Labelled Tableaux for Distributed Temporal Logic

Abstract

The distributed temporal logic DTL is a logic for reasoning about temporal properties of discrete distributed systems from the local point of view of the system's agents, which are assumed to execute sequentially and to interact by means of synchronous event sharing. We present a sound and complete labelled tableaux system for full DTL. To achieve this, we first formalize a labelled tableaux system for reasoning locally at each agent and afterwards we combine the local systems into a global one by adding rules that capture the distributed nature of DTL. We also provide examples illustrating the use of DTL and our tableaux system.

A Labeled Tableaux System for the Distributed Temporal Logic DTL

“…We omit this translation for the sake of space and refer the reader to [1]. Since LTL is decidable, any decision procedure for LTL entailment can thus also be used for DTL (and since our translation is polynomial, the asymptotic complexity is identical).…”

“…The translation relies on the fact that given a distributed life-cycle λ = { E i , ≤ i } i∈Id , it is always possible to linearize the global order on events E, ≤ : one can define an injective function f : E → N that preserves the global causality relation, i.e., if e < e then f (e) < f (e ). However, the result given in [1] is actually independent of the chosen linearization function f and in general there may be many such functions. This means that DTL is traceconsistent in the sense of [24]; namely, DTL properties can be checked by considering one arbitrary linearization of the distributed model, as opposed to checking all possible linearizations.…”

“…This essentially amounts to a tableaux system for full future-time LTL (see [1] for the extension with past-time operators).…”

“…First, we introduce a labeled tableaux system for full future-time LTL, where reasoning is local. Due to lack of space, we do not consider here past-time operators like since, although all the results presented in this paper extend straightforwardly to full LTL (and thus to full DTL) as we show in [1].…”

“…We conclude, in §5, by comparing with related work and discussing future work. Due to lack of space, examples have been shortened and proofs have been omitted; full details are given in [1]. Applications of the logic are also presented in [1], as well as in [3,4,8,9].…”