Improving legibility of natural deduction proofs is not trivial

In formal proof checking environments such as Mizar it is not merely thevalidity of mathematical formulas that is evaluated in the process of adoptionto the body of accepted formalizations, but also the readability of the proofsthat witness validity. As in case of computer programs, such proof scripts maysometimes be more and sometimes be less readable. To better understand thenotion of readability of formal proofs, and to assess and improve theirreadability, we propose in this paper a method of improving proof readabilitybased on Behaghel's First Law of sentence structure. Our method maximizes thenumber of local references to the directly preceding statement in a prooflinearisation. It is shown that our optimization method is NP-complete.Comment: 33 page