(Ω, Ξ)-Logic: On the Algebraic Extension of Coalgebraic Specifications

We present an extension of standard coalgebraic specification techniques for statebased systems which allows us to integrate constants and n-ary operations in a smooth way and, moreover, leads to a simplification of the coalgebraic structure of the models of a specification. The framework of (Ω,Ξ)-logic can be considered as the result of a translation of concepts of observational logic (cf. [9]) into the coalgebraic world. As a particular outcome we obtain the notion of an (Ω, Ξ)- structure and a sound and complete proof system for (first-order) observational properties of specifications

Swarm Coordination for Pursuit Evasion Games Using Sensor Networks

Abstract — In this work we consider the problem of pursuit evasion games (PEGs) where a group of pursuers is required to detect, chase and capture a group of evaders with the aid of a sensor network in minimum time. Differently from standards PEGs where the environment and the location of evaders is unknown and a probabilistic map is built based on the pursuer onboard sensors, here we consider a scenario where a sensor network, previously deployed in the region of concern, can detect the presence of moving vehicles and can relay this information to the pursuers. Here we propose a general framework for the design of a hierarchical control architecture that exploit the advantages of a sensor networks by combining both centralized and decentralized real-time control algorithms. We also propose a coordination scheme for the pursuers to minimize the time-to-capture of all evaders. In particular, we focus on PEGs with sensor networks orbiting in space for artificial space debris detection and removal. Index Terms — Sensor networks, pursuit evasion games, vehicle coordination, space vehicles, space debris over the area of interest. This constraint makes designing a cooperative pursuit algorithm harder because lack of complete observability only allows for suboptimal pursuit policies. See Figure 1(left). Furthermore, a smart evaders makes the map-building process dynamic since their location changes over time. The map-learning phase is, by itself, time-consuming and computationally intensive even for simple two-dimensional rectilinear environments [5]. Moreover, inaccurate sensors complicate this process and a probabilistic approach is often required [21]. I

Definability, Canonical Models, and Compactness for Finitary Coalgebraic Modal Logic

This paper studies coalgebras from the perspective of the finitary observations that can be made of their behaviours. Based on the terminal sequence, notions of finitary behaviours and finitary predicates are introduced. A category Behω(T) of coalgebras with morphisms preserving finitary behaviours is defined. We then investigate definability and compactness for finitary coalgebraic modal logic, show that the final object in Behω(T) generalises the notion of a canonical model in modal logic, and study the topology induced on a coalgebra by the finitary part of the terminal sequence

Coalgebraische Similarität

Bereits bekannt erhält jeder Funktor genau dann schwache Pullbacks, wenn jede Kongruenz eine difunktionale Bisimulation ist. In Kapitel 3 fanden wir äquivalente Aussagen für die schwache Kerpaarerhaltung und die Urbilderhaltung. Ausserdem definierten wir eine Funktorabänderung, die wir Urbildbereinigung nannten. Der resultierende Funktor erhält Urbilder. Die Idee war inspiriert von der Transformation, so dass daraus ein gesunder Funktor entsteht. Der Urbilder erhaltende Funktor hat auch den Vorteil, dass seine Unterfunktoren genau die Urbilder erhaltende Unterfunktoren des ursprünglichen Funktors sind. In Kapitel 4 zeigten wir, dass die monotonen trennbaren Boxen eine korrekte und vollständige Modallogik liefern. Interessant ist, dass die Urbild-Bereinigung des allgemeinen Nachbarschaftsfunktors einen Funktor liefert, der schwache Pullbacks erhält