In natural systems, many species are able to coordinate their individual intelligences to perform complex tasks. Swarm Intelligence also denotes the concept of distributed intelligence which relies on the coordination between a massive number of individual intelligences. In this paper, we develop a logical approach to consider distributed intelligence. Our proposal is based on a pedestrian safety issue. So, we extend the bases of a distributed non-monotonic theory to model the “vehicle-pedestrian” interaction system. This extension concerns the preliminary approach proposed in our previous work. Non-monotonic reasoning processes for distributed intelligent logic agents strongly contribute to the development of Pedestrian Collision Warning Systems. These systems benefit greatly from the efficiency of pedestrian detection which has reached a high level thanks to several technologies. We demonstrate the validity of our construction and we specify the knowledge representation of driver-pedestrian interaction in the context of the proposed theory.