Abstract

We have here a systematic examination of systems of logic cast in "natural deduction" form, in the widest sense of that word. Naturally enough, the author begins with Gentzen-style systems, moves by means of the inversion principle in int-elim logics to deductions of classical and intuitionistic logic which have a canonical "normal form"; more briefly, but always with clarity, Prawitz examines natural deduction for second-order and modal logics, and also systems with even less usual forms of implication. Three appendices cover the Sequenzen-kalkül of Gentzen, a system of set theory of Fitch, and some alternative formulations of natural deductions due to Jáskowski and others. There is a short bibliography. There are also some hilarious misprints, few serious.—P. J. M.