要是我們對『declarative 』的了解僅止於『陳述的』、『說明的』或『宣告的』，一般來說並無助於理解

Thus, executing a program means searching for a proof. In traditional (imperative) programming languages, the program is a procedural specification of how a problem needs to be solved. In contrast, a logic program concentrates on a declarative specification of what the problem is.

這一段話的內容。這是因為我們還不知道『declarative 』語詞在『邏輯編程』語境中的『意指』，將之對比於『procedural』程序的，也只能帶來模糊的印象而已。如果用昨兒的互動程式為例，

pi@raspberrypi ~ $ python3
Python 3.2.3 (default, Mar  1 2013, 11:53:50) 
[GCC 4.6.3] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> from pyDatalog import pyDatalog
>>> pyDatalog.create_terms('X單位, Y單位, Z單位, V數值, 單位轉換, 重量轉換')
>>> 單位轉換['公斤', '公克'] = 1000
>>> 單位轉換['台斤', '公克'] = 600
>>> 單位轉換['市斤', '公克'] = 500
>>> 單位轉換['英磅', '公克'] = 453.59237
>>> 單位轉換[X單位, Y單位] = 單位轉換[X單位, Z單位] * 單位轉換[Z單位, Y單位]
>>> 單位轉換[X單位, Y單位] = 1 / 單位轉換[Y單位, X單位]
>>> print(單位轉換['公斤', '台斤'] == V數值)
V數值               
------------------
1.6666666666666667
>>> print(單位轉換['英磅', '台斤'] == V數值)
V數值               
------------------
0.7559872833333334
>>> 單位轉換['台斤', '台兩'] = 16
>>> 重量轉換[V數值, X單位, Y單位] = V數值 * 單位轉換[X單位, Y單位]
>>> print(重量轉換[1, '公斤', '台兩'] == V數值)
V數值               
------------------
26.666666666666668
>>> 

，是否會令人懷疑，讀了那篇文章所說的種種，真的足以『寫作』且『詮釋』那個『程式』的嗎？假使有一人宣稱他已經仔細閱讀過那些種種，他將發現自己處於『術語叢林』，面對『理解 A 』得先『理解 B 』…… ，需要『理解 X 』，它卻又依賴於『理解 A 』。舉例講嬰兒學會母語，是那麼的天經地義，然而這個『能力』是因為『天生的』── 本能 ──？『環境的』── 學習 ── ？總在爭論中！彼此誰也不能完全說服了誰！！

雖話說如此，那些『術語』還是有『親疏遠近』，或許不該一開始就『捨近求遠』，如是我們會認為『知識表示』與『推理』

Knowledge representation and reasoning

The starting point for knowledge representation is the knowledge representation hypothesis first formalized by Brian C. Smith in 1985:^[7]

Any mechanically embodied intelligent process will be comprised of structural ingredients that a) we as external observers naturally take to represent a propositional account of the knowledge that the overall process exhibits, and b) independent of such external semantic attribution, play a formal but causal and essential role in engendering the behavior that manifests that knowledge.

和『邏輯編程』的關係較為緊密。而且能夠設想『 □□ 知識』就是『 ○○ 理論』裡，關於『 ☆☆ 世界』中的『事實』或是『定律』 。這樣我們可以揣測

單位轉換[□, ○]= ??

說的就是某個世界中的約定『事實』。更由

單位轉換[□, ○]=單位轉換[□,☆]   乘   單位轉換[☆,○]

單位轉換[□,○]=1   除以  單位轉換[○,□]

知道符合一般單位轉換運算『性質』。

當這些『具足』時，『pyDatalog』就能『自動推導』作單位轉換，而且可以『添加』新事實以及新規則。於是從『作中學』Learning by doing ，我們可以了解，這跟用一般的程式語言寫作方式不同，這時『宣告的』一詞或許就有了『操作』 Operational 上的『意義』 ，它與『程序的』一詞的『對比』，也將更為『鮮明』。至於那個程式『中文化』的目的，大概只能始於『臆想』？用著『試誤法』作初步『嘗試』，閱讀『pyDatalog』原始碼意圖『確認』。藉著對『派生三』 Python3 萬國碼的了解，做出的『待證明』假設吧！？看過《M♪o 之學習筆記本》系列文本 TPG Toy Parser Generator 的讀者，大概對此『中文表現』並不陌生，主要不過是希望程式能夠『易讀』，寫來比較精簡清楚罷了。

