In this book, Neil Tennant presents an original logical system. Core Logic is the first system that ensures both relevance and adequacy for the formalization of all scientific and constructive mathematical reasoning. It is an elegant kernel lying deep within Classical Logic, a canon for constructive and relevant deduction furnishing faithful formalizations of informal constructive mathematical proofs. It provides transitivity of deduction with potential epistemic gain. Classical Core does the same for informal non-constructive mathematical proofs. Because of its clarity about the true internal structure of proofs, Core Logic also affords advantages for the automation of deduction and our appreciation of the paradoxes. Tennant describes all the theoretically interesting aspects of Core Logic: philosophical, metamathematical, proof-theoretic, methodological, computational and revision-theoretic. Here for the first time they are all examined together in a single work.

A unified and all-encompassing treatment of Core Logic is called for because its many and various aspects have thus far been dealt with in relative isolation from each other, within different sub-specialist realms of the literature. No single work has yet drawn together all the different aspects to show how they are mutually illuminating and how they fruitfully interconnect Book jacket.