Class, Internet, and the Industrial System (fwd)

glevy at glevy at
Fri Aug 4 20:41:08 MDT 1995

Another forwarded message from Paul Cockshott:

Jerry asked:

If you discuss the issue again, could you please describe
the difference between "formal" and "natural" language.

A natural language is one that has evolved historically
such as German or French and, in either written or spoken
form, is used in everyday human intercourse.

Formal languages have their origin in the proposal by Leibnitz
to develop a logical language that would allow unambiguous
resolution of philosophical argument. The idea was further
develop by George Boole in 'The Laws of Thought', where he
showed that logical argument could be expressed in terms of
the standard laws of algebra but with the additional axiom
that 1+1=1. In transforming logical statements into algebraic
expressions, he also clarified the notion of an algebra,
by giving a formal recursive definition to algebraic

Thus he defined an algebraic expression to be either
a. an atomic term such as a variable or the numbers 0 and 1
b. an expression in brackets
c. two expressions joined by the operators + , - and . ( where . was

Thus the following would be expressions

x               rule a
(x)             rules b,a
x+y             rules c,a,a
(x+y).(1-x)     rules c,b,c,a,a,b,c,a,a

This can be thought of as a simple language, but one whose grammar is
formally defined allowing unambigous parsing of an expression. Such
parses are given in terms of the rules which have to be applied to
generate the expression.

The idea of formal languages developed through symbolic logic to
Norman Chomskys work on generative grammars. He defined a hierarchy of
classes of languages in terms of the generality with which their
grammar rules were constructed. He numbered these classes 0 to
3, with class 0 having the most general grammars and class 3 the
most restrictive.

In terms of Chomsky's hierarchy of languages, Boole's algebra would
be of class 2, and a natural language like French would be of
class 0.

Whatever the applicability of his idea of generative grammars to
natural languages, they provided an enormous advance in the
theorisation of formal linguistics. From the 1960's on, computer
scientists attempting to define new programming languages explicitly
based themselves on Chomskys language hierarchy. In general, they
attempt to construct languages that have Chomsky class 2 or at
worst class 1 grammars.

This restriction is observed because there is a one to one
correspondance between Chomsky's grammar classes, and the
classes of automata that are capable of either parsing or
generating them. A relatively simple automaton - the pushdown
automaton is all that is needed to handle a class 2 grammar,
making it suitable for fast efficient handling by computers.

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