所以學會

《如何閱讀□○？？》

，往往是學習者在『反思學習』時，所應作的第一件事。

如果想要了解『邏輯編程』的理論旨趣，掌握『pyDatalog』語言的『符號』、『語法』以及『語意』，可以多遍的重複閱讀

《 Simply Logical
Intelligent Reasoning by Example 》

的第二章

2 Clausal logic and resolution: theoretical backgrounds

In this chapter we develop a more formal view of Logic Programming by means of a rigorous treatment of clausal logic and resolution theorem proving. Any such treatment has three parts: syntax,   semantics, and proof theory. Syntax defines the logical language we are using, i.e. the alphabet, different kinds of ‘words’, and the allowed ‘sentences’. Semantics defines, in some formal way, the meaning of words and sentences in the language. As with most logics, semantics for clausal logic is truth-functional, i.e. the meaning of a sentence is defined by specifying the conditions under which it is assigned certain truth values (in our case: true or false). Finally, proof theory specifies how we can obtain new sentences (theorems) from assumed ones (axioms) by means of pure symbol manipulation (inference rules).

Of these three, proof theory is most closely related to Logic Programming, because answering queries is in fact no different from proving theorems. In addition to proof theory, we need semantics for deciding whether the things we prove actually make sense. For instance, we need to be sure that the truth of the theorems is assured by the truth of the axioms. If our inference rules guarantee this, they are said to be sound. But this will not be enough, because sound inference rules can be actually very weak, and unable to prove anything of interest. We also need to be sure that the inference rules are powerful enough to eventually prove any possible theorem: they should be complete.

Concepts like soundness and completeness are called meta-theoretical, since they are not expressed in the logic under discussion, but rather belong to a theory about that logic (‘meta’ means above). Their significance is not merely theoretical, but extends to logic programming languages like Prolog. For example, if a logic programming language is unsound, it will give wrong answers to some queries; if it is incomplete, it will give no answer to some other queries. Ideally, a logic programming language should be sound and
complete; in practice, this will not be the case. For instance, in the next chapter we will see that Prolog is both unsound and incomplete. This has been a deliberate design choice: a sound and complete Prolog would be much less efficient. Nevertheless, any Prolog
programmer should know exactly the circumstances under which Prolog is unsound or incomplete, and avoid these circumstances in her programs.

……

，直到熟悉內容為止。在此『熟悉』並不是說『理解』，而是對『全盤』有個鳥瞰，知道有哪些『概念』彼此相關，認識一些重要的『術語』，明白某些『理論』需要先行了解，……如此才能開始敲門叩關。或許可想想『為什麼』

Prolog 故意的設計成既不『健全』 Sound 又不『完備』 Complete 的呢？？

在

《 Simply Logical
Intelligent Reasoning by Example 》

之第一部份起頭處， Peter Flach 開宗明義的講︰

Logic and Logic Programming

Logic Programming is the name of a programming paradigm which was developed in the 70s. Rather than viewing a computer program as a step-by-step description of an algorithm, the program is conceived as a logical theory, and a procedure call is viewed as a theorem of which the truth needs to be established. Thus, executing a program means searching for a proof. In traditional (imperative) programming languages, the program is a procedural specification of how a problem needs to be solved. In contrast, a logic program concentrates on a declarative specification of what the problem is. Readers familiar with imperative programming will find that Logic Programming requires quite a different way of thinking. Indeed, their knowledge of the imperative paradigm will be partly incompatible with the logic paradigm.

This is certainly true with regard to the concept of a program variable. In imperative languages, a variable is a name for a memory location which can store data of certain types. While the contents of the location may vary over time, the variable always points to the
same location. In fact, the term ‘variable’ is a bit of a misnomer here, since it refers to a value that is well-defined at every moment. In contrast, a variable in a logic program is a variable in the mathematical sense, i.e. a placeholder that can take on any value. In this respect, Logic Programming is therefore much closer to mathematical intuition than imperative programming.

