In this paper the notion of urban infrastructure resilience is formulated being expressed verbally and strictly in conditional probability terms. It is further used to formulate several most important features of a smart city. This multidisciplinary and multifaceted approach is used to explain the concept of quantitative resilience in urban design, operation, managing urban risk and mitigating of the consequences of a natural or industrial disaster. The extremely urgent problem is formulated on how to connect the physical and spatial (core) resiliencies with the functional, organizational, economic and social resiliencies.