Unified Foundations of Team Semantics via Semirings

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. Contributed talk given by Nina Pardal

Authors

• Nina Pardal Conicet UBA

Keywords

No keywords are indexed for this paper.