MLL proof nets as error-correcting codes

Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. 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 introduce a metric space for each family. In each family, 1. an MLL proof net is a real code 2. a proof structure that is not an MLL proof net is a false code. In this paper we show that in the framework one error-detecting is possible but one error-correcting not. Moreover, we show that affile logic and MLL + MIX are not appropriate for this framework. That explains why MLL is better than such similar logics.