Unified foundations of team semantics via semirings

PARDAL, NINA; TIMON BARLAG; MIIKA HANNULA; JUHA KONTINEN; JONNI VIRTEMA

Kassel

Conferencia; Highlights of Logic, Automata and Games 2023; 2023

Universität Kassel

Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula.Team semantics is a framework for studying logics of dependence and independence in diverse contexts such as databases, quantum mechanics, and statistics by extending first-order logic with atoms that describe dependencies between variables. Combining these two, we propose a unifying approach for analysing the concepts of dependence and independence via a novel semiring team semantics, which subsumes all the previously considered variants for first-order team semantics.In particular, we study the preservation of satisfaction of dependencies and formulae between different semirings. In addition we create links to reasoning tasks such as provenance, counting, and repairs.This is joint work with Timon Barlag, Miika Hannula, Juha Kontinen, and Jonni Virtema.