Istituto di Scienza e Tecnologie dell'Informazione     
Ciancia V., Latella D., Loreti M., Massink M. Model checking spatial logics for closure spaces. In: Logical Methods in Computer Science, vol. 12 (4) pp. 1 - 51. Logical Methods in Computer Science, 2016.
Spatial aspects of computation are becoming increasingly relevant in Computer Science, especially in the field of collective adaptive systems and when dealing with systems distributed in physical space. Traditional formal verification techniques are well suited to analyse the temporal evolution of programs; however, properties of space are typically not taken into account explicitly. We present a topology-based approach to formal verification of spatial properties depending upon physical space. We define an appropriate logic, stemming from the tradition of topological interpretations of modal logics, dating back to earlier logicians such as Tarski, where modalities describe neighbourhood. We lift the topological definitions to the more general setting of closure spaces, also encompassing discrete, graph-based structures. We extend the framework with a spatial surrounded operator, a propagation operator and with some collective operators. The latter are interpreted over arbitrary sets of points instead of individual points in space. We define efficient model checking procedures, both for the individual and the collective spatial fragments of the logic and provide a proof-of-concept tool.
URL: http://https://lmcs.episciences.org/2067
DOI: 10.2168/LMCS-12(4:2)2016
Subject Modal Logics
Spatial Logics
Spatial Logics Model-checking
Topological Spaces
Closure Spaces
Collective Adaptive Systems
D.2.4 SOFTWARE ENGINEERING. Software/Program Verification
03B45 Modal logic
68Q60 Specification and verification
54A05 Topological spaces and generalizations

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