(译)为什么要学习人工语言——一阶逻辑

译自《LANGUAGE, PROOF AND LOGIC》

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Why learn an artificial language?

This language of frst-order logic is very important. Like Latin, the language is not spoken, but unlike Latin, it is used every day by mathematicians, philosophers, computer scientists, linguists, and practitioners of artificial intelligence. Indeed, in some ways it is the universal language, the lingua franca,of the symbolic sciences. Although it is not so frequently used in other forms of rational inquiry, like medicine and fnance, it is also a valuable tool for understanding the principles of rationality underlying these disciplines as well.

一阶逻辑语言是非常重要的。它像拉丁语一样不是用来口头交流的；它不像拉丁语在于它被数学家、哲学家、计算机科学家、语言学家和人工智能的实践者每天使用着。事实上，从某些方面上看，一阶逻辑语言是符号科学的一种通用语言。尽管一阶逻辑不常作为一种理性质询（rational inquiry）工具用于很多学科（像医学、经济学），但一阶逻辑对于理解这些学科的原理及知识应是一个很有价值的工具。

The language goes by various names: the lower predicate calculus, the functional calculus, the language of first-order logic, and fol.The last of these is pronounced ef-oh-el,not fall,and is the name we will use.

一阶逻辑这种人造语言有很多别名：谓词演算、函数演算、一阶逻辑语言和FOL。我们这里使用FOL。

Certain elements of fol go back to Aristotle, but the language as we know it today has emerged over the past hundred years. The names chiefly associated with its development are those of Gottlob Frege, Giuseppe Peano, and Charles Sanders Peirce. In the late nineteenth century, these three logicians independently came up with the most important elements of the language, known as the quantifers. Since then, there has been a process of standardization and simplifcation, resulting in the language in its present form. Even so, there remain certain dialects of fol,differing mainly in the choice of the particular symbols used to express the basic notions of the language. We will use the dialect most common in mathematics, though we will also tell you about several other dialects along the way.

一阶逻辑语言的历史可以追溯回亚里士多德，不过我们今天所学的一阶逻辑语言是近几百年才出现的。创始人和完善者包括弗雷格、皮亚诺和Peirce。在19世纪末，这三位逻辑学家分别提出了一阶逻辑语言的一个重要元素--量词。一阶逻辑语言在发展过程中派生了相当的方言。各种方言的不同在于选择不同的符号来表达语言的基本概念。

Fol is used in different ways in different fields. In mathematics, it is used in an informal way quite extensively. The various connectives and quantifers find their way into a great deal of mathematical discourse, both formal and informal, as in a classroom setting. Here you will often find elements of fol interspersed with English or the mathematician’s native language. If you've ever taken calculus you have probably seen such formulas as: ∀∈> 0 ∃δ> 0 ... Here, the unusual, rotated letters are taken directly from the language fol.

FOL在不同的领域被以不同的方式使用着。在数学领域，FOL被以非形式化方式广泛地使用着。它的各种联接词和量词被大量的用在数学课堂，形式与非形式的方式都有。一阶逻辑语言的符号往往夹杂着英文和数学其它符号一起使用。

logic and philosophy

In philosophy, fol and enrichments of it are used in two different ways. As in mathematics, the notation of fol is used when absolute clarity, rigor, and lack of ambiguity are essential. But it is also used as a case study of making informal notions (like grammaticality, meaning, truth, and proof) precise and rigorous. The applications in linguistics stem from this use, since linguistics is concerned, in large part, with understanding some of these same informal notions.

从哲学方面看，FOL以及它的丰富的内容被以两种不同的方式使用着。首先，在数学中，FOL用于当概念的清晰性、严格性和和无歧义性变得很重要时。其次，FOL也用于将一些非形式的观念（像‘符合语法规则’、‘意义’、‘真理’和‘证明’）精确化和严格化。

logic and artificial intelligence

In artificial intelligence, fol is also used in two ways. Some researchers take advantage of the simple structure of fol sentences to use it as a way to encode knowledge to be stored and used by a computer. Thinking is modeled by manipulations involving sentences of fol.The other use is as a precise specification language for stating axioms and proving results about artificial agents.

人工智能方面，FOL也有两种使用方式。一部分研究者看出FOL语句结构的简单性的优点，因此用它来为知识编码并存入计算机，给计算机使用。思维的机制也是用对这些语句的处理来模拟和建模。其次，FOL被用作一种标准的语言，用来表达有关人工代理机的公理和证明结果。

logic and computer science

In computer science, fol has had an even more profound influence. The very idea of an artificial language that is precise yet rich enough to program computers was inspired by this language. In addition, all extant programming languages borrow some notions from one or another dialect of fol.Finally, there are so-called logic programming languages, like Prolog, whose programs are sequences of sentences in a certain dialect of fol. We will discuss the logical basis of Prolog a bit in Part III of this book.

在计算机科学，FOL则有着更深刻的影响了。编制计算机需要一种足够精确和丰富的人工语言的思想正是从FOL获得灵感的。此外，现存的所有编程语言都从FOL的方言借用了相当的概念。不仅如此，还有所谓的逻辑编程语言，像Prolog，它的程序就是一种FOL方言的语句序列。

artificial languages

Fol serves as the prototypical example of what is known as an artificial language. These are languages that were designed for special purposes, and are contrasted with so-called natural languages, languages like English and Greek that people actually speak. The design of artificial languages within the symbolic sciences is an important activity, one that is based on the success of fol and its descendants.

FOL作为一种原型的例子，说明了什么叫人工语言。现在已经有很多的为特殊用途而设计的语言了。这些语言与我们日常使用的自然语言是相对的。

Even if you are not going to pursue logic or any of the symbolic sciences, the study of fol can be of real benefit. That is why it is so widely taught. For one thing, learning fol is an easy way to demystify a lot of formal work. It will also teach you a great deal about your own language, and the laws of logic it supports. First, fol,while very simple, incorporates in a clean way some of the logic and ordinary language important features of human languages. This helps make these features much more transparent. Chief among these is the relationship between language and the world.

尽管你以后不从事逻辑或任何的符号科学工作，研究一下FOL仍然是很有益处的。从FOL在广泛地被讲授就可以看出这一点。一方面，学习FOL是揭秘大量形式活动原理（KEMIN:formal work可能是指我们日常常用到的画图、用符号等非自然语言表达的活动？）的一种简单方法。另一方面，学习FOL能教你更多的有关的母语的知识，包括它的逻辑规律。第一，FOL混合了人类语言的一些逻辑和初始语言的重要特征。这样有助于这些特性更具透明性（KEMIN:什么特性？请补充！）。其中最主要的就是语言与世界之间的关系。

But, second, as you learn to translate English sentences into fol you will also gain an appreciation of the great subtlety that resides in English, subtlety that cannot be captured in fol or similar languages, at least not yet. Finally, you will gain an awareness of the enormous ambiguity present in almost every English sentence, ambiguity which somehow does not prevent us from understanding each other in most situations

第二，当你学习把英语句子翻译成FOL时，你将还认识出英语里存在大量的细微的差别，这些细微的差别还不能被FOL所表达，至少目前还不能。最后，你将体会到几乎在每一句英语句子中存在歧义的内容，这些歧义在大多数的情况并不影响我们互相交流。