Formal and formal language

Formal在computer science中有着非常重要的地位，计算机科学家门围绕着它创建了很多理论。

Formal

所以我们需要首先搞清楚它的含义。下面我们先通过一些例子来认识formal，然后再来进行总结。

Examples of formal

example 1

Deep Learning的Chapter 1 Introduction的如下描述：

In the early days of artificial intelligence, the field rapidly tackled and solved problems that are intellectually difficult for human beings but relatively straightforward for computers—problems that can be described by a list of formal, mathematical rules. The true challenge to artificial intelligence proved to be solving the tasks that are easy for people to perform but hard for people to describe formally—problems that we solve intuitively, that feel automatic, like recognizing spoken words or faces in images.

可以使用“formal， mathematical rules“描述的问题，具备着固定的rule，所以使用computer program是非常任意实现的。而与它相反的一类问题，是无法使用rule进行描述的，这类问题，在上面这段话中使用”intuitive“来表示，解决这类问题的方法是AI。

example 2

Deep Learning的Chapter 5.1 Learning Algorithms的如下描述：

“A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P , if its performance at tasks in T , as measured by P , improves with experience E .” One can imagine a very wide variety of experiences E , tasks T , and performance measures P , and we do not make any attempt in this book to provide a formal definition of what may be used for each of these entities. Instead, the following sections provide intuitive descriptions and examples of the different kinds of tasks, performance measures and experiences that can be used to construct machine learning algorithms.

formal language-》 formal definition

natural language-》intuitive description

examples

Examples of formal description

https://dictionary.cambridge.org/example/english/formal-description

In this section and the next, we turn our attention to providing a more formal description of the underlying type system.

什么是formal？

关于formal的直觉是：

• 有固定的规则

从词源说起

https://simple.wikipedia.org/wiki/Formal

Formal is a word used to describe anything that has form or structure. So it is something which is used or done in accordance with rules or ceremonies.

上面这句中的form其实就可以理解为rule。

In mathematics, formal logic is a way of thinking about mathematics questions using strict rules.

https://www.yourdictionary.com/formal

维基百科formal汇总

我们需要重点关注三个科学学科：

Linguistics、Logic and mathematics、Computer science

这三个学科中的formal是密切相关的。

Formalism

文章Formalism (philosophy), Formalism (philosophy of mathematics)将formal描述为一种科学的思想，显然它从更高的哲学的角度来概括formal，我觉得以它作为掌握formal的入口是非常好的，因为科学总数遵循相同的哲学思想，或者说哲学指导着科学。

Formal language

显然，这个词由formal来进行修饰，所以它肯定是具备前面所描述的formal的性质的：即有固定规则，就formal language而言，它的formal是源于它的grammar上，它的语法是formal grammar，这种语法的规则是固定的。所以对于这种语言，只要向computer描述清楚它的grammar，那么computer就可以“读懂”它，即这种语言是machine-readable的。

关于formal language的machine readable，可以参见：https://en.wikipedia.org/wiki/Semantic_Web

Formal definition

使用formal language来描述的definition就是formal definition。

Formal language的优势

Formal language的优势在于它的formal，即有固定的rule。在逻辑学，rule对于的是推导规则，所以formal language是可以进行推导。

思考：Formal与人工智能

deep learning book的chapter one