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An innovative approach to the semantics of logic, proof-theoretic semantics seeks the meaning of propositions and logical connectives within a system of inference. Gerhard Gentzen invented proof-theoretic semantics, and Dag Prawitz, the author of this study, extended its analytic proofs to systems of natural deduction. Prawitz's theories form the basis of intuitionistic type theory, and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics. The proof-theoretical system represents a simpler and more illuminating method than alternative approaches, and this volume offers a succinct, coherent illustration of its applications to natural deduction.