Pure future local temporal logics are

We investigate the semantics of messages, and argue that the meaning of a message is naturally and usefully given in terms of how it a#ects the knowledge of the agents involved in the communication. We see that the semantics depends on the protocol used by the agents, and this leads us to knowledge based specification of protocols. While these notions are natural for distributed computations, we suggest that the considerations discussed here may be relevant in more general linguistic contexts.

A basic result concerning LTL, the propositional temporal logic of linear time, is that it is expressively complete; it is equal in expressive power to the first order theory of sequences. We present here a smooth extension of this result to the class of partial orders known as Mazurkiewicz traces. These partial orders arise in a variety of contexts in concurrency theory and they provide the conceptual basis for many of the partial order reduction methods that have been developed in connection with LTL-specifications. We show that LTrL, our linear time temporal logic, is equal in expressive power to the first order theory of traces when interpreted over (finite and) infinite traces. This result fills a prominent gap in the existing logical theory of infinite traces. LTrL also constitutes a characterisation of the so called trace consistent (robust) LTL-specifications. These are specifications expressed as LTL formulas that do not distinguish between different linearisations of the same trace and hence are amenable to partial order reduction methods.

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The complexity of LTrL, a global linear time temporal logic over traces is investigated. The logic is global because the truth of a formula is evaluated in a global state, also called conguration. The logic is shown to be non-elementary with the main reason for this complexity being the nesting of until operators in formulas. The fragment of the logic without the until operator is shown to be EXPSPACE-complete. 1 Introduction Innite words, which linear orders on events, are often used to model executions of systems. Innite traces, which are partial orders on events, are often used to model concurrent systems when we do not want to put some arbitrary ordering on actions occurring concurrently. A state of a system in the linear model is just a prex of an innite word; it represents the actions that have already happened. A state of a system in the trace model is a conguration, i.e., a nite downwards closed set of events that already happened. Temporal logics over traces come in t...

A long standing open problem in the theory of (Mazurkiewicz) traces has been the question whether LTL (Linear Time Logic) is expressively complete with respect to the rst order theory. We solve this problem positively for nite and in nite traces and for the simplest temporal logic, which is based only on next and until modalities. Similar results were established previously, but they were all weaker, since they used additional past or future modalities. Another feature of our work is that our proof is direct and does not use any reduction to the word case.

Mazurkiewicz traces ⋆

. In this paper, we present two logics that allow for specifying distributed information systems, emphasizing communication among sites. The low-level logic D 0 offers features that are easy to implement but awkward to use for specification, while the high-level logic D 1 offers convenient specification features that are not easy to implement. We show that D 1 specifications may be automatically translated to D 0 in a sound and complete way. In order to prove soundness and completeness, we define our translation as a simple map of institutions. Our result may be useful for making implementation platforms like Corba easier accessible by providing high-level planning and specification methods for communication. 1 Introduction Two logics are presented that allow for specifying distributed information systems, emphasizing communication among sites. The low-level logic D 0 offers features that are easy to implement but awkward to use for specification, while the high-level logic D 1 offers...

Mazurkiewicz traces are a widely accepted model of concurrent systems. We introduce a linear time temporal logic LTL f which has the same expressive power as the first order theory FO(<) of finite (infinite resp.) traces. The main contribution of the paper is that we only use future tense modalities in order to obtain expressive completeness. Our proof is direct using no reduction to words and Kamp's theorem for both finite and infinite words becomes a corollary. This direct approach became possible due to a proof technique of Wilke developed for the case of finite words.

Abstract. Recently, local logics for Mazurkiewicz traces are of increasing interest. This is mainly due to the fact that the satisfiability problem has the same complexity as in the word case. If we focus on a purely local interpretation of formulae at vertices (or events) of a trace, then the satisfiability problem of linear temporal logics over traces turns out to be PSPACE–complete. But now the difficult problem is to obtain expressive completeness results with respect to first order logic. The main result of the paper shows such an expressive completeness result, if the underlying dependence alphabet is a cograph, i.e., if all traces are series parallel posets. Moreover, we show that this is the best we can expect in our setting: If the dependence alphabet is not a cograph, then we cannot express all first order properties.