Related papers: A Spatial Logic for Simplicial Models
This paper introduces a model that identifies spatial relationships for a structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer…
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…
The interplay between process behaviour and spatial aspects of computation has become more and more relevant in Computer Science, especially in the field of collective adaptive systems, but also, more generally, when dealing with systems…
The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. As biological systems are generally not…
We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible…
Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style…
All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as…
Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
This paper presents the foundational ideas for a new way of modeling social aggregation. Traditional approaches have been using network theory, and the theory of random networks. Under that paradigm, every social agent is represented by a…
Executing complex manipulation in cluttered environments requires satisfying coupled geometric and temporal constraints. Although Spatio-Temporal Logic (SpaTiaL) offers a principled specification framework, its use in gradient-based…
Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. They have been used to reason about beliefs, lies, and group epistemic behaviour inspired by social…
In recent years, several authors have been investigating simplicial models, a model of epistemic logic based on higher-dimensional structures called simplicial complexes. In the original formulation, simplicial models were always assumed to…
Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability…
Service robots are expected to reliably make sense of complex, fast-changing environments. From a cognitive standpoint, they need the appropriate reasoning capabilities and background knowledge required to exhibit human-like Visual…
Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…
The usual semantics of multi-agent epistemic logic is based on Kripke models, defined in terms of binary relations on a set of possible worlds. Recently, there has been a growing interest in using simplicial complexes rather than graphs, as…
Simplicial complexes describe collaboration networks, protein interaction networks and brain networks and in general network structures in which the interactions can include more than two nodes. In real applications, often simplicial…
In this extended abstract a view on the role of Formal Methods in System Engineering is briefly presented. Then two examples of useful analysis techniques based on solid mathematical theories are discussed as well as the software tools…
Collective adaptive systems are an emerging class of networked computational systems, particularly suited in application domains such as smart cities, complex sensor networks, and the Internet of Things. These systems tend to feature large…