A Logic for True Concurrency

We propose a logic for true concurrency whose formulae predicate about events in computations and their causal dependencies. The induced logical equivalence is hereditary history preserving bisimilarity, and fragments of the logic can be identified which correspond to other true concurrent behavioural equivalences in the literature: step, pomset and history preserving bisimilarity. Standard Hennessy-Milner logic, and thus (interleaving) bisimilarity, is also recovered as a fragment. We also propose an extension of the logic with fixpoint operators, thus allowing to describe causal and concurrency properties of infinite computations. We believe that this work contributes to a rational presentation of the true concurrent spectrum and to a deeper understanding of the relations between the involved behavioural equivalences.Comment: 31 pages, a preliminary version appeared in CONCUR 201

The complexity of independence-friendly fixpoint logic

Abstract. We study the complexity of model-checking for the fixpoint extension of Hintikka and Sandu’s independence-friendly logic. We show that this logic captures ExpTime; and by embedding PFP, we show that its combined complexity is ExpSpace-hard, and moreover the logic includes second order logic (on finite structures).

TAPAs: A Tool for the Analysis of Process Algebras

Process algebras are formalisms for modelling concurrent systems that permit mathematical reasoning with respect to a set of desired properties. TAPAs is a tool that can be used to support the use of process algebras to specify and analyze concurrent systems. It does not aim at guaranteeing high performances, but has been developed as a support to teaching. Systems are described as process algebras terms that are then mapped to labelled transition systems (LTSs). Properties are verified either by checking equivalence of concrete and abstract systems descriptions, or by model checking temporal formulae over the obtained LTS. A key feature of TAPAs, that makes it particularly suitable for teaching, is that it maintains a consistent double representation of each system both as a term and as a graph. Another useful didactical feature is the exhibition of counterexamples in case equivalences are not verified or the proposed formulae are not satisfied

Imperfect Information in Logic and Concurrent Games

Abstract. This paper builds on a recent definition of concurrent games as event structures and an application giving a concurrent-game model for predicate calculus. An extension to concurrent games with imperfect information, through the introduction of ‘access levels ’ to restrict the allowable strategies, leads to a concurrent-game semantics for a variant of Hintikka and Sandu’s Independence-Friendly (IF) logic

On independence-friendly fixpoint logics

Nous introduisons une extension aux points fixes de la logique IF (faite pour l’indépendance) de Hintikka et Sandu. Nous donnons des résultats sur sa complexité et son pouvoir expressif. Nous la relions aux jeux de parité à information imparfaite, et nous montrons une application à la définition d’un mu-calcul modal fait pour l’indépendance.We introduce a fixpoint extension of Hintikka and Sandu’s IF (independence-friendly) logic. We obtain some results on its complexity and expressive power. We relate it to parity games of imperfect information, and show its application to defining independence-friendly modal mu-calculi

Game theoretical semantics for some non-classical logics

Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest’s Logic of Paradox, Dunn’s First-Degree Entailment, Routleys’ Relevant Logics, McCall’s Connexive Logic and Belnap’s four-valued logic. We also present a game theoretical characterisation of a translation between Logic of Paradox/Kleene’s K3 and S5. We underline how non-classical logics require different verification games and prove the correctness theorems of their respective game theoretical semantics. This allows us to observe that paraconsistent logics break the classical bidirectional connection between winning strategies and truth values

Game theoretical semantics for some non-classical logics

Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest’s Logic of Paradox, Dunn’s First-Degree Entailment, Routleys’ Relevant Logics, McCall’s Connexive Logic and Belnap’s four-valued logic. We also present a game theoretical characterisation of a translation between Logic of Paradox/Kleene’s K3 and S5. We underline how non-classical logics require different verification games and prove the correctness theorems of their respective game theoretical semantics. This allows us to observe that paraconsistent logics break the classical bidirectional connection between winning strategies and truth values