Imperative programming and Logic Programming also differ with respect to the machine model they assume. A machine model is an abstraction of the computer on which programs are executed. The imperative paradigm assumes a dynamic, state-based machine model, where the state of the computer is given by the contents of its memory. The effect of a program statement is a transition from one state to another. Logic Programming does not assume such a dynamic machine model. Computer plus program represent a certain amount
of knowledge about the world, which is used to answer queries.

，指出『邏輯編程』和『 Von Neumann 程式語言』──

摘自《 CPU 機器語言的『解譯器』》︰

事實上 Von Neumann 的計算機架構，對於電腦程式語言的發展，有著極為深遠的影響，產生了現在叫做 Von Neumann 程式語言，與Von Neumann 的計算機架構，同形 isomorphism 同構︰

program variables ↔ computer storage cells
程式變數 對映  計算機的儲存單元

control statements ↔ computer test-and-jump instructions
控制陳述 對映 計算機的『測試．跳至』指令

assignment statements ↔ fetching, storing instructions
賦值陳述 對映 計算機的取得、儲存指令

expressions ↔ memory reference and arithmetic instructions.
表達式 對映 記憶體參照和算術指令

── 之『觀點』有極大的不同。通常這造成了學過一般程式語言的人『理解』上的困難。也可以說『邏輯編程』之『推導歸結』得到『證明』的想法遠離『圖靈機』的『狀態轉移』到達『接受』狀態 。反倒是比較接近『 λ運算』與『 Thue 字串改寫系統』抽象建構。讀者可以試著參考讀讀那些文章， 看看能否將『思考』方式的

Logic Programming requires quite a different way of thinking. Indeed, their knowledge of the imperative paradigm will be partly incompatible with the logic paradigm.

『不相容性』鎔鑄成整體思維之『結晶』，嫻熟用於解決各式各樣的『問題』！

也許『學習』到了一定的時候，或早或遲人們需要想想『學習方法 』，經由對自己的了解，找到『事半功倍』的有效作法。雖說人人都是獨特的，然而在『學習』上確實有很多類似的『難處』。比方說一般寫程式的思維，有所謂『從上往下』 Top-Down 以及『由底向頂』 Button-Up 思路取向不同。一者類似『歐式幾何』，從公理公設出發，逐步推演定理定律，邏輯清楚明白。然而一旦要自己去證明 □□ 定理時，有時總覺的無處下手。這是因為由『公理』通往『定理』的『推導歸結』之道路遙遠，常常看不出 ○□ 兩個『概念 』間竟然有如此的『聯繫』。另一彷彿『學會做菜』，由觀察親朋做菜開始，知道什麼菜要怎麼洗？怎麼切？用什麼方法調理？久而久之，學會了一道二道三道很多很多的菜的作法。也可以講，這樣的『學法』知道了許多『如何作』 Know-How ，很少思考『為什麼 』 Know-Why 這麼作，也很少形成一般『這一類』 Know-What 的菜，多半這樣作的『通則』。我們將要如何回答別人，自己『想都沒想過』，這菜『卻得這麼作』的『問題』？或許異地嫁娶之人，更能體會，這種『不同』就是『不同』的意思。

既然打算『勇闖』，並非『暴虎馮河』，而是『有勇有謀』，想那『新世界』的『智能機器』，難到不會『自我學習』？何不就假借此時『野人獻曝』，用著談『學習之法』來學此法！體會『遞迴』之『遞迴』也許正是『邏輯』的『原點』？？『方法』的『方法』或者恰是『智慧』之『菩提』！！

就讓我們效法『科學家』的精神，用著探索『大自然』的方法，弄明白他到底如何研究『未知』。假設已知『 pyDatalog 』 源於

‧ Datalog ，也知道一般『邏輯編程』是什麼

‧ Logic programming ，還知道關鍵句式是『霍恩子句』

‧ Horn clause

。同時據該作者講︰

pyDatalog is derived from previous work by John D. Ramsdell

，那麼在閱讀

《 Datalog User Manual 》

5 Syntax

In Datalog input, whitespace characters are ignored except when they separate adjacent tokens or when they occur in strings. Comments are also considered to be whitespace. The character ‘%’ introduces a comment, which extends to the next line break. Comments do not occur inside strings.

