00100	FIRST ORDER LOGIC AND SET THEORY IN ARTIFICIAL INTELLIGENCE
00200	
00300	
00400		First   order  logic  provides  the  simplest  languages  for
00500	expressing the facts about the world that a computer program needs in
00600	order  to  behave intelligently. If we express what the program knows
00700	as a collection of  sentences  in  first  order  logic,  then  it  is
00800	determined  whether  the  solution  to  a  problem  follows from this
00900	knowledge or whether additional  knowledge  has  to  be  obtained  by
01000	interaction  with  the world. The same facts can be expressed in many
01100	ways within first order logic, and it is often not  obvious  what  is
01200	the best way for a given purpose. Set theory, formulated within first
01300	order logic, provides very general and powerful formalisms.
01400	
01500		The  student  of  computer  science  should  note  the  basic
01600	distinction  between logical languages and programming languages.  In
01700	a logical language the sentences  represent  assertions.   Additional
01800	assertions  can  be  obtained  as consequences of assertions accepted
01900	earlier.  In a programming language  we  express  procedures,  and  a
02000	computer  can  execute  these  procedures.   Programming  and logical
02100	languages can have certain relations.  In the first  place,  programs
02200	can  manipulate sentences in logical languages, e.g. attempt to prove
02300	theorems.  Secondly, we can have assertions about programs, and these
02400	assertions  have logical consequences. Besides these relations, it is
02500	sometimes possible to interpret a program as asserting a fact and  it
02600	is sometimes possible to interpret a set of sentences as describing a
02700	procedure.
02800