A Non-wellfounded, Labelled Proof System for Propositional Dynamic Logic

We define a infinitary labelled sequent calculus for PDL, G3PDL^{\infty}. A finitarily representable cyclic system, G3PDL^{\omega}, is then given. We show that both are sound and complete with respect to standard models of PDL and, further, that G3PDL^{\infty} is cut-free complete. We additionally investigate proof-search strategies in the cyclic system for the fragment of PDL without tests

Equivalence of Probabilistic mu-Calculus and p-Automata

An important characteristic of Kozen’s µ-calculus is its strong connection with parity alternating tree automata. Here, we show that the probabilistic µ-calculus µ^p-calculus and p-automata (parity alternating Markov chain automata) have an equally strong connection. Namely, for every µ^p-calculus formula we can construct a p-automaton that accepts exactly those Markov chains that satisfy the formula. For every p-automaton we can construct a µ^p-calculus formula satisfied in exactly those Markov chains that are accepted by the automaton. The translation in one direction relies on a normal form of the calculus and in the other direction on the usage of vectorial µ^p-calculus. The proofs use the game semantics of µ^p-calculus and automata to show that our translations are correct

The mu-calculus and Model Checking

International audienceThis chapter presents a part of the theory of the mu-calculus that is relevant to the, broadly understood, model-checking problem. The mu-calculus is one of the most important logics in model-checking. It is a logic with an exceptional balance between expressiveness and algorithmic properties. The chapter describes in length the game characterization of the semantics of the mu-calculus. It discusses the theory of the mu-calculus starting with the tree model property, and bisimulation invariance. Then it develops the notion of modal automaton: an automaton-based model behind the mu-calculus. It gives a quite detailed explanation of the satisfiability algorithm, followed by the results on alternation hierarchy, proof systems, and interpolation. Finally, the chapter discusses the relations of the mu-calculus to monadic second-order logic as well as to some program and temporal logics. It also presents two extensions of the mu-calculus that allow us to address issues such as inverse modalities