Metamathematics for Systems Design

Ichiro Hasuo

doi:10.1007/s00354-017-0023-1

Abstract

This position paper describes the context, the goal, the strategy and the tactics of the ERATO MMSD project (2016–2022). The project aims at enhanced quality assurance measures for industry products like cars. In doing so, we follow a recent trend and exploit formal methods, a body of mathematical techniques originally developed for computer systems. However, there are fundamental gaps in application of formal methods to industry products: additional concerns in industry products such as continuous dynamics of physical components and quantitative measures such as probability, time, and cost make problems fundamentally different from those about software. Formal methods that accommodate these concerns is an active research area, which shows that it is a hard problem. There are several successful theoretical developments in this direction. They typically combine one individual technique with one specific concern, such as hybrid automata that extend automata with continuous dynamics. Our project aims to contribute to this hard problem in a unique way. In our project we will take a unique metamathematical strategy to bridging the gaps: instead of creating one technique for each concern, we want to find a meta-level theory that describes how to develop such techniques for many potential concerns in general. Through this strategy, together with our emphasis on real-world applications in industry, we expect a new prototype of applied mathematics will emerge. In this prototype, abstraction and genericity—characteristics of modern mathematics that are not often associated with application—are turned into crucial advantages in applications.

Highlights

Modern-day manufacturing undergoes one of the biggest changes ever, with computers tightly integrated in industry products
There have already been quite a few large-scale organized efforts towards formal methods applied to cyber-physical systems (CPS), and these programs have successfully brought notable research outcomes
Accumulation of small ‘‘success stories’’ will give further momentum to formal methods applied to CPS, and hopefully lead to more systematic efforts towards formal specification in CPS design

Summary

Introduction

Modern-day manufacturing undergoes one of the biggest changes ever, with computers tightly integrated in industry products. The term cyber-physical systems (CPS) refers to those systems that combine physical components with digital control by computers; modern industry products such as cars are representative of CPS. Computers in industry products pose one of the greatest challenges on manufacturing, too. As a consequence it is as hard as ever to reason about industry products, e.g. for their safety guarantee. Nowadays most cars are equipped with electronic throttle control (drive-by-wire); such systems not behaving in an expected manner can lead to severe consequences including loss of human lives. Industry products play increasingly important roles and, their safety and correct behavior is a pressing issue

Objectives

Methods

Conclusion