Elimination rules are logical rules used in proof systems that allow for the removal of a specific logical operator from a formula, enabling the conclusion to be derived from premises containing that operator. These rules are crucial in both natural deduction and sequent calculus, as they help define how one can infer new statements from existing ones by breaking down complex expressions into simpler components. The concept also ties into proof-theoretic semantics, emphasizing how the meaning of logical constructs can be understood through their usage in proofs.
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