In this first installment of a two-part series, the V-nets are presented, an innovative formal model of artificial intelligence (AI) for managing and diagnosing complex discrete event systems, with a particular emphasis on industrial applications. V-nets offer a groundbreaking approach to addressing the challenges inherent in system diagnosis, such as simultaneous events, false positives, and partial recognition of event sequences. This paper lays the theoretical foundation for V-nets by providing a detailed formal definition and exploring key properties that establish their effectiveness. It is demonstrated how V-nets when integrated with automata, enhance the supervision and analysis of control actions. A case study in an industrial setting showcases the practical utility of V-nets in diagnosing and analyzing complex systems, highlighting their potential as a robust tool for managing discrete events.