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The modal μ-calculus hierarchy over restricted classes of transition systems
TLDR
First, it is proved that over transitive systems the hierarchy collapses to the alternation-free fragment, and it is shown that the hierarchy is strict over reflexive frames by proving the finite model theorem for reflexive systems.
The Power of the Weak
TLDR
This work proves two results of the same kind, one for the alternationfree fragment of μML (μDML) and one for weak MSO (WMSO), and introduces classes of parity automata characterising the expressiveness of WMSO and NMSO (on tree models) and of μCML and μDML (for all transition systems).
A Polarity Theory for Sets of Desirable Gambles
TLDR
A new (lexicographic) polarity theory for general convex cones is introduced and then applied in order to establish an analogous correspondence between coherent sets of desirable gambles and convex sets of lexicographic probabilities.
On Modal μ-Calculus and Gödel-Löb Logic
TLDR
The modal μ~-calculus is introduced by allowing fixpoint constructors for any formula where the fixpoint variable appears guarded but not necessarily positive and it is shown that this calculus over GL collapses to the modal fragment, too.
Model theory of monadic predicate logic with the infinity quantifier
TLDR
It is obtained that the four semantic properties of M E ∞, a variation of monadic first-order logic that features the generalised quantifier exists, are decidable for L -sentences.
Evaluating the effects of social interactions on a distributed demand side management system for domestic appliances
TLDR
An algorithmic framework that models the effect of social interactions in a distributed demand side management system and shows that such interactions can increase the flexibility of users’ schedules and lower the peak power, resulting in a smoother usage of energy throughout the day.
Rabin-Mostowski Index Problem: A Step beyond Deterministic Automata
TLDR
This work investigates a wider class of regular languages, recognisable by so-called game automata, which can be seen as the closure of deterministic ones under complementation and composition and shows that it is decidable whether a given regular language can be recognised by a game automaton.
A Gleason-Type Theorem for Any Dimension Based on a Gambling Formulation of Quantum Mechanics
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 $$n=2$$n=2. The theorem states that
Quantum mechanics: The Bayesian theory generalized to the space of Hermitian matrices
We consider the problem of gambling on a quantum experiment and enforce rational behavior by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality
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