Abstract
This chapter establishes the logic of and in reality (LIR) as a formal logic, whose axioms are given first in standard form. An initial discussion of reality and levels of reality is provided as the basis for the extension of logic to real entities, phenomena and processes. A semantics for LIR is proposed and then compared with the logical concepts and processes underlying classical bivalent logic. Comparisons are also made with many of the major kinds of classical and non-classical logics, including fuzzy and modal logics, in order to bring out the critical differences that a departure from logic as a linguistic system entails. The closer relation of LIR to inductive, abductive logics and quantum logics and probability is suggested, and the LIR axioms are restated in formal probabilistic terms.