Satisfiability and Model Checking in Team Based Logics

Julian-Steffen Müller

Aug. 2014 · Cuvillier Verlag

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Dependence and independence between properties is occurring in many different scientific disciplines, for example in the description of discrete systems or during the evaluation of physical experiments. During this thesis we will study a variety of team based logics, which can express some form of dependence or independence. The concept of expressing functional dependencies between terms by atomic FO-formulae was introduced by Väänänen in 2007. He showed that dependence logic is equally expressive as existential second order logic and thus dependence logic characterises NP. In the first chapter of this thesis we are obtaining a Horn fragment of dependence logic which characterises P. In the second part of this thesis we will study the concept of dependence and independence in the context of team based modal logics. We will study several decision problems for these modal logics, like satisfiability and model checking. Furthermore we will investigate the expressive power of these modal logics. Finally we will give a general notion of team atoms and the properties that they are describing.