Complexity Results for Modal Dependence Logic

Studia Logica 101 (2):343-366 (2013)
  Copy   BIBTEX

Abstract

Modal dependence logic was introduced recently by Väänänen. It enhances the basic modal language by an operator = (). For propositional variables p 1, . . . , p n , = (p 1, . . . , p n-1, p n ) intuitively states that the value of p n is determined by those of p 1, . . . , p n-1. Sevenster (J. Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for nondeterministic exponential time.In this paper we consider fragments of modal dependence logic obtained by restricting the set of allowed propositional connectives. We show that satisfiability for poor man’s dependence logic, the language consisting of formulas built from literals and dependence atoms using ${\wedge, \square, \lozenge}$ (i. e., disallowing disjunction), remains NEXPTIME-complete. If we only allow monotone formulas (without negation, but with disjunction), the complexity drops to PSPACE-completeness.We also extend Väänänen’s language by allowing classical disjunction besides dependence disjunction and show that the satisfiability problem remains NEXPTIME-complete. If we then disallow both negation and dependence disjunction, satisfiability is complete for the second level of the polynomial hierarchy. Additionally we consider the restriction of modal dependence logic where the length of each single dependence atom is bounded by a number that is fixed for the whole logic. We show that the satisfiability problem for this bounded arity dependence logic is PSPACE-complete and that the complexity drops to the third level of the polynomial hierarchy if we then disallow disjunction.In this way we completely classify the computational complexity of the satisfiability problem for all restrictions of propositional and dependence operators considered by Väänänen and Sevenster

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,247

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

On Definability in Dependence Logic.Juha Kontinen & Jouko Väänänen - 2009 - Journal of Logic, Language and Information 18 (3):317-332.
Generalized Quantifiers in Dependence Logic.Fredrik Engström - 2012 - Journal of Logic, Language and Information 21 (3):299-324.
Epistemic Operators in Dependence Logic.Pietro Galliani - 2013 - Studia Logica 101 (2):367-397.
On the Restraining Power of Guards.Erich Grädel - 1999 - Journal of Symbolic Logic 64 (4):1719-1742.
Fragments of Language.Ian Pratt-Hartmann - 2004 - Journal of Logic, Language and Information 13 (2):207-223.
Lewis Dichotomies in Many-Valued Logics.Simone Bova - 2012 - Studia Logica 100 (6):1271-1290.
A Remark on Negation in Dependence Logic.Juha Kontinen & Jouko Väänänen - 2011 - Notre Dame Journal of Formal Logic 52 (1):55-65.
An Event-Based Fragment of First-Order Logic Over Intervals.Savas Konur - 2011 - Journal of Logic, Language and Information 20 (1):49-68.

Analytics

Added to PP
2013-03-13

Downloads
34 (#340,403)

6 months
1 (#415,205)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Propositional Logics of Dependence.Fan Yang & Jouko Väänänen - 2016 - Annals of Pure and Applied Logic 167 (7):557-589.
Propositional Team Logics.Fan Yang & Jouko Väänänen - 2017 - Annals of Pure and Applied Logic 168 (7):1406-1441.
The Expressive Power of Modal Dependence Logic.Lauri Hella, Kerkko Luosto, Katsuhiko Sano & Jonni Virtema - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 294-312.

View all 8 citations / Add more citations