Holger Giese, Maria Maximova, Lucas Sakizloglou, Sven Schneider

Metric Temporal Graph Logic over Typed Attributed Graphs

ISBN: 978-3-86956-433-3
29 pages, Monographie
Release year 2018

Series: Technische Berichte des Hasso-Plattner-Instituts für Softwaresystemtechnik an der Universität Potsdam , 123

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Various kinds of typed attributed graphs are used to represent states of systems from a broad range of domains. For dynamic systems, established formalisms such as graph transformations provide a formal model for defining state sequences. We consider the extended case where time elapses between states and introduce a logic to reason about these sequences. With this logic we express properties on the structure and attributes of states as well as on the temporal occurrence of states that are related by their inner structure, which no formal logic over graphs accomplishes concisely so far. Firstly, we introduce graphs with history by equipping every graph element with the timestamp of its creation and, if applicable, its deletion. Secondly, we define a logic on graphs by integrating the temporal operator until into the well-established logic of nested graph conditions. Thirdly, we prove that our logic is equally expressive to nested graph conditions by providing a suitable reduction. Finally, the implementation of this reduction allows for the tool-based analysis of metric temporal properties for state sequences.

Various kinds of typed attributed graphs are used to represent states of systems from a broad range of domains. For dynamic systems, established formalisms such as graph transformations provide a formal model for defining state sequences. We consider the extended case where time elapses between states and introduce a logic to reason about these sequences. With this logic we express properties on the structure and attributes of states as well as on the temporal occurrence of states that are related by their inner structure, which no formal logic over graphs accomplishes concisely so far. Firstly, we introduce graphs with history by equipping every graph element with the timestamp of its creation and, if applicable, its deletion. Secondly, we define a logic on graphs by integrating the temporal operator until into the well-established logic of nested graph conditions. Thirdly, we prove that our logic is equally expressive to nested graph conditions by providing a suitable reduction. Finally, the implementation of this reduction allows for the tool-based analysis of metric temporal properties for state sequences.