Model Checking Dynamic-Epistemic Spatial Logic

In this paper we focus on Dynamic Spatial Logic, the extension of Hennessy-Milner logic with the parallel operator. We develop a sound complete Hilbert-style axiomatic system for it comprehending the behavior of spatial operators in relation with dynamic/temporal ones. Underpining on a new congruence we define over the class of processes - the structural bisimulation - we prove the finite model property for this logic that provides the decidability for satisfiability, validity and model checking against process semantics. Eventualy we propose algorithms for validity, satisfiability and model checking

Graphical Verification of a Spatial Logic for the Graphical Verification of a Spatial Logic for the pi-calculus

The paper introduces a novel approach to the verification of spatial properties for finite [pi]-calculus specifications. The mechanism is based on a recently proposed graphical encoding for mobile calculi: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Spatial properties for reasoning about the behavior and the structure of pi-calculus processes are then expressed in a logic introduced by Caires, and they are verified on the graphical encoding of a process, rather than on its textual representation. More precisely, the graphical presentation allows for providing a simple and easy to implement verification algorithm based on the graphical encoding (returning true if and only if a given process verifies a given spatial formula)

Graphical Encoding of a Spatial Logic for the pi-Calculus

This paper extends our graph-based approach to the verification of spatial properties of π-calculus specifications. The mechanism is based on an encoding for mobile calculi where each process is mapped into a graph (with interfaces) such that the denotation is fully abstract with respect to the usual structural congruence, i.e., two processes are equivalent exactly when the corresponding encodings yield isomorphic graphs. Behavioral and structural properties of π-calculus processes expressed in a spatial logic can then be verified on the graphical encoding of a process rather than on its textual representation. In this paper we introduce a modal logic for graphs and define a translation of spatial formulae such that a process verifies a spatial formula exactly when its graphical representation verifies the translated modal graph formula

A Spatial-Epistemic Logic for Reasoning about Security Protocols

Reasoning about security properties involves reasoning about where the information of a system is located, and how it evolves over time. While most security analysis techniques need to cope with some notions of information locality and knowledge propagation, usually they do not provide a general language for expressing arbitrary properties involving local knowledge and knowledge transfer. Building on this observation, we introduce a framework for security protocol analysis based on dynamic spatial logic specifications. Our computational model is a variant of existing pi-calculi, while specifications are expressed in a dynamic spatial logic extended with an epistemic operator. We present the syntax and semantics of the model and logic, and discuss the expressiveness of the approach, showing it complete for passive attackers. We also prove that generic Dolev-Yao attackers may be mechanically determined for any deterministic finite protocol, and discuss how this result may be used to reason about security properties of open systems. We also present a model-checking algorithm for our logic, which has been implemented as an extension to the SLMC system.Comment: In Proceedings SecCo 2010, arXiv:1102.516

The spatial logic of fear

Peripersonal space (PPS) refers to the space surrounding the body. PPS is characterised by distinctive patterns of multisensory integration and sensory-motor interaction. In addition, facial expressions have been shown to modulate PPS representation. In this study we tested whether fearful faces lead to a different distribution of spatial attention, compared to neutral and joyful faces. Participants responded to tactile stimuli on the cheeks, while watching looming neutral, joyful (Experiment 1) or fearful (Experiment 2) faces of an avatar, appearing in far or near space. To probe spatial attention, when the tactile stimulus was delivered, a static ball briefly appeared central or peripheral in participant's vision, respectively ≈1° or ≈10° to the left or right of the face. With neutral and joyful faces, simple reactions to tactile stimuli were facilitated in near rather than in far space, replicating classic PPS effects, and in the presence of central rather than peripheral ball, suggesting that attention may be focused in the immediate surrounding of the face. However, when the face was fearful, response to tactile stimuli was modulated not only by the distance of the face from the participant, but also by the position of the ball. Specifically, in near space only, response to tactile stimuli was additionally facilitated by the peripheral compared to the central ball. These results suggest that as fearful faces come closer to the body, they promote a redirection of attention towards the periphery. Given the sensory-motor functions of PPS, this fear-evoked redirection of attention would enhance the defensive function of PPS specifically when it is most needed, i.e. when the source of threat is nearby, but its location has not yet been identified

A SPATIAL LOGIC FOR SIMPLICIAL MODELS

Collective Adaptive Systems often consist of many heterogeneous components typically organised in groups. These entities interact with each other by adapting their behaviour to pursue individual or collective goals. In these systems, the distribution of these entities determines a space that can be either physical or logical. The former is defined in terms of a physical relation among components. The latter depends on logical relations, such as being part of the same group. In this context, specification and verification of spatial properties play a fundamental role in supporting the design of systems and predicting their behaviour. For this reason, different tools and techniques have been proposed to specify and verify the properties of space, mainly described as graphs. Therefore, the approaches generally use model spatial relations to describe a form of proximity among pairs of entities. Unfortunately, these graph-based models do not permit considering relations among more than two entities that may arise when one is interested in describing aspects of space by involving interactions among groups of entities. In this work, we propose a spatial logic interpreted on simplicial complexes. These are topological objects, able to represent surfaces and volumes efficiently that generalise graphs with higher-order edges. We discuss how the satisfaction of logical formulas can be verified by a correct and complete model checking algorithm, which is linear to the dimension of the simplicial complex and logical formula. The expressiveness of the proposed logic is studied in terms of the spatial variants of classical bisimulation and branching bisimulation relations defined over simplicial complexes

Challenging the imperial mode of living by challenging ELSEWHERE: spatial narratives and justice

This article frames imperial lifestyles as a problem of global justice and discusses the spatial logic that engenders the actual discrepancy between this moral standard of equal rights and reality. It claims that the notion of ELSEWHERE, as Brand and Wissen (2022) put it, plays a central role in understanding the conditions that allow this grossly unjust global separation between responsibility and effect to be stable. In doing this, it establishes the concept of communities of justice that determine the boundaries of moral responsibility and analyses the global spatial logic that underlies the course of these boundaries, as they are experienced in everyday life. The Westphalian system of sovereign nation states is its main component but certainly not the only one. Finally, it sheds light on current attempts to challenge this spatial logic as well as their potentials and limitations

Checking for choreography conformance using spatial logic model-checking

We illustrate with a simple example how the Spatial Logic Model Checker can be used to check choreography conformance propertie

A Spatial Logic for a Simplicial Complex Model

Collective Adaptive Systems often consist of many heterogeneous components typically organised in groups. These entities interact with each other by adapting their behaviour to pursue individual or collective goals. In these systems, the distribution of these entities determines a space that can be either physical or logical. The former is defined in terms of a physical relation among components. The latter depends on logical relations, such as being part of the same group. In this context, specification and verification of spatial properties play a fundamental role to support the design of a system and predict its behaviour. For this reasons, different tools and techniques have been proposed to specify and verify the properties of space. However, these approaches are mainly based on graphs. These are used to model spatial relations, describing a form of proximity among pairs of entities. Unfortunately, these graph-based models do not permit considering relations among more than two entities that may arise when one is interested in describing \emph{multi-dimensional} aspects of space. In this work, we propose a spatial logic interpreted on \emph{simplicial complexes}. These are topological objects able to represent surfaces and volumes efficiently that generalise graphs with higher-order edges. We discuss how the satisfaction of logical formulas can be verified by a correct and complete model checking algorithm, which is linear to the dimension of the simplicial complex and logical formula. The expressiveness of the proposed logic is studied in terms of the spatial variants of classical \emph{bisimulation} and \emph{branching bisimulation} relations defined over simplicial complexes