The characters in Datalog input are collected into tokens according to the rules that follow. There are four classes of tokens: punctuations, variables, identifiers, and strings.

The punctuation tokens are: ‘(’, ‘,’, ‘)’, ‘=’, ‘:-’, ‘.’, ‘~’, ‘?’, and ‘”’.

A variable is a sequence of Latin capital and small letters, digits, and the underscore character. A variable must begin with a Latin capital letter.

An identifier is a sequence of printing characters that does not contain any of the following characters: ‘(’, ‘,’, ‘)’, ‘=’, ‘:’, ‘.’, ‘~’, ‘?’, ‘”’, ‘%’, and space. An identifier must not begin with a Latin capital letter. Note that the characters that start punctuation are forbidden in identifiers, but the hyphen character is allowed.

A string is a sequence of characters enclosed in double quotes. Characters other than double quote, newline, and backslash can be directly included in a string. The remaining characters can be specified using escape characters, ‘\”’, ‘\n’, and ‘\\’ respectively.

Other escape characters can be used to improve the readability of the input. If a string is too long to fit conveniently on one line, all but the final line containing the string can be ended with a backslash character, and each backslash newline pair is ignored. The character escape codes from the C programming language are allowed—‘\a’, ‘\b’, ‘\f’, ‘\n’, ‘\r’, ‘\t’, ‘\v’, ‘\’’, and ‘\?’. The numeric escape codes consist of one, two, or three octal digits. Thus the ASCII character newline is ‘\012’, and zero is ‘\000’. A printed Datalog string is also a string constant in C.

5.1 Literals

A literal, is a predicate symbol followed by an optional parenthesized list of comma separated terms. A predicate symbol is either an identifier or a string. A term is either a variable or a constant. As with predicate symbols, a constant is either an identifier or a string.

The following are literals:

parent(john, douglas)
zero-arity-literal
aBcD(-0, “\n\377”)
“=”(3,3)
“”(-0-0-0,&&&,***,”\0”)

5.2 Clauses

A clause is a head literal followed by an optional body. A body is a comma separated list of literals. A clause without a body is called a fact, and a rule when it has one. The punctuation ‘:-’ separates the head of a rule from its body. A clause is safe if every variable in its head occurs in some literal in its body.

The following are safe clauses:

parent(john, douglas)
ancestor(A, B) :-
parent(A, B)
ancestor(A, B) :-
parent(A, C),
ancestor(C, B)

5.3 Programs

A Datalog reader consumes a Datalog program. A program is a sequence of zero or more statements, followed by an optional query. A statement is an assertion or a retraction. An assertion is a clause followed by a period, and it adds the clause to the database if it is safe. A retraction is a clause followed by a tilde, and it removes the clause from the database. A query is a literal followed by a question mark. The effect of reading a Datalog program is to modify the database as directed by its statements, and then to return the literal designated as the query. If no query is specified, a reader returns a literal know to have no answers.

The following is a program:

edge(a, b). edge(b, c). edge(c, d). edge(d, a).
path(X, Y) :- edge(X, Y).
path(X, Y) :- edge(X, Z), path(Z, Y).
path(X, Y)?

