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Complexity Results for Modal Dependence Logic

Peter Lohmann, Heribert Vollmer
2013 Studia Logica: An International Journal for Symbolic Logic  
Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for nondeterministic exponential time.  ...  Modal dependence logic was introduced very recently by Väänänen. It enhances the basic modal language by an operator dep.  ...  Modal dependence logic (MDL) is defined by introducing these dependence atoms to modal logic [15, 13] .  ... 
doi:10.1007/s11225-013-9483-6 fatcat:ytuq27d56fd7bk55jjkesofqdy

Complexity Results for Modal Dependence Logic [chapter]

Peter Lohmann, Heribert Vollmer
2010 Lecture Notes in Computer Science  
Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for nondeterministic exponential time.  ...  Modal dependence logic was introduced very recently by Väänänen. It enhances the basic modal language by an operator dep.  ...  Modal dependence logic (MDL) is defined by introducing these dependence atoms to modal logic [15, 13] .  ... 
doi:10.1007/978-3-642-15205-4_32 fatcat:fl5t4ahopvdj3czkl2ccbndc3e

Complexity Results for Modal Dependence Logic [article]

Peter Lohmann, Heribert Vollmer
2011 arXiv   pre-print
Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for nondeterministic exponential time.  ...  Modal dependence logic was introduced recently by V\"a\"an\"anen. It enhances the basic modal language by an operator =(). For propositional variables p_1,...,p_n, =(p_1,...  ...  Modal dependence logic (MDL) is defined by introducing these dependence atoms to modal logic [Vää08, Sev09] .  ... 
arXiv:1104.0607v1 fatcat:nfq3q4gr4retzhfukgojkloqhu

Expressivity and Complexity of Dependence Logic [chapter]

Arnaud Durand, Juha Kontinen, Heribert Vollmer
2016 Dependence Logic  
While we mentioned a number of complexity results on modal dependence logic and some of its extensions, this issue remains unsettled for full MTL.  ...  Complexity of satisfiability for fragments of modal dependence logic Theorem 48. Poor man's modal dependence logic is NEXPTIME-complete. The proof relies as before on a reduction from Dependence-QBF.  ... 
doi:10.1007/978-3-319-31803-5_2 fatcat:rsvfibtfwzcntandlijfcjzhxi

Logics for Dependence and Independence (Dagstuhl Seminar 15261)

Erich Grädel, Juha Kontinen, Jouka Väänänen, Heribert Vollmer, Marc Herbstritt
2016 Dagstuhl Reports  
This report documents the programme and outcomes of Dagstuhl Seminar 15261 'Logics for Dependence and Independence'.  ...  This seminar served as a follow-up seminar to the highly successful seminar 'Dependence Logic: Theory and Applications' (Dagstuhl Seminar 13071).  ...  Complexity of Propositional Inclusion and Independence Logic We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence and inclusion  ... 
doi:10.4230/dagrep.5.6.70 dblp:journals/dagstuhl-reports/GradelKVV15 fatcat:wqkpzm2ywbcjdke2zyvvw4dlny

Model Checking for Modal Dependence Logic: An Approach through Post's Lattice [chapter]

Julian-Steffen Müller, Heribert Vollmer
2013 Lecture Notes in Computer Science  
This classification is done for all fragments of the logical language allowing modalities ♦ and , the dependence atom, and logical symbols for arbitrary Boolean functions.  ...  Modal dependence logic was recently introduced by Jouko Väänänen by extending modal logic by a the dependence atom dep(·).  ...  Conclusion We obtained a complete classification of the complexity of the model checking problem for modal dependence logic for formulas that may contain dependence atoms, one or two modalities, and symbols  ... 
doi:10.1007/978-3-642-39992-3_21 fatcat:2k73zomrf5btnkrxpk3lnyja7u

Model Checking for Modal Dependence Logic: An Approach Through Post's Lattice [article]

Julian-Steffen Müller, Heribert Vollmer
2013 arXiv   pre-print
This classification is done for all fragments of the logical language allowing modalities and , the dependence atom, and logical symbols for arbitrary Boolean functions.  ...  Modal dependence logic was recently introduced by Jouko Väänänen by extending modal logic by a the dependence atom dep(.).  ...  Conclusion We obtained a complete classification of the complexity of the model checking problem for modal dependence logic for formulas that may contain dependence atoms, one or two modalities, and symbols  ... 
arXiv:1303.6424v1 fatcat:3aszdvnbj5fidl7hxlij7q37oy

