Abstract: In this talk, I will introduce natural deduction with alternatives, explaining how this framework can provide a simple well-behaved single conclusion natural deduction system for a range of logical systems, including classical logic, (classical) linear logic, relevant logic and affine logic, by varying the policy for managing discharging of assumptions and retrieval of alternatives. Along the way, the talk will touch on (1) the connection between normalisation of a natural deduction proof and cut elimination in a corresponding sequent calculus; (2) the separation between the operational rules governing the connectives and the “antecedently given context of deducibility”, to borrow a phrase from Nuel Belnap’s essay, “Tonk, Plonk and Plink” (1962); and (3) the sense in which the operational rules for a connective might be understood as providing a definition of that connective.
I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ From August 2021, I will be the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.