，同時參考

Datalog tutorial

……

，以及了解安裝方法

#
sudo pip-3.2 install pyDatalog
sudo pip-3.2 install sqlalchemy 
#

後，我們是否就已學會且能詮釋

pi@raspberrypi ~ $ python3
Python 3.2.3 (default, Mar  1 2013, 11:53:50) 
[GCC 4.6.3] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> from pyDatalog import pyDatalog
>>> pyDatalog.create_terms('X單位, Y單位, Z單位, V數值, 單位轉換, 重量轉換')
>>> 單位轉換['公斤', '公克'] = 1000
>>> 單位轉換['台斤', '公克'] = 600
>>> 單位轉換['市斤', '公克'] = 500
>>> 單位轉換['英磅', '公克'] = 453.59237
>>> 單位轉換[X單位, Y單位] = 單位轉換[X單位, Z單位] * 單位轉換[Z單位, Y單位]
>>> 單位轉換[X單位, Y單位] = 1 / 單位轉換[Y單位, X單位]
>>> print(單位轉換['公斤', '台斤'] == V數值)
V數值               
------------------
1.6666666666666667
>>> print(單位轉換['英磅', '台斤'] == V數值)
V數值               
------------------
0.7559872833333334
>>> 單位轉換['台斤', '台兩'] = 16
>>> 重量轉換[V數值, X單位, Y單位] = V數值 * 單位轉換[X單位, Y單位]
>>> print(重量轉換[1, '公斤', '台兩'] == V數值)
V數值               
------------------
26.666666666666668
>>> 

這個程式的『意指』的呢？

就讓我們從《人工智慧！！》一文中所講的『哲學爭論』︰

一九八零年希爾勒寫了一篇論文《心靈、大腦、與程式》Minds, Brains, and Programs，講到一個稱作『中文房間』Chinese room 的思想實驗︰

希爾勒認為，儘管門裡的人很能夠以假亂真，讓門外的人以為他本就是華語使用者，然而他卻是壓根不懂中文的啊！假使門裡的人是『不可能』透過英文手冊來『理解』中文的話，那麼電腦也是不可能借著程式來獲得這個『理解力』的吧！！

有 批評者這麼說︰人們都認為人是擁有智慧的，然而人的智慧卻是來自於腦細胞的物理訊息轉換作用，單一個腦細胞並不能理解字詞的意義，難道不是大量的腦細胞造 就了人 類的認知與理解能力的嗎？這跟有眾多指令組成的整體程式又能有什麼實質的差異呢？所以為什麼電腦就不可能會有『理解力』的呢？？

，展開『新世界』科技的探索。首先讀讀

，可以對於『人工智慧』的進程、主張以及批評，有個初步了解。知道此一語詞早在一九五五年，就由約翰‧麥卡錫  John McCarthy 所鑄造︰

Artificial intelligence (AI) is the intelligence exhibited by machines or software. It is also the name of the academic field of study which studies how to create computers and computer software that are capable of intelligent behavior. Major AI researchers and textbooks define this field as “the study and design of intelligent agents”,^[1] in which an intelligent agent is a system that perceives its environment and takes actions that maximize its chances of success.^[2] John McCarthy, who coined the term in 1955,^[3] defines it as “the science and engineering of making intelligent machines”.^[4]

，至今也已經有了一甲子了。這樣看來，也許人類尚未能理解如何創造科學怪人的奧秘。

那位 LISP 之父，約翰‧麥卡錫，也於二零一一年十月辭世。──

《樹莓 λ 者 Lisps》︰

一九五四年美國艾倫‧紐厄爾 Allen Newell、克里夫‧蕭 Cliff Shaw 和赫伯特‧西蒙 Herbert Alexander Simon 等人於蘭德公司與卡內基技術學院研發了資訊處理語言 IPL Information Processing Language 。它以『圖靈測試』為目標，被認為是史上第一個用於『人工智慧』── 『符號演算』系統可以衍生出智慧 ── 領域的語言，首先使用了『串列』 Link List 結構與『遞迴』，啟發了之後『Lisp』的發展。一九五八年約翰‧麥卡錫 John McCarthy ── 在一九五五年的達特矛斯會議上提出了『人工智慧』這個概念── 於麻省理工學院發明了 Lisp 這個程式語言。其中採用了 IPL 語言的特徵。一九六零年麥卡錫在《ACM 通訊》上發表了一篇名為《遞迴函式的符號表達式以及由機器運算的方式，第一部》 Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I 之論文。在這篇論文中，他展示了只要透過一些簡單的運算子以及函式的記號法，也就可以建立一個具有『圖靈完備性』的 λ 演算法語言。約翰‧麥卡錫的學生史帝芬‧羅素 Steve Russell ── 著名程式設計師與計算機科學家，曾在 PDP-1 上創造了第一個電子遊戲 Spacewar ！ ── 在閱讀完此論文後，認為 Lisp 程式語言當中的『eval 函式』可以用『機器碼』來實做。他於是在IBM 704 機器上，完成了第一個 LISP 『解譯器』 Interpreter。Lisp 的名稱來自於『串列處理器』 List Processor 之縮寫，最初拼寫為『LI SP』，是一個僅次於 Fortran 語言之歷史悠久的泛函式計算機程式語言，以『波蘭表示法』編程，擁有多種方言家族。

