Modal Logics for Mobile Processes Revisited

We revisit the logical characterisations of various bisimilarity relations for the finite fragment of the ?-calculus. Our starting point is the early and the late bisimilarity, first defined in the seminal work of Milner, Parrow and Walker, who also proved their characterisations in fragments of a modal logic (which we refer to as the MPW logic). Two important refinements of early and late bisimilarity, called open and quasi-open bisimilarity, respectively, were subsequently proposed by Sangiorgi and Walker. Horne, et. al., showed that open and quasi-bisimilarity are characterised by intuitionistic modal logics: OM (for open bisimilarity) and FM (for quasi-open bisimilarity). In this work, we attempt to unify the logical characterisations of these bisimilarity relations, showing that they can be characterised by different sublogics of a unifying logic. A key insight to this unification derives from a reformulation of the four bisimilarity relations (early, late, open and quasi-open) that uses an explicit name context, and an observation that these relations can be distinguished by the relative scoping of names and their instantiations in the name context. This name context and name substitution then give rise to an accessibility relation in the underlying Kripke semantics of our logic, that is captured logically by an S4-like modal operator. We then show that the MPW, the OM and the FM logics can be embedded into fragments of our unifying classical modal logic. In the case of OM and FM, the embedding uses the fact that intuitionistic implication can be encoded in modal logic S4

Modal logics for mobile processes

In process algebras, bisimulation equivalence is typically defined directly in terms of the operational rules of action; it also has an alternative characterisation in terms of a simple modal logic (sometimes called Hennessy-Milner logic . This paper first defines two forms of bisimulation equivalence for the\031-calculus , a process algebra which allows dynamic reconfiguration among processes; it then explores a family of possible logics, with different modal operators. It is proven that two of these logics characterise the two bisimulation equivalences. Also, the relative expressive power of all the logics is exhibited as a lattice

Model Checking Dynamic-Epistemic Spatial Logic

In this paper we focus on Dynamic Spatial Logic, the extension of Hennessy-Milner logic with the parallel operator. We develop a sound complete Hilbert-style axiomatic system for it comprehending the behavior of spatial operators in relation with dynamic/temporal ones. Underpining on a new congruence we define over the class of processes - the structural bisimulation - we prove the finite model property for this logic that provides the decidability for satisfiability, validity and model checking against process semantics. Eventualy we propose algorithms for validity, satisfiability and model checking

A Proof Theoretic Approach to Operational Semantics

AbstractProof theory can be applied to the problem of specifying and reasoning about the operational semantics of process calculi. We overview some recent research in which λ-tree syntax is used to encode expressions containing bindings and sequent calculus is used to reason about operational semantics. There are various benefits of this proof theoretic approach for the π-calculus: the treatment of bindings can be captured with no side conditions; bisimulation has a simple and natural specification in which the difference between bound input and bound output is characterized using difference quantifiers; various modal logics for mobility can be specified declaratively; and simple logic programming-like deduction involving subsets of second-order unification provides immediate implementations of symbolic bisimulation. These benefits should extend to other process calculi as well. As partial evidence of this, a simple λ-tree syntax extension to the tyft/tyxt rule format for name-binding and name-passing is possible that allows one to conclude that (open) bisimilarity is a congruence

Handling Data-Based Concurrency in Context-Aware Service Protocols

Dependency analysis is a technique to identify and determine data dependencies between service protocols. Protocols evolving concurrently in the service composition need to impose an order in their execution if there exist data dependencies. In this work, we describe a model to formalise context-aware service protocols. We also present a composition language to handle dynamically the concurrent execution of protocols. This language addresses data dependency issues among several protocols concurrently executed on the same user device, using mechanisms based on data semantic matching. Our approach aims at assisting the user in establishing priorities between these dependencies, avoiding the occurrence of deadlock situations. Nevertheless, this process is error-prone, since it requires human intervention. Therefore, we also propose verification techniques to automatically detect possible inconsistencies specified by the user while building the data dependency set. Our approach is supported by a prototype tool we have implemented.Comment: In Proceedings FOCLASA 2010, arXiv:1007.499

Multi labelled transition systems: a semantic framework for nominal calculi

Action Labelled transition systems (LTS) have proved to be a fundamental model for describing and proving properties of concurrent systems. In this paper, Multiple Labelled Transition Systems (MLTS) are introduced as generalizations of LTS that permit dealing also with systems features that are becoming more and more important when considering languages and models for network aware programming. MLTS permit describing not only the actions systems can perform but also system's resources usage and their handling (creation, revelation ...) of names. To show adeguacy of our proposal we show how MLTS can be used to describe the operational semantics of one of the most studied calculus for mobility: the asynchronous [pi]-calculus