A Coding Theoretical Study on MLL proof nets
Coding theory is very useful for real world applications. A n otable example is digital television. Basically, coding theory is to study a way of detecting and/o r correcting data that may be true or false. Moreover coding theory is an area of mathematics, in which th ere is an interplay between many branches of mathematics, e.g., abstract algebra, combinatorics, di screte geometry, information theory, etc. In this paper we propose a novel approach for analyzing proof nets of Multiplicative Linear Logic (MLL) by coding theory. We define families of proof structures and int roduce a metric space for each family. In each family, 1. an MLL proof net is a true code element; 2. a proof structure that is not an MLL proof net is a false (or c orrupted) code element. The definition of our metrics reflects the duality of the multi plicative connectives elegantly. In this paper we show that in the framework one error-detecting is possibl e but one error-correcting not. Our proof of the impossibility of one error-correcting is interestin g i the sense that a proof theoretical property is proved using a graph theoretical argument. In addition, we s how that affine logic and MLL + MIX are not appropriate for this framework. That explains why MLL is bet ter than such similar logics.