexity of weighted team definability for a fixed formula phi of central team-based logics. Given a first-order structure A and the parameter value k as input, the question is to determine whether A,T models phi for some team T of size k. We show several results on the complexity of this problem for dependence, independence, and inclusion logic formulas. Moreover, we also relate the complexity of weighted team definability to the complexity classes in the well-known W-hierarchy as well as paraNP.