Graphs of Plural Cuts

Details Graphs of Plural Cuts Graphs of Plural Cuts

2011-04-20

arxiv.org/abs/1104.4064v6

Mathematics

Logic

26 pages, references updated

Scientific paper

Plural (or multiple-conclusion) cuts are inferences made by applying a structural rule introduced by Gentzen for his sequent formulation of classical logic. As singular (single-conclusion) cuts yield trees, which underlie ordinary natural deduction derivations, so plural cuts yield graphs of a more complicated kind, related to trees, which this paper defines. Besides the inductive definition of these oriented graphs, which is based on sequent systems, a non-inductive, graph-theoretical, combinatorial, definition is given, and to reach that other definition is the main goal of the paper. As trees underlie multicategories, so the graphs of plural cuts underlie polycategories. The graphs of plural cuts are interesting in particular when the plural cuts are appropriate for sequent systems without the structural rule of permutation, and the main body of the paper deals with that matter. It gives a combinatorial characterization of the planarity of the graphs involved.

Affiliated with

Also associated with

No associations

Rating

Graphs of Plural Cuts 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 Graphs of Plural Cuts, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Graphs of Plural Cuts will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-433313