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On the equivalence of game and denotational semantics for the probabilistic mu-calculus

Matteo Mio.

The probabilistic (or quantitative) modal mu-calculus is a fixed-point logic de- signed for expressing properties of probabilistic labeled transition systems (PLTS). Two semantics have been studied for this logic, both assigning to every process state a value in the interval [0,1] representing the&nbsp;[&hellip;]

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Probabilistic modal {\mu}-calculus with independent product

Matteo Mio.

The probabilistic modal {\mu}-calculus is a fixed-point logic designed for expressing properties of probabilistic labeled transition systems (PLTS's). Two equivalent semantics have been studied for this logic, both assigning to each state a value in the interval [0,1] representing the probability&nbsp;[&hellip;]

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Monadic Second Order Logic with Measure and Category Quantifiers

Matteo Mio ; Michał Skrzypczak ; Henryk Michalewski.

We investigate the extension of Monadic Second Order logic, interpreted over infinite words and trees, with generalized "for almost all" quantifiers interpreted using the notions of Baire category and Lebesgue measure.

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Probabilistic logics based on Riesz spaces

Robert Furber ; Radu Mardare ; Matteo Mio.

We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz spaces, a mature field of mathematics at the intersection of&nbsp;[&hellip;]

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Proof Theory of Riesz Spaces and Modal Riesz Spaces

Christophe Lucas ; Matteo Mio.

We design hypersequent calculus proof systems for the theories of Riesz spaces and modal Riesz spaces and prove the key theorems: soundness, completeness and cut elimination. These are then used to obtain completely syntactic proofs of some interesting results concerning the two theories. Most&nbsp;[&hellip;]

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