The definition of LIR as a formal system in this chapter is based on a calculus that defines reality values of actualization, potentialization and T-state axiomatically set out in Chapter 1 that are the LIR equivalents of truth values in standard logics. The further essential aspect is a view of logical implication as a dynamic process, that is, a formal structure that is applicable to physical reality. These operational aspects of the LIR calculus relate these values to the real process entities that are the elements of LIR as systems of systems of processes, showing the trends or tendencies of these chains of elements toward contradiction or non-contradiction. Other properties of LIR as a logic are discussed including the LIR definitions of conjunction and disjunction and a classification table for its connectives. A brief comparison is made to calculi of events and relations.