The components of LIR that will constitute it as a formal ontology, an interpreted formal system, from which the categories of LIR will be constructed, are completed in this chapter. The three components are: (1) its axioms; (2) the "language" of LIR and its rather unusual semantics; and (3) the ontological constants and predicates which correspond to interpretations of the language. Additional sections address three concepts that are critical for the development of the LIR categories – dynamisms, processes and properties. A new definition of intrinsic and extrinsic properties is suggested. Comparison with classical logic is made in a section that reviews the metalogical properties of classical logics with those of LIR. The problem of the logical foundation of reality – being and existence – is discussed in relation to the fundamental LIR principle of dynamic opposition, and the position defended that metaphysics grounds logic and not the contrary. A brief discussion of abstract or non-spatio-temporal objects concludes the chapter.