A Complete Temporal and Spatial Logic for Distributed Systems ⋆ Dirk Pattinson 1 and Bernhard Reus 2 1 LMU München, Institut für Informatik, 80538 München 2 University of Sussex, Informatics, Brighton BN1 9QH Abstract. In this paper, we introduce a spatial and temporal logic for reason- ing about distributed computation. The logic is a combination of an extension of hybrid logic, that allows us to reason about the spatial structure of a computa- tion, and linear temporal logic, which accounts for the temporal aspects. On the pragmatic side, we show the wide applicability of this logic by means of many examples. Our main technical contribution is completeness of the logic both with respect to spatial/temporal structures and a class of spatial transition systems. 1 Introduction With the advent of the Internet, mobility and spatial distribution of information systems have established themselves as a new computational paradigm. Distributed and mobile systems, however, require new specification and verification methodologies. Program logics have to account for space and time in a single, unified framework, stating where and when certain computations happen. A further challenge consists of the fact that these systems run on heterogeneous platforms using various different programming languages. The formal modelling of distributed and mobile systems has traditionally been the domain of process calculi. Several approaches can be found in the literature, for ex- ample the π-calculus [22], the ambient calculus [9], and Klaim [12]. In all of these approaches, distributed processes are represented as terms in the language of the un- derlying calculus. For each of these calculi, corresponding formal logics have been proposed to reason about the behaviour of distributed computation. For example, see [23,7,4,5] for the π-calculus, [9] for the Ambient-calculus, and [24] for Klaim, to name but a few. From a practical perspective, it seems unrealistic to assume that all entities participating in a distributed (or mobile) system can be specified in a single syntac- tic framework: by its very nature, distributed computation integrates various different platforms, operating systems, and programming languages. A single semantic framework is, however, desirable as it supports the analysis and comparison of different logics and calculi. This paper bridges the gap between theory and practice and introduces syntax-independent models of distributed and mobile sys- tems together with an associated logic, that allows to reason about the behaviour of ⋆ This work was partially sponsored by the DAAD and the British Council in the ARC project 1205 “Temporal and Spatial Logic for Mobile Systems”. B. Gramlich (Ed.): FroCoS 2005, LNAI 3717, pp. 122–137, 2005. © Springer-Verlag Berlin Heidelberg 2005