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# The Mathematical
Linguistics of Pattern Recognition

**
András Kornai
**

Section: Language and Computation

Level: Advanced

## Description

Physicists speak of mesoscopic systems when these contain, say,
fifty atoms: too large to be given a microscopic quantum-mechanical
description but too small for the classical macroscopic properties to
dominate the behavior of the system. Linguistic systems are mesoscopic
in the same broad sense: they have thousands of rules and axioms,
compared to the handful of axioms and axiom schemes used in most
branches of mathematics. Statistical techniques, by their very nature,
can yield only approximations for mesoscopic systems. Deductive
techniques, though in principle easy to extend to the mesoscopic
domain, are in practice also prone to all kinds of bugs, ranging from
plain errors of fact (which are hard to avoid once we deal with
thousands of axioms) to more subtle, and often systematic, errors and
omissions. Students of logic often feel very uncomfortable with the
idea that a given system is only 70%, 95%, or even 99.99% correct:
after all, isn't a single contradiction or empirically false
prediction enough to render a theory invalid? In this course we
develop the tools needed to address this question.

## Materials

lecture notes

## Lecturer

András Kornai

Northern Light

222 3rd St., Cambridge MA 02142

Tel: (617) 621-5694

Fax: (617) 621-5695

andras@kornai.com