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  1.  19
    Luca Alberucci & Alessandro Facchini (2009). The Modal Μ-Calculus Hierarchy Over Restricted Classes of Transition Systems. Journal of Symbolic Logic 74 (4):1367 - 1400.
    We study the strictness of the modal μ-calculus hierarchy over some restricted classes of transition systems. First, we prove that over transitive systems the hierarchy collapses to the alternationfree fragment. In order to do this the finite model theorem for transitive transition systems is proved. Further, we verify that if symmetry is added to transitivity the hierarchy collapses to the purely modal fragment. Finally, we show that the hierarchy is strict over reflexive frames. By proving the finite model theorem for (...)
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  2.  1
    Luca Alberucci & Gerhard Jäger (2005). About Cut Elimination for Logics of Common Knowledge. Annals of Pure and Applied Logic 133 (1):73-99.
    The notions of common knowledge or common belief play an important role in several areas of computer science , in philosophy, game theory, artificial intelligence, psychology and many other fields which deal with the interaction within a group of “agents”, agreement or coordinated actions. In the following we will present several deductive systems for common knowledge above epistemic logics –such as K, T, S4 and S5 –with a fixed number of agents. We focus on structural and proof-theoretic properties of these (...)
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  3.  25
    Luca Alberucci & Alessandro Facchini (2009). On Modal Μ -Calculus and Gödel-Löb Logic. Studia Logica 91 (2):145 - 169.
    We show that the modal µ-calculus over GL collapses to the modal fragment by showing that the fixpoint formula is reached after two iterations and answer to a question posed by van Benthem in [4]. Further, we introduce the modal µ~-calculus by allowing fixpoint constructors for any formula where the fixpoint variable appears guarded but not necessarily positive and show that this calculus over GL collapses to the modal fragment, too. The latter result allows us a new proof of the (...)
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    Max A. Freund, A. Modal Sortal Logic, R. Logic, Luca Alberucci, Vincenzo Salipante & On Modal (2004). David J. Anderson and Edward N. Zalta/Frege, Boolos, and Logical Objects 1–26 Michael Glanzberg/A Contextual-Hierarchical Approach to Truth and the Liar Paradox 27–88 James Hawthorne/Three Models of Sequential Belief Updat. [REVIEW] Journal of Philosophical Logic 33:639-640.
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  5.  23
    Luca Alberucci & Vincenzo Salipante (2004). On Modal Μ-Calculus and Non-Well-Founded Set Theory. Journal of Philosophical Logic 33 (4):343-360.
    A finitary characterization for non-well-founded sets with finite transitive closure is established in terms of a greatest fixpoint formula of the modal μ-calculus. This generalizes the standard result in the literature where a finitary modal characterization is provided only for wellfounded sets with finite transitive closure. The proof relies on the concept of automaton, leading then to new interlinks between automata theory and non-well-founded sets.
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