Complexity of validity for propositional dependence logics

Jonni Virtema
2014 Electronic Proceedings in Theoretical Computer Science  
We study the validity problem for propositional dependence logic, modal dependence logic and extended modal dependence logic.  ...  In addition, we establish that the corresponding problem for modal dependence logic and extended modal dependence logic is NEXPTIME-hard and in NEXPTIME^NP.  ...  Acknowledgements The author would like to thank the anonymous reviewers for their detailed and constructive comments.  ... 
doi:10.4204/eptcs.161.5 fatcat:izxvibr46rc2xlt3ckkmyeigei

Validity and Entailment in Modal and Propositional Dependence Logics

Miika Hannula, Marc Herbstritt
2017 Annual Conference for Computer Science Logic  
These complexity bounds follow as corollaries from a more general result showing that the entailment problem for (extended) modal dependence and propositional dependence logics is complete for co-NEXPTIME  ...  satisfiability problem for modal dependence logic.  ...  First, combining results from this paper and [27, 30] we observe that similarly to the standard modal logic case the complexity of validity and satisfiability coincide for (extended) modal dependence  ... 
doi:10.4230/lipics.csl.2017.28 dblp:conf/csl/Hannula17 fatcat:5q6fmjg4bzdnbal3e3gonibn2m

The Data Complexity of MDatalog in Basic Modal Logics [chapter]

Linh Anh Nguyen
2006 Lecture Notes in Computer Science  
We study the data complexity of the modal query language MDatalog and its extension eMDatalog in basic modal logics.  ...  This algorithm is very similar to Algorithm 5.1 in [8] , which constructs a least L-model for a given positive propositional modal logic program.  ...  I would like to thank the reviewers for useful comments.  ... 
doi:10.1007/11821069_63 fatcat:6a333pvd4jcuvi3uwpmgajd3lu

Special Issue on Hybrid Logics

Carlos Areces, Patrick Blackburn
2010 Journal of Applied Logic  
The framework can be used to uniformly prove general results, like preservation under bisimulations, for a wide family of logics.  ...  Coinductive models and normal forms for modal logics by C. Areces and D. Gorín.  ... 
doi:10.1016/j.jal.2010.10.001 fatcat:zqbmgbrokvel5jrjrkym3bg3vy

Parameterized Modal Satisfiability [article]

Antonis Achilleos, Michael Lampis, Valia Mitsou
2009 arXiv   pre-print
We investigate the parameterized computational complexity of the satisfiability problem for modal logic and attempt to pinpoint relevant structural parameters which cause the problem's combinatorial explosion  ...  We show fixed-parameter tractability results using these measures where the exponential dependence on the parameters is much milder than in the case of modality depth thus leading to FPT algorithms for  ...  For an introduction to modal logic and its complexity see [10, 5] .  ... 
arXiv:0912.4941v1 fatcat:j4t6t77txnh4bbkrykzpnnizgm

Parameterized Modal Satisfiability [chapter]

Antonis Achilleos, Michael Lampis, Valia Mitsou
2010 Lecture Notes in Computer Science  
We investigate the parameterized computational complexity of the satisfiability problem for modal logic and attempt to pinpoint relevant structural parameters which cause the problem's combinatorial explosion  ...  We show fixed-parameter tractability results using these measures where the exponential dependence on the parameters is much milder (doubly and singly exponential respectively) than in the case of modality  ...  In this paper we will focus on the standard modal logic K. For an introduction to modal logic and its complexity see [10, 5] .  ... 
doi:10.1007/978-3-642-14162-1_31 fatcat:kufrmxsw2badllrmhjn73dq574

Validity and Entailment in Modal and Propositional Dependence Logics [article]

Miika Hannula
2019 arXiv   pre-print
satisfiability problem for modal dependence logic.  ...  In particular, we address the question of the complexity of validity in modal dependence logic.  ...  First, combining results from this paper and [27, 30] we observe that similarly to the standard modal logic case the complexity of validity and satisfiability coincide for (extended) modal dependence  ... 
arXiv:1608.04301v5 fatcat:vedbmg5cjjhenf4wlmujidgxe4

Parameterized Modal Satisfiability

Antonis Achilleos, Michael Lampis, Valia Mitsou
2011 Algorithmica  
We investigate the parameterized computational complexity of the satisfiability problem for modal logic and attempt to pinpoint relevant structural parameters which cause the problem's combinatorial explosion  ...  We show fixed-parameter tractability results using these measures where the exponential dependence on the parameters is much milder (doubly and singly exponential respectively) than in the case of modality  ...  In this paper we will focus on the standard modal logic K. For an introduction to modal logic and its complexity see [10, 5] .  ... 
doi:10.1007/s00453-011-9552-z fatcat:sltkoayeubfmzdsm4yu4z6l2lm
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