The Brouwer-Heyting-Kolmogorov (BHK) interpretation of intuitionistic logic — a proposition is true if and only if there is a proof of it; the meaning of each logical connective is defined in terms of what counts as a proof.
A conjunction A∧B is proved by providing a proof of A and a proof of B. A disjunction A∨B is proved by providing a proof of A or a proof of B (and saying which). An implication A→B is proved by providing a construction that transforms any proof of A into a proof of B. This proof-theoretic semantics grounds the entire constructive mathematical tradition.
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