A Logic Language for Run Time Assessment of Spatial Properties in Self-Organizing Systems

Abstract

Abstract-The assessment of emergent global behaviors of self-organizing applications is an important task to accomplish before employing such systems in real scenarios, yet their intrinsic complexity make this activity still challenging. In this paper we present a logic language used to verify graph-based global properties of self-organizing systems at run-time. The logic language extends a chemical-based coordination model based on logic inference recently proposed. The logic formulae defined by using the language operators depict the intended global spatial properties arising from local interactions among components. Logic formulae are evaluated in a distributed manner by using an inference procedure which checks them against the current global state of the system, verifying whether the intended emergent global behavior actually appears in the system. As examples of spatial properties we consider color patterns: at first we show how to verify specified patterns of identified colors in sets of nodes directly connected, then we present other formulae verifying the appearance of global patterns of colors without specifying the colors themselves. We conclude the examples with the computation of mathematical functions, like the verification of the existence of a maximum value in a specific node of the system.

Spatial Edge Services - From Coordination Model to Actual Applications

“…Our model is defined independently of any specific logic, an actual instantiation and implementation of the model can use its own logic(s). We also defined a spatial language to verify graph-based spatial properties of self-organising systems [6], a multi-valued logic [7] and an approximate reasoning [13]. The language encapsulates Logic Fragments in statements that are evaluated in a distributed manner at run-time, involving several system entities at the same time.…”

“…-By resorting to logic programming, interactions among components are driven by logic inference and system components can be considered as units performing formal reasoning processes on the distributed state of the system. By resorting to this feature, components can be exploited to evaluate distributed system properties at run-time [11].…”

A Mechanism for Recognizing and Suppressing the Emergent Behavior of UAV Swarm

“…It needs to be emphasized that there is no uniform computation method to measure emergence at present, and it is necessary to make specific analysis on different complex systems. At the same time, some input 2 Mathematical Problems in Engineering variables in certain computation methods can be the individual property parameters in other complex systems, such as in the measurement of emergence of complex systems, Angelis, Birdsey, and Szabo et al [6][7][8], respectively, put forward a logical operator and Hausdorff distance, the degree of interactivity, and other specific metric variables; these variables should be calculated with the knowledge of the interaction radius between individuals within the system. Through the following analysis and discussion, we can see that these methods do not apply to the specific application environment studied in this article.…”

A Spatial Logic for Simplicial Models

“…Logics for graphs have been studied in the context of databases and process calculi such as[CGG02,GL07], and for collective adaptive systems[DAS15]. In[Gal99,Gal03,Gal14], digital images are studied by using models inspired by topological spaces without any generalising and specialising these structures, while[RLG12] presents discrete mereotopology, i.e., a first-ordered spatial logic that fuses together the theory of parthood relations and topology to model discrete in image-processing applications.…”