Inclusion and Exclusion Dependencies in Team Semantics: On Some Logics of Imperfect Information

TL;DR

This paper introduces new logics of imperfect information incorporating inclusion and exclusion dependencies, explores their properties and relationships, and develops a game theoretic semantics, ultimately characterizing the expressive power of independence logic.

Contribution

It presents novel logics with inclusion and exclusion dependencies, analyzes their properties, and provides a game theoretic semantics, solving an open problem about independence logic.

Findings

Characterization of the expressive power of independence logic

Development of a game theoretic semantics for the new logics

Analysis of properties and relationships with existing logics

Abstract

We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other logics of imperfect information are then studied. Furthermore, a game theoretic semantics for these logics is developed. As a corollary of these results, we characterize the expressive power of independence logic, thus answering an open problem posed in (Gr\"adel and V\"a\"an\"anen, 2010).