Rewriting logic is naturally concurrent: several subterms of the state term can be rewritten simultaneously. But state terms are global, which makes compositionality difficult to achieve. Compositionality here means being able to decompose a complex system into its functional components and code each as an isolated and encapsulated system. Our goal is to help bringing compositionality to system specification in rewriting logic. The base of our proposal is the operation that we call synchronous composition. We discuss the motivations and implications of our proposal, formalize it for rewriting logic and also for transition structures, to be used as semantics, and show the power of our approach with some examples. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).
Several temporal logics have been proposed that make joint use of actions and propositions on states: ACTL* @cite_34 , RLTL @cite_0 , SE-LTL @cite_4 , TLR* @cite_25 . There are also transition structures with mixed ingredients: LKS @cite_4 , L2TS @cite_54 . Although all of them bring actions (or transitions) to the focus, none tries to be utterly egalitarian, as we do.
@cite_4 @cite_54 @cite_0 @cite_34 @cite_25
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A temporal logic based on actions rather than on states is presented and interpreted over labelled transition systems. It is proved that it has essentially the same power as CTL*, a temporal logic interpreted over Kripke structures. The relationship between the two logics is established by introducing two mappings from Kripke structures to labelled transition systems and viceversa and two transformation functions between the two logics which preserve truth. A branching time version of the action based logic is also introduced. This new logic for transition systems can play an important role as an intermediate between Hennessy-Milner Logic and the modal μ-calculus. It is sufficiently expressive to describe safety and liveness properties but permits model checking in linear time. Three temporal logics are introduced which induce on labeled transition systems the same identifications as branching bisimulation. The first is an extension of Hennessy-Milner logic with a kind of unit operator. The second is another extension of Hennessy-Milner logic which exploits the power of backward modalities. The third is CTL* with the next-time operator interpreted over all paths, not just over maximal ones. A relevant side effect of the last characterization is that it sets a bridge between the state- and event-based approaches to the semantics of concurrent systems. > A unifying framework for the study of real-time logics is developed. In analogy to the untimed case, the underlying classical theory of timed state sequences is identified, it is shown to be nonelementarily decidable, and its complexity and expressiveness are used as a point of reference. Two orthogonal extensions of PTL (timed propositional temporal logic and metric temporal logic) that inherit its appeal are defined: they capture elementary, yet expressively complete, fragments of the theory of timed state sequences, and thus are excellent candidates for practical real-time specification languages. This paper presents the linear temporal logic of rewriting (LTLR) model checker under localized fairness assumptions for the Maude system. The linear temporal logic of rewriting extends linear temporal logic (LTL) with spatial action patterns that describe patterns of rewriting events. Since LTLR generalizes and extends various state-based and event-based logics, mixed properties involving both state propositions and actions, such as fairness properties, can be naturally expressed in LTLR. However, often the needed fairness assumptions cannot even be expressed as propositional temporal logic formulas because they are parametric, that is, they correspond to universally quantified temporal logic formulas. Such universal quantification is succinctly captured by the notion of localized fairness; for example, fairness is localized to the object name parameter in object fairness conditions. We summarize the foundations, and present the language design and implementation of the Maude Fair LTLR model checker, developed at the C++ level within the Maude system by extending the existing Maude LTL model checker. Our tool provides not only an efficient LTLR model checking algorithm under parameterized fairness assumptions but also suitable specification languages as part of its user interface. The expressiveness and effectiveness of the Maude Fair LTLR model checker are illustrated by five case studies. This is the first tool we are aware of that can model check temporal logic properties under parameterized fairness assumptions. We develop the LTLR model checker under localized fairness assumptions.The linear temporal logic of rewriting (LTLR) extends LTL with action patterns.Localized fairness specifies parameterized fairness over generic system entities.We present the foundations, the language design, and the implementation of our tool.We illustrate the expressiveness and effectiveness of our tool with case studies.