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Title: Inversion principles and introduction rules
Author(s): Milne, Peter
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Editor(s): Wansing, H
Citation: Milne P (2015) Inversion principles and introduction rules. In: Wansing H (ed.) Dag Prawitz on Proofs and Meaning. first ed. Outstanding Contributions to Logic, 7. Cham, Heidelberg, New York, Dordrecht, London: Springer, pp. 189-224.
Keywords: Introduction rules
Elimination rules
General elimination rules
Inversion principle
Sequent calculus
Issue Date: 2015
Date Deposited: 10-Jul-2015
Series/Report no.: Outstanding Contributions to Logic, 7
Abstract: Following Gentzen’s practice, borrowed from intuitionist logic, Prawitz takes the introduction rule(s) for a connective to show how to prove a formula with the connective dominant. He proposes an inversion principle to make more exact Gentzen’s talk of deriving elimination rules from introduction rules. Here I look at some recent work pairing Gentzen’s introduction rules with general elimination rules. After outlining a way to derive Gentzen’s own elimination rules from his introduction rules, I give a very different account of introduction rules in order to pair them with general elimination rules in such a way that elimination rules can be read off introduction rules, introduction rules can be read off elimination rules, and both sets of rules can be read off classical truth-tables. Extending to include quantifiers, we obtain a formulation of classical first-order logic with the subformula property.
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