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A substructural logic for layered graphs

机译：分层图的子结构逻辑

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摘要

Complex systems, be they natural or synthetic, are ubiquitous. In particular, complex networks of devices and services underpin most of society's operations. By their very nature, such systems are difficult to conceptualize and reason about effectively. The concept of layering is widespread in complex systems, but has not been considered conceptually. Noting that graphs are a key formalism in the description of complex systems, we establish a notion of a layered graph. We provide a logical characterization of this notion of layering using a non-associative, non-commutative substructural, separating logic. We provide soundness and completeness results for a class of algebraic models that includes layered graphs, which give a mathematically substantial semantics to this very weak logic. We explain, via examples, applications in information processing and security.
机译：无论是天然的还是合成的，复杂的系统无处不在。特别是，复杂的设备和服务网络是社会大多数活动的基础。就其本质而言，这样的系统很难概念化和有效地推理。分层的概念在复杂的系统中很普遍，但从概念上尚未考虑。注意图是描述复杂系统的关键形式，我们建立了分层图的概念。我们使用非关联，非交换子结构，分离逻辑来提供这种分层概念的逻辑特征。我们为包括分层图的一类代数模型提供了稳健性和完备性结果，这些模型为这种非常弱的逻辑提供了数学上实质性的语义。我们通过示例解释信息处理和安全性中的应用程序。

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