Extension Of Hennessy-Milner Logic Research Articles

Causal Reasoning for Safety in Hennessy Milner Logic

Determining and computing root causes in system failures is a significant issue in science and engineering. In this paper, we introduce a notion of causality for explaining counterexamples in system analysis based on formal models. The counter-examples are produced by checking for hazardous situations expressed in the Hennessy-Milner Logic, in the context of Labelled Transition System models. We also introduce CauseJMu, a tool for automatically identifying such causal computations within a system model. CauseJMu relies on encoding causality in terms of an extension of Hennessy-Milner Logic to recursive formulae with data. The encodings enable deciding whether a certain computation is causal or not, using the mCRL2 model checker.

A Logic for Choreographies

We explore logical reasoning for the global calculus, a coordination model based on the notion of choreography, with the aim to provide a methodology for specification and verification of structured communications. Starting with an extension of Hennessy-Milner logic, we present the global logic (GL), a modal logic describing possible interactions among participants in a choreography. We illustrate its use by giving examples of properties on service specifications. Finally, we show that, despite GL is undecidable, there is a significant decidable fragment which we provide with a sound and complete proof system for checking validity of formulae.

On decidability and model checking for a first order model logic for value-passing processes

A semantic interpretation of a first order extension of Hennessy-Milner logic for value-passing processes, named HML(FO), is presented. The semantics is based on symbolic transition graphs with assignment. It is shown that the satisfiability of the two-variable sub-logic HML(FO 2 ) of HML(FO) is decidable, and the complexity discussed. Finally, a decision procedure for model checking the value-passing processes with respect to HML(FO 2 ) is obtained.

Three logics for branching bisimulation

Three temporal logics are introduced that induce on labeled transition systems the same identifications as branching bisimulation, a behavioral equivalence that aims at ignoring invisible transitions while preserving the branching structure of systems. The first logic is an extension of Hennessy-Milner Logic with an “until” operator. The second one is another extension of Hennessy-Milner Logic, which exploits the power of backward modalities. The third logic is CTL* without the next-time operator. A relevant side-effect of the last characterization is that it sets a bridge between the state- and action-based approaches to the semantics of concurrent systems.

Proof systems for satisfiability in Hennessy-Milner Logic with recursion

An extension of Hennessy-Milner Logic with recursion is presented. A recursively specified formula will have two standard interpretations: a minimal one and a maximal one. Minimal interpretations of formulas are useful for expressing liveness properties of processes, whereas maximal interpretations are useful for expressing safety properties. We present sound and complete proof systems for both interpretations for when a process satisfies a (possibly recursive) formula. The rules of the proof systems consist of an introduction rule for each possible structure of a formula and are intended to extend the work of Stirling and Winskel. Moreover the proof systems may be presented directly in PROLOG to yield a decision procedure for verifying when a finite-state process satisfies a specification given as a (possibly recursive) formula.