4 found
Order:
  1.  23
    The Modal Μ-Calculus Hierarchy Over Restricted Classes of Transition Systems.Luca Alberucci & Alessandro Facchini - 2009 - 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 (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  2.  43
    On Modal Μ -Calculus and Gödel-Löb Logic.Luca Alberucci & Alessandro Facchini - 2009 - 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 (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  3.  4
    On Modal Μ-Calculus and Gödel-Löb Logic.Luca Alberucci & Alessandro Facchini - 2009 - 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  4.  2
    A Gleason-Type Theorem for Any Dimension Based on a Gambling Formulation of Quantum Mechanics.Alessio Benavoli, Alessandro Facchini & Marco Zaffalon - 2017 - Foundations of Physics 47 (7):991-1002.
    Based on a gambling formulation of quantum mechanics, we derive a Gleason-type theorem that holds for any dimension n of a quantum system, and in particular for \. The theorem states that the only logically consistent probability assignments are exactly the ones that are definable as the trace of the product of a projector and a density matrix operator. In addition, we detail the reason why dispersion-free probabilities are actually not valid, or rational, probabilities for quantum mechanics, and hence should (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography