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Expressivity and Complexity of Dependence Logic

In: Dependence Logic

Author

Listed:
  • Arnaud Durand

    (Université Paris Diderot, IMJ-PRG, CNRS UMR 7586)

  • Juha Kontinen

    (University of Helsinki, Department of Mathematics and Statistics)

  • Heribert Vollmer

    (Leibniz Universität Hannover, Institut für Theoretische Informatik)

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 Väänänen 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 x 1, …, x n−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.

Suggested Citation

  • Arnaud Durand & Juha Kontinen & Heribert Vollmer, 2016. "Expressivity and Complexity of Dependence Logic," Springer Books, in: Samson Abramsky & Juha Kontinen & Jouko Väänänen & Heribert Vollmer (ed.), Dependence Logic, pages 5-32, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-31803-5_2
    DOI: 10.1007/978-3-319-31803-5_2
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