1) CONCEP[E76,JMC] and 2) CONCEP[F78,JMC]	7-03-79 16:19	pages 1,1

**** File 1) CONCEP[E76,JMC], Page 1 line 7
1)	C00033 00005	.BB FUNCTIONS FROM THINGS TO CONCEPTS OF THEM
1)	C00037 00006	.BB RELATIONS BETWEEN KNOWING WHAT AND KNOWING THAT
1)	C00040 00007	.bb UNQUANTIFIED MODAL LOGIC
1)	C00047 00008	.bb MORE PHILOSOPHICAL EXAMPLES - MOSTLY WELL KNOWN
1)	C00058 00009	.bb PROPOSITIONS EXPRESSING QUANTIFICATION
1)	C00070 00010	.bb POSSIBLE APPLICATIONS TO ARTIFICIAL INTELLIGENCE
1)	C00078 00011	.bb ABSTRACT LANGUAGES
1)	C00082 00012	.bb BIBLIOGRAPHY
1)	C00093 ENDMK
1)	C⊗;
1)	.require "memo.pub[let,jmc]" source;
1)	.once center
1)	draft
1)	.skip 20
**** File 2) CONCEP[F78,JMC], Page 1 line 7
2)	C00035 00005	.BB FUNCTIONS FROM THINGS TO CONCEPTS OF THEM
2)	C00039 00006	.BB RELATIONS BETWEEN KNOWING WHAT AND KNOWING THAT
2)	C00042 00007	.bb REPLACING MODAL OPERATORS BY MODAL FUNCTIONS
2)	C00049 00008	.bb MORE PHILOSOPHICAL EXAMPLES - MOSTLY WELL KNOWN
2)	C00060 00009	.bb PROPOSITIONS EXPRESSING QUANTIFICATION
2)	C00072 00010	.bb POSSIBLE APPLICATIONS TO ARTIFICIAL INTELLIGENCE
2)	C00080 00011	.bb ABSTRACT LANGUAGES
2)	C00084 00012	.bb ACKNOWLEDGMENTS AND BIBLIOGRAPHY
2)	C00095 ENDMK
2)	C⊗;
2)	.require "memo.pub[let,jmc]" source;
2)	.every heading (,%4Theories of Individual Concepts%1,{PAGE})
2)	.skip 20
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**** File 1) CONCEP[E76,JMC], Page 2 line 12
1)	and in artificial intelligence.
1)	.if false then begin
1)	%7This draft of CONCEP[E76,JMC] PUBbed at {time} on {date}.%1
1)	%3McCarthy, John (1979)%1: "First Order Theories of Individual
1)	Concepts and Propositions", in Michie, Donald (ed.)
1)	%2Machine Intelligence 9%1, also available on disk at SU-AI as
1)	CONCEP[E76,JMC].
1)	.end
1)	.skip to column 1
**** File 2) CONCEP[F78,JMC], Page 2 line 11
2)	and in artificial intelligence.  We do not treat general concepts,
2)	and we do not present any full axiomatizations but rather show
2)	how various facts can be expressed.
2)	%7This draft of CONCEP[F78,JMC] PUBbed at {time} on {date}.%1
2)	.skip to column 1
  1) CONCEP[E76,JMC] and 2) CONCEP[F78,JMC]	7-03-79 16:19	pages 2,2

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**** File 1) CONCEP[E76,JMC], Page 3 line 14
1)		According to the ideas of
1)	Frege (1892), the meaning of the phrase %2"Mike's
1)	telephone number"%1 in the sentence %2"Pat knows Mike's telephone number"%1
1)	is the concept of Mike's telephone number, whereas its meaning in the
1)	sentence %2"Pat dialed Mike's telephone number"%1 is the number itself.
1)	Thus if we also have %2"Mary's telephone number = Mike's telephone
1)	number"%1, then %2"Pat dialed Mary's telephone number"%1 follows, but
1)	%2"Pat knows Mary's telephone number"%1 does not.
1)		Frege further proposed that a phrase has a ⊗sense 
1)	which is a ⊗concept and is its ⊗meaning in ⊗oblique ⊗contexts 
1)	like knowing and wanting, and a ⊗denotation which is its
1)	⊗meaning in ⊗direct ⊗contexts.  
1)	⊗Denotations are the basis of the semantics of first
**** File 2) CONCEP[F78,JMC], Page 3 line 14
2)		In this paper
2)	we will show how various individual concepts
2)	and propositions can be expressed.  We are not yet ready to present a
2)	full collection of axioms.  Moreover, our purpose is not to
2)	explicate what concepts are in a philosophical sense but rather to
2)	develop a language of concepts for representing facts about knowledge,
2)	belief, etc. in the memory of a computer.
2)		Frege (1892) discussed the need to distinguish direct and indirect
2)	use of words.  According to one interpretation of Frege's ideas, the meaning of
2)	the phrase %2"Mike's telephone number"%1 in the sentence %2"Pat knows
2)	Mike's telephone number"%1 is the concept of Mike's telephone number,
2)	whereas its meaning in the sentence %2"Pat dialed Mike's telephone
2)	number"%1 is the number itself.  Thus if we also have %2"Mary's telephone
2)	number = Mike's telephone number"%1, then %2"Pat dialed Mary's telephone
2)	number"%1 follows, but %2"Pat knows Mary's telephone number"%1 does not.
2)		It was further proposed that a phrase has a ⊗sense 
2)	which is a ⊗concept and is its ⊗meaning in ⊗oblique ⊗contexts 
2)	like knowing and wanting, and a ⊗denotation which is its
2)	⊗meaning in ⊗direct ⊗contexts like dialing.
2)	⊗Denotations are the basis of the semantics of first
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**** File 1) CONCEP[E76,JMC], Page 3 line 36
1)		The problem identified by Frege - of suitably limiting the
**** File 2) CONCEP[F78,JMC], Page 3 line 43
2)	Robert Moore's forthcoming dissertation also uses concepts in first
2)	order logic.
2)		The problem identified by Frege - of suitably limiting the
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  1) CONCEP[E76,JMC] and 2) CONCEP[F78,JMC]	7-03-79 16:19	pages 3,3



