Expressivity and Complexity of Dependence Logic

Abstract

In this article we review recent results on expressivity and complexity of first-order, modal, and propositional dependence logic and some of its variants such as independence and inclusion logic. Dependence logic was introduced by Jouko Vaananen in [56]. On the syntactic side, it extends usual first-order logic by the so-called dependence atoms the meaning of which is that the value of x n is functionally determined by the values of x1, …, xn−1. The semantics of dependence logic is defined using sets of assignments, teams, rather than single assignments as in first-order logic. Since the introduction of dependence logic in 2007, the area of team semantics has evolved into a general framework for logics in which various notions of dependence and independence can be formalized and studied. In this paper we mainly consider variants of dependence logic arising by replacing/supplementing dependence atoms with further dependency notions, and we also study propositional and modal variants.