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2.3.1: Introduction
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The purpose of derivation systems is to provide a purely syntactic method of establishing entailment and validity.
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2.3.2: The Sequent Calculus
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While many derivation systems operate with arrangements of sentences, the sequent calculus operates with sequents.
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2.3.3: Natural Deduction
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Natural deduction is a derivation system intended to mirror actual reasoning (especially the kind of regimented reasoning employed by mathematicians).
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2.3.4: Tableaux
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While many derivation systems operate with arrangements of sentences, tableaux operate with signed formulas.
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2.3.5: Axiomatic Derivations
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Axiomatic derivations are the oldest and simplest logical derivation systems. Its derivations are simply sequences of sentences.