**** File 1) CONCEP[E76,JMC], Page 3 line 44
1)		Our approach involves leaving the logic unchanged and treating
1)	concepts as one kind of object in an ordinary first order theory.
**** File 2) CONCEP[F78,JMC], Page 3 line 54
2)		Our approach involves treating
2)	concepts as one kind of object in an ordinary first order theory.
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**** File 1) CONCEP[E76,JMC], Page 3 line 61
1)		It seems surprising that such a straightforward and easy
1)	approach should not have been more fully explored than it apparently
1)	has.
1)	.skip 1
**** File 2) CONCEP[F78,JMC], Page 3 line 71
2)		This is a preliminary paper in that we don't give a
2)	comprehensive set of axioms for concepts.  Instead we merely
2)	translate some English sentences into our formalism to give an
2)	idea of the possibilities.
2)	.skip 1
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**** File 1) CONCEP[E76,JMC], Page 4 line 25
1)	Whether the function ⊗Telephone can be identified with the general
1)	concept of a person's telephone number is not settled.  For the present,
1)	please suppose not.
1)		#. If ⊗P is a person concept and ⊗X is another concept, then
**** File 2) CONCEP[F78,JMC], Page 4 line 25
2)	We do not propose to identify the function ⊗Telephone the general
2)	concept of a person's telephone number.
2)		#. If ⊗P is a person concept and ⊗X is another concept, then
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**** File 1) CONCEP[E76,JMC], Page 4 line 39
1)		#. %2true Q%1 is the truth value, ⊗t or ⊗f, of the proposition ⊗Q, 
**** File 2) CONCEP[F78,JMC], Page 4 line 38
2)		#. It is often convenient to write %2know(pat,Telephone_Mike)%1
2)	instead of %2true_Know(Pat,Telephone_Mike)%1 when we don't intend to
2)	iterate knowledge further.  %2know%1 is a predicate in the logic, so
2)	we cannot apply any knowledge operators to it.  We will have
2)	!!ee0:	%2know(pat,Telephone Mike) ≡ true Know(Pat,Telephone Mike)%1.
2)		#. We expect that the proposition %2Know(Pat, Telphone Mike)%1
2)	will be useful accompanied by axioms that allow inferring that Pat will
2)	use this knowledge under appropriate circumstances, i.e. he will dial it
  1) CONCEP[E76,JMC] and 2) CONCEP[F78,JMC]	7-03-79 16:19	pages 4,4

