I ON THE PRIMITIVE TERM OF LOGISTICf IN this article I propose to establish a theorem belonging to logistic concerning some connexions, not widely known, ...

This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4–9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.

In the first part of this paper we indicate how Meredith's condensed detachment may be used to give a new proof of Belnap's theorem that if every axiom x of a calculus S has the two-property that every variable which occurs in x occurs exactly twice in x, then every theorem of S is a substitution instance of a theorem of S which has the two-property. In the remainder of the paper we discuss the use of mechanical theorem-provers, based either (...) on condensed detachment or on the resolution rule of J. A. Robinson, to investigate various calculi whose axioms all have the two-property. Particular attention is given to D-groupoids, i.e. sets of formulae which are closed under condensed detachment. (shrink)