{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article2671","name":"Complexity Results for Modal Dependence Logic","abstract":"Modal dependence logic was introduced very recently by V\u00e4\u00e4n\u00e4nen. It\r\nenhances the basic modal language by an operator dep. For propositional\r\nvariables p_1,...,p_n, dep(p_1,...,p_(n-1);p_n) intuitively states that\r\nthe value of p_n only depends on those of p_1,...,p_(n-1). Sevenster (J.\r\nLogic and Computation, 2009) showed that satisfiability for modal\r\ndependence logic is complete for nondeterministic exponential time.\r\n\r\nIn this paper we consider fragments of modal dependence logic obtained\r\nby restricting the set of allowed propositional connectives. We show\r\nthat satisfibility for poor man's dependence logic, the language\r\nconsisting of formulas built from literals and dependence atoms using\r\nconjunction, necessity and possibility (i.e., disallowing disjunction),\r\nremains NEXPTIME-complete. If we only allow monotone formulas (without\r\nnegation, but with disjunction), the complexity drops to\r\nPSPACE-completeness. We also extend V\u00e4\u00e4n\u00e4nen's language by allowing\r\nclassical disjunction besides dependence disjunction and show that the\r\nsatisfiability problem remains NEXPTIME-complete. If we then disallow\r\nboth negation and dependence disjunction, satistiability is complete for\r\nthe second level of the polynomial hierarchy.\r\n\r\nIn this way we completely classify the computational complexity of the\r\nsatisfiability problem for all restrictions of propositional and\r\ndependence operators considered by V\u00e4\u00e4n\u00e4nen and Sevenster.","keywords":["Dependence logic","satisfiability problem","computational complexity","poor man's logic"],"author":[{"@type":"Person","name":"Lohmann, Peter","givenName":"Peter","familyName":"Lohmann"},{"@type":"Person","name":"Vollmer, Heribert","givenName":"Heribert","familyName":"Vollmer"}],"position":3,"pageStart":1,"pageEnd":15,"dateCreated":"2010-04-26","datePublished":"2010-04-26","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Lohmann, Peter","givenName":"Peter","familyName":"Lohmann"},{"@type":"Person","name":"Vollmer, Heribert","givenName":"Heribert","familyName":"Vollmer"}],"copyrightYear":"2010","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.10061.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume791","volumeNumber":10061,"name":"Dagstuhl Seminar Proceedings, Volume 10061","dateCreated":"2010-04-26","datePublished":"2010-04-26","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article2671","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume791"}}}