A Labeled Tableaux System for the Distributed Temporal Logic DTL

Abstract

DTL is a distributed temporal logic for reasoning about temporal properties of 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 labeled tableaux system for future-time DTL. To achieve this, we first formalize a labeled tableaux system for reasoning locally at each agent, which provides a system for full future-time LTL, and afterwards we combine the local systems into a global one by adding rules that capture the distributed nature of DTL.

Distributed temporal logic for the analysis of security protocol models

“…DTL was proposed in [34] as a logic for specifying and reasoning about distributed information systems and several versions were given, reflecting different perspectives on how non-local information can be accessed by each agent [8,16,17]. In this paper, we use the simplest and most expressive formulation, from [8]. We stick with a propositional language, which suits our purposes, as we describe our schema axioms by taking advantage of explicit meta-level quantifications and of the inductive definition of closed sets of messages.…”

“…As is well known, this is particularly important in the area of Information Security, where researchers often have well-developed intuitions, but their models and proofs are prone to subtle errors. Although we have developed a tableau system for DTL [7,8], our proofs in this paper are semantic. We prefer semantic arguments because they are shorter and far more intuitive than tableau proofs.…”

“…In contrast, proofs with the tableau system can be machine checked. We note, in this regard, that the validity of DTL formulas can be decided by using a trace-consistent translation to LTL [8], which also makes DTL amenable to model checking.…”

Labeled Natural Deduction Systems for a Family of Tense Logics

“…Moreover, it can be proven to correspond to a logic "larger" than STL for which the condition of linearity (or connectedness) on the relation ≺ holds: we call this logic Medium Temporal Logic MTL. 8 We could also introduce rules for the operators since and until, but they would be quite complex and problematic from a proof-theoretical point of view; see [2] for a labeled tableaux system for a distributed temporal logic that comprises full LTL, and [5] for tableaux-like ND rules for LTL.…”

Labelled Tableaux for Distributed Temporal Logic

“…To our knowledge, this is the first labelled system given for full, discrete-time LTL with the until and since operators. 1 …”