A Decision Procedure Revisited: Notes on Direct Logic, Linear Logic and its Implementation

Bellin, G. and J. Ketonen, A decision procedure revisited: Notes on direct logic, linear logic and its implementation, Theoretical Computer Science 95 (1992) 115-142. This paper studies decidable fragments of predicate calculus. We will focus on the structure of direct predicate calculus as defined in Ketonen and Weyhrauch (1984) in the light of the recent work of Girard (Girard 1987, 1988) on linear logic. Several graph-theoretic results are used to prove correspondences between systems of natural deduction, direct predicate logic, and linear logic. In addition, the implementation of a decision procedure for direct predicate logic is sketched.