A useful theoretical lens that has emerged for understanding urban resilience is the four basic types of interdependencies in critical infrastructures: the physical, geographic, cyber, and logical types. This paper is motivated by a conceptual and methodological limitation—although logical interdependencies (where two infrastructures affect the state of each other via human decisions) are regarded as one of the basic types of interdependencies, the question of how to apply the notion and how to quantify logical relations remains under-explored. To overcome this limitation, this study focuses on institutions (rules), for example, rules and planned tasks guiding human interactions with one another and infrastructure. Such rule-mediated interactions, when linguistically expressed, have a syntactic form that can be translated into a network form.

We provide a foundation to delineate these two forms to detect logical interdependence. Specifically, we propose an approach to quantify logical interdependence based on the idea that (1) there are certain network motifs indicating logical relations, (2) such network motifs can be discerned from the network form of rules, and that (3) the higher the frequency of these motifs between two infrastructures, the greater the extent of logical interdependency. We develop a set of such motifs and illustrate their usage using an example. We conclude by suggesting a revision to the original definition of logical interdependence. This rule-focused approach is relevant to understanding human error in risk analysis of socio-technical systems, as human error can be seen as deviations from constraints that lead to accidents.