929 research outputs found

    Modal mu-calculi

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    Fredkin Gates for Finite-valued Reversible and Conservative Logics

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    The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram

    Team logic : axioms, expressiveness, complexity

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    Team semantics is an extension of classical logic where statements do not refer to single states of a system, but instead to sets of such states, called teams. This kind of semantics has applications for example in mathematical logic, verification of dynamic systems as well as in database theory. In this thesis, we focus on the propositional, modal and first-order variant of team logic. We study the classical questions of formal logic: Expressiveness (can we formalize sufficiently interesting properties of models?), axiomatizability (can all true statements be deduced in some formal system?) and complexity (can problems such as satisfiability and model checking be solved algorithmically?). Finally, we classify existing team logics and show approaches how team semantics can be defined for arbitrary other logics.Team-Semantik ist eine Erweiterung klassischer Logik, bei der Aussagen nicht ĂŒber einzelne ZustĂ€nde eines Systems getroffen werden, sondern ĂŒber Mengen solcher ZustĂ€nde, genannt Teams. Diese Art von Semantik besitzt unter anderem Anwendungen in der mathematischen Logik, in der Verifikation dynamischer Systeme sowie in der Datenbanktheorie. In dieser Arbeit liegt der Fokus auf der aussagenlogischen, der modallogischen und der prĂ€dikatenlogischen Variante der Team-Logik. Es werden die klassischen Fragestellungen formaler Logik untersucht: Ausdruckskraft (können hinreichend interessante Eigenschaften von Modellen formalisiert werden?), Axiomatisierbarkeit (lassen sich alle wahren Aussagen in einem KalkĂŒl ableiten?) und KomplexitĂ€t (können Probleme wie ErfĂŒllbarkeit und ModellprĂŒfung algorithmisch gelöst werden?). Schlussendlich werden existierende Team-Logiken klassifiziert und es werden AnsĂ€tze aufgezeigt, wie Team-Semantik fĂŒr beliebige weitere Logiken definiert werden kann
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