Logic in Reality argues that the fundamental physical structure of the world is logical as well as mathematical. The applicable formal logic of and in reality proposed (LIR) represents a radical departure from the standard notion of logic and its function. The book establishes LIR as a non-propositional logic with a unique calculus, one however that can be used intuitively with minimum symbolism. A new relational ontology is developed that demonstrates the fit of the LIR axioms with modern physics. The axioms and ontology of LIR together constitute a framework for describing and explaining complex real world processes, entities and events. Examples from the literature of on-going issues in philosophy, metaphysics and ontology are analyzed accordingly, including problems of causality, time and space, emergence and evolution. – This book is at the interface of logic, philosophy and science. It is intended for readers with interest and/or current involvement in process philosophy, ontology and in the philosophy or metaphysical aspects of science, especially, quantum physics, biology and cosmology. – The critical extension in LIR of categorial non-separability to macroscopic interactive processes defines dynamic structural principles that underlie both scientific theories and their domains. LIR thus provides logical support for current metaphysical versions of structural realism. The author encourages readers to exercise a "new skepticism", since LIR is a way to interpret and accept dichotomies and contradictory explanations and to manage inconsistency in both philosophy and science. – Acknowledgements. - Foreword; Lorenzo Magnani. - Introduction. - 1. Logic in Reality (LIR) as a Formal Logic. - 2. LIR as a Formal System. - 3. LIR as a Formal Ontology. - 4. The Categories of LIR. - 5. The Core Thesis of LIR: Structure and Explanation. - 6. LIR, Metaphysics and Philosophy. - 7. LIR and Physical Science: Time, Space and Cosmology. - 8. Emergence, Living Systems and Closure. - Conclusion : New Directions and a New Skepticism. M.-M. V.