Correspondences between Classical, Intuitionistic and Uniform Provability

Details Correspondences between Classical, Intuitionistic and Uniform Provability Correspondences between Classical, Intuitionistic and Uniform Provability

1998-09-10

arxiv.org/abs/cs/9809015v1

Computer Science

Logic in Computer Science

31 pages

Scientific paper

Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform provability, a restriction of intuitionistic provability that embodies a special form of goal-directedness. We determine, first, the circumstances in which the former relations imply the latter. Using this result, we identify the richest versions of the so-called abstract logic programming languages in classical and intuitionistic logic. We then study the reduction of classical and, derivatively, intuitionistic provability to uniform provability via the addition to the assumption set of the negation of the formula to be proved. Our focus here is on understanding the situations in which this reduction is achieved. However, our discussions indicate the structure of a proof procedure based on the reduction, a matter also considered explicitly elsewhere.

Affiliated with

Also associated with

No associations

Rating

Correspondences between Classical, Intuitionistic and Uniform Provability does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Correspondences between Classical, Intuitionistic and Uniform Provability, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Correspondences between Classical, Intuitionistic and Uniform Provability will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-230155