A Decidable Fragment of Predicate Calculus

Abstract We describe a decision procedure for what we call direct predicate calculus . This fragment of predicate logic coincides with those formulas that can be proved in the Gentzen sequent calculus with the rule of contraction eliminated. It arose by thinking about what kinds of inferences should be considered ‘obvious’ and in that sense characterizes fragments of logic by the tools available for proving results rather than by syntactic properties of formulas.