00100	                 SEMANTICS OF NATURAL LANGUAGE
00200	
00300	                       by John McCarthy
00400	                  Computer Science Department
00500	
00600		This paper is intended as a reconnaisance of  the  idea
00700	that  the  semantics of natural language can best be treated in
00800	the same way as the semantics of  functional  calculus  or  set
00900	theory.   Obstacles arise that require elaborating the methods,
01000	but the approach still seems right.
01100	
01200		In analogy with logic, the first major goal is to  give
01300	a  definition  of  the  truth  of a sentence.  For example, the
01400	definition  should  tell  us  under  what   circumstances   the
01500	sentence,  "John  thought  that  if she were going to come, she
01600	should have arrived by now." should be regarded as true.    Our
01700	first  step  is  to  be  more  ambitious  and  require that the
01800	semantics tell us also what certain constituent phrases of  the
01900	sentence designate. In the above example, we would like to know
02000	what "she" designates, and it would seem that  determining  the
02100	truth   of  the  sentence  requires  determining  what  certain
02200	constituent phrases designate.  We shall  leave  open  for  now
02300	what  sub-phrases  of  a  sentence  are to be given independent
02400	meaning.
02500	
02600		To try to anticipate the most obvious objections,  here
02700	are some immediate remarks:
02800	
02810		1. We are prepared to very modest in our goals.
02820	Namely, we shall try to give a Fregean semantics to a fragment
02830	of language concerned with numbers, material objects, situations
02840	in which material objects have relations with each other and
02850	with numbers, events, actions and the new situations that result
02860	from them.  If we get into difficulties, we will prefer to limit
02870	the scope of our theory rather than be vague or give up Fregean
02880	semantics.  The criterion for non-vagueness is that sentences which
02890	are common sense consequences of a collection of sentences must
02895	be formal consequences of these sentences and a body of sentences
02897	taken to constitute common sense.
02900		2.   The truth of a sentence or the meaning of a phrase
03000	clearly depends on the  situation  in  which  the  sentence  is
03100	uttered  and to which it may be presumed to refer. The rules we
03200	give will have to take this explicitly into account.
03300	
03400		2.   Our  approach  is  supported  by  the  notion   of
03500	understanding of text that is used in intelligence and aptitude
03600	tests.   The subject must read a paragraph and answer questions
03700	like,  "Who is Jane's father?" or "Did Jane see Billy?".  If he
03800	can answer the questions he is considered  to  have  understood
03900	the   text.     This  criterion  of  understanding  shows  that
04000	definitions that merely say, '"It is raining." is true  if  and
04100	only if it is raining' are too limited.  A child must do better
04200	than that in order to be regarded as understanding the  meaning
04300	of a paragraph.
04400	
04500		3.  In English not all well-formed sentences or phrases
04600	have a meaning in  all  circumstances.    In  the  semantics  I
04700	propose,  it will be possible for a sentence or a phrase not to
04800	have a designatum.  Examples of sentences or phrases that  have
04900	no  designatum  in  some  or  all  circumstances include, "This
05000	sentence is false.", "Pegasus", "John's son" (if  he  hasn't  a
     

00100	son).   It is often proposed to exclude meaningless phrases and
00200	sentences by grammatical criteria.  This  won't  work  for  two
00300	reasons:  First, whether a sentence is meaningful may depend on
00400	the circumstances.  Second,  even  in  a  mathematical  context
00500	wherein  meaningfulness  does not depend on circumstances there
00600	may  be  no  recursive  rule  that  excludes  all   intuitively
00700	meaningless  sentences  without  also  excluding some sentences
00800	that intuitively seem meaningful.  In the  above,  I  have  not
00900	made  a  distinction  between  having  a  sense  and  having  a
01000	denotation.  I shall return to this matter later.
01100	
01200		4. We insert at this point a remark about the controversy
01300	between Chomsky and some of his critics about whether the deep
01400	structure of language is biologically determined.  In my view,
01500	any definition of deep structure that will hold up will have
01600	to be much more explicit about the semantics than Chomsky
01700	has been, but in that case it may turn out to be determined
01800	not merely biologically but simply by the units of information
01900	about the world that are available to humans.  For example, suppose
02000	that the question, "Where is the book?" is to be answered,
02100	and the book is on the table.  Then the deep structure of the
02200	reply must include the assertion, "The book is on the
02300	table" and this would hold true whether the the answerer is
02400	an American, a Chinese, a Martian, or a computer.  (We consider
02500	that, "on the table" and "The book is on the table" have the
02600	same deep structure in this situation).
02700	
02800		We shall deal only with declarative sentences, and we 
02900	start by trying to give the semantics of certain limited classes
03000	of sentences.
03100	
03200		First, consider sentences like "The book is on the
03300	table".    When this sentence is uttered seriously and is not 
03400	merely being referred to, the speaker has a particular book known
03500	both to him and to the hearer in mind.  Moreover, the assertion
03600	is confined to a certain situation.  Therefore, we shall regard
03700	this sentence as equivalent to a sentence of the predicate calculus
03800	of the form  on(Book,Table,Situation)  where the capital
03900	letters indicate that "Book", "Table", and "Situation" are proper
04000	names of particular entities.  on is a three term relation.
04100	The reader will note that we have introduced into our ontology
04200	entities called situations in addition to books and tables.
04300	We hope we shall not have to introduce too many such entities.
04400	the reader is referred to (McCarthy and Hayes 1969)
04500	for a more extended treatment of situations.
04600	
04700		Next, consider "Three is under ten".  We shall consider
04800	that this sentence has a different semantic structure than
04900	the preceding sentence, namely
05000		less(3,10)	
05100	and a situation is not involved.