Chapter (in Edited Book) ()
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.
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.
Introduction rules; Elimination rules; General elimination rules; Inversion principle; Sequent calculus
|Title of series||Outstanding Contributions to Logic|
|Number in series||7|
|Place of publication||Cham, Heidelberg, New York, Dordrecht, London|
|ISSN of series||2211-2758|