2)	or retell it when appropriate.  There will also be axioms asserting that
2)	he will know it after being told it or looking it up in the telephone
2)	book.
2)		#.  While the sentence %2"Pat knows Mike"%1 is in common use,
2)	it is harder to see how %2Know(Pat, Mike)%1 is to be used and
2)	axiomatized.  I suspect that new methods will be required to treat
2)	knowing a person.
2)		#. %2true Q%1 is the truth value, ⊗t or ⊗f, of the proposition ⊗Q, 
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**** File 1) CONCEP[E76,JMC], Page 4 line 84
1)	proposition means knowing that it has a particular value, namely ⊗t. 
1)	There is no reason to impose this infirmity on robots.
**** File 2) CONCEP[F78,JMC], Page 4 line 102
2)	proposition means knowing that it has a particular value, namely ⊗true. 
2)	There is no reason to impose this infirmity on robots.
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**** File 1) CONCEP[E76,JMC], Page 6 line 31
1)		Using the ⊗standard ⊗concept function ⊗Concept1,
1)	we might replace ({eq e12}) by
**** File 2) CONCEP[F78,JMC], Page 6 line 31
2)		Using the ⊗standard ⊗concept function ⊗Concept1, 
2)	we might replace ({eq e12}) by
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**** File 1) CONCEP[E76,JMC], Page 7 line 1
1)	.bb UNQUANTIFIED MODAL LOGIC
1)		In %2unquantified modal logic%1, the arguments of the
1)	modal functions will not involve quantification although quantification
**** File 2) CONCEP[F78,JMC], Page 7 line 1
2)	.bb REPLACING MODAL OPERATORS BY MODAL FUNCTIONS
2)		Using concepts we can translate the content of modal logic
2)	into ordinary logic.  We need only replace the modal operators by
2)	%2modal functions%1.  The axioms of modal logic then translate into
2)	ordinary first order axioms.  In this section we will treat only
2)	%2unquantified modal logic%1.  The arguments of the
2)	modal functions will not involve quantification although quantification
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**** File 1) CONCEP[E76,JMC], Page 9 line 9
1)		We want to continue describing concepts within first order
**** File 2) CONCEP[F78,JMC], Page 9 line 8
2)	We are not very confident of the approach presented here.
  1) CONCEP[E76,JMC] and 2) CONCEP[F78,JMC]	7-03-79 16:19	pages 9,9

2)		We want to continue describing concepts within first order
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**** File 1) CONCEP[E76,JMC], Page 10 line 57
1)		We have considered a set of axioms for knowledge that
1)	would permit deduction from %2"Pat knows Mike's telephone number"%1 and
1)	%2Pat wants Joe to know Mike's telephone number"%1 that %2Joe will
**** File 2) CONCEP[F78,JMC], Page 10 line 57
2)		In Appendix I, we give a set of axioms for knowledge that
2)	permits deduction from %2"Pat knows Mike's telephone number"%1 and
2)	%2Pat wants Joe to know Mike's telephone number"%1 that %2Joe will
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**** File 1) CONCEP[E76,JMC], Page 10 line 70
1)		A proof from these axioms that Joe will know
1)	Mike's telephone number took about 15 steps.  Since there
1)	is only one action - Pat telling Joe Mike's telephone number, the
**** File 2) CONCEP[F78,JMC], Page 10 line 70
2)		The proof from these axioms that Joe will know
2)	Mike's telephone number has about 15 steps.  Since there
2)	is only one action - Pat telling Joe Mike's telephone number, the
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**** File 1) CONCEP[E76,JMC], Page 12 line 1
1)	.bb BIBLIOGRAPHY
1)		The treatment given here should be compared with that in (Church 1951b)
**** File 2) CONCEP[F78,JMC], Page 12 line 1
2)	.bb ACKNOWLEDGMENTS AND BIBLIOGRAPHY
2)		The treatment given here should be compared with that in (Church 1951b)
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**** File 1) CONCEP[E76,JMC], Page 12 line 31
1)	the paradoxes discussed in (Kaplan and Montague 1960) and (Montague
1)	1963).  Our intuition is that the paradoxes can be avoided by restricting
**** File 2) CONCEP[F78,JMC], Page 12 line 31
2)	the paradoxes discussed in (Montague and Kaplan 1961) and (Montague
2)	1963).  Our intuition is that the paradoxes can be avoided by restricting
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**** File 1) CONCEP[E76,JMC], Page 12 line 42
1)	.skip 3
1)	.BB REFERENCES:
1)	%3Carnap, Rudolf%1 (1956), %2Meaning and Necessity%1, University of Chicago
  1) CONCEP[E76,JMC] and 2) CONCEP[F78,JMC]	7-03-79 16:19	pages 12,12

**** File 2) CONCEP[F78,JMC], Page 12 line 43
2)		I am indebted to
2)	Lewis Creary,
2)	Patrick Hayes,
2)	Donald Michie,
2)	Barbara Partee and
2)	Peter Suzman
2)	for discussion of a draft of this paper.  Creary in particular has shown
2)	the inadequacy of the formalism for expresing all readings of the
2)	ambiguous sentence %2"Pat knows that Mike knows what Joan last asserted"%1.
2)	There has not been time to modify the formalism to fix this inadequacy,
2)	but it seems likely that concepts of concepts are required for an
2)	adequate treatment.
2)	.BB References:
2)	%3Carnap, Rudolf%1 (1956), %2Meaning and Necessity%1, University of Chicago
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**** File 1) CONCEP[E76,JMC], Page 12 line 106
1)	.if false then begin
1)	.SKIP 2
**** File 2) CONCEP[F78,JMC], Page 12 line 120
2)	.SKIP 2
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**** File 1) CONCEP[E76,JMC], Page 12 line 115
1)	.end
**** File 2) CONCEP[F78,JMC], Page 12 line 128
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