00100	RELATIONS BETWEEN REPRESENTATIONS OF PROBLEMS
00200	
00300	by John McCarthy
00400	
00500	
00600	
00700	
00800	Abstract: We shall formalize the relation
00900	between representations of problems by collections
01000	of sentences (e.g. Advice Taker) and representations
01100	by state spaces in which an initial state is to
01200	be transformed into another by allowed 
01300	transformations (e.g. GPS).
01400	We shall contend that problems arise naturally
01500	in the sentential representation, but heuristic
01600	search is often more convenient in a transformation
01700	representation.  We then formalize the problem of
01800	going from a sentential representation to a
01900	suitable transformation representation.
     

00100	RELATIONS BETWEEN REPRESENTATIONS OF PROBLEMS
00200	
00300	by John McCarthy
00400	
00500	1. Sentential and transformational representations of problems.
00600		The following well known puzzle has been discussed
00700	from varying points of view in the literature of
00800	artificial intelligence.  See Newell, Amarel
00900	
01000		Three missionaries and three cannibals must cross
01100	a river using a boat that can hold two persons.
01200	The difficulty is that if the cannibals on either bank
01300	of the river ever outnumber the missionaries there, the
01400	missionaries will be eaten which is to be avoided.
01500	In what order shall the boat cross the river back and
01600	forth carrying missionaries and cannibals?
01700	
01800		In the formalism of (McCarthy and Hayes 1969), it
01900	is easy to get a sentential representation of the problem.
02000	The initial situation is represented by the sentences:
02100	at(M1,left(River),s0)
02200	at(M2,left(River),s0)
02300	at(M3,left(River),s0)
02400	at(C1,left(River),s0)
02500	at(C2,left(River),s0)
02600	at(C3,left(River),s0)
02700	at(Boat,left(River)s0)