── 。

據聞，

「簡約派（the neats）」：邏輯，Prolog語言和專家系統

早在 1958 年，John McCarthy 就提出了名為「納諫者（Advice Taker）」的一個程序構想，將邏輯學引入了 AI 研究界。^[94] 1963年，J. Alan Robinson發現了在計算機上實現推理的簡單方法：歸結（resolution）與合一（unification）算法。然而，根據 60 年代末McCarthy 和他的學生們的工作，對這一想法的直接實現具有極高的計算複雜度：即使是證明很簡單的定理也需要天文數字的步驟。^[95] 70 年代 Robert Kowalsky 在Edinburgh大學的工作則更具成效：法國學者 Alain Colmerauer 和 Phillipe Roussel 在他的合作下開發出成功的邏輯程式語言 Prolog。^[96]

Dreyfus等人針對邏輯方法的批評觀點認為，人類在解決問題時並沒有使用邏輯運算。心理學家 Peter Wason，Eleanor Rosch，阿摩司·特沃斯基，Daniel Kahneman 等人的實驗證明了這一點。^[97] McCarthy 則回應說，人類怎麼思考是無關緊要的：真正想要的是解題機器，而不是模仿人類進行思考的機器。

，是目前這場革命中的皎皎者。

由於實務上的學習考量，並不打算詳細介紹『Prolog』這個語言。有興趣深入的讀者可以下載閱讀

Simply Logical

Intelligent Reasoning by Example

by Peter Flach

這本教科書。

我們將把『輕量級』的『邏輯編程』帶入『派生』 Python 世界裡，探一探這個『典範』的主旨，嚐一嚐『人工智慧』的味道，談一談 pyDatalog 的一些應用。

from pyDatalog import pyDatalog
pyDatalog.create_terms('factorial, N')

factorial[N] = N*factorial[N-1] 

factorial[1] = 1
print (factorial[3==N) # prints N=6

Core technology

假使閱讀維基百科『工業 4.0』詞條︰

『工業 4.0』  Industry 4.0 是一個德國政府提出的高科技戰略計劃，由德國聯邦教育及研究部和聯邦經濟技術部聯合資助，投資預計達 2 億歐元，用來提昇製造業的電腦化、數位化、與智能化。目標是建立具有適應性、資源效率、及人因工程學的『智慧工廠』 Smart Factory ，在商業流程及價值流程中整合客戶以及商業夥伴。其技術基礎是『智慧整合感控系統』 CPS Cyber-Physical System ,  及『物聯網』 IoT Internet of Things 。如果架構陸續成真，最終將能建構出一個有智能意識的工業世界。

『工業 4.0』一詞是指第四次工業革命，第一次工業革命是利用水力及蒸汽的力量作為動力源，第二次工業革命則使用電力為大量生產提供動力，第三次工業革命則是使用電子設備及資訊技術 IT 來增進工業製造的自動化。

，也許該看看一九三一年，英國作家阿道斯‧雷歐那德‧赫胥黎 Aldous Leonard Huxley 所寫作的

美麗新世界 Brave New World

這本書。顯然他對『科技』能夠產生『烏托邦』這件事很不看好。他是那時代之知識精英，認為人類終將進入莎士比亞的《暴風雨》當中，喊著︰

How beauteous mankind is!
O brave new world,
that has such people in it.

。所以自己最好在思考過後，再做出抉擇︰

當『工具觀』已經對上了『道德觀』之時

，尚不知熟對熟錯？！且也不知誰是誰非！？

僅憑對未來相信，勇敢踏上這條《美麗新世界》科技探索的道路。