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\markboth{JOHN MCCARTHY}{ARTIFICIAL INTELLIGENCE AND LOGIC}  

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\centerline{\footnotesize JOHN MCCARTHY}
\vspace*{.7cm}

\begin{center}
ARTIFICIAL INTELLIGENCE, LOGIC\\[.05in] 
AND FORMALIZING COMMON SENSE 
\end{center}

\vspace*{.05cm}
  
\begin{center}
{\footnotesize 1. INTRODUCTION} %\jplsection{Introduction}
\end{center}

%thomason comments in f88.in[let,jmc]/575p

\vspace*{-.05cm}


	This is a position paper about the relations among
artificial intelligence (AI), mathematical logic and the
formalization of common-sense knowledge and reasoning.  It also
treats other problems of concern to both AI and philosophy.  I thank
the editor for inviting it.  The position advocated is that
philosophy can contribute to AI if it treats some of its
traditional subject matter in more detail and that this will
advance the philosophical goals also.  Actual formalisms (mostly
first order languages) for expressing common-sense facts are
described in the references.

	Common-sense knowledge includes the basic facts
about\linebreak events (including actions) and their effects, facts
about knowledge and how it is obtained, facts about beliefs and
desires.  It also includes the basic facts about material objects and
their properties.

%\smallskip\centerline{Copyright \copyright\ 1989 by John McCarthy}

	One path to human-level AI uses mathematical logic to
formalize common-sense knowledge in such a way that common-sense
problems can be solved by logical reasoning.  This methodology
requires understanding the common-sense world well \linebreak enough
to formalize facts about it and ways of achieving goals in it.
Basing AI on understanding the common-sense world is different from
basing it on understanding human psychology or neurophysiology.  This
approach to AI, based on logic and computer science, is complementary
to approaches that start from the fact that humans exhibit
intelligence, and that explore human psychology or human
neurophysiology.

	This article discusses the problems and difficulties, the
results so far, and some improvements in logic and logical languages
that may be required to formalize common sense.  Fundamental
conceptual advances are almost certainly required.  The \\
object of the
paper is to get more help for AI from philosophical logicians.  Some
of the requested help will be mostly philosophical and some will be
logical.  Likewise the concrete AI approach may fertilize
philosophical logic as physics has repeatedly fertilized mathematics.

	There are three reasons for AI to emphasize common-sense
knowledge rather than the knowledge contained in scientific
theories.

	(1) Scientific theories represent compartmentalized
knowledge.  In presenting a scientific theory, as well as in
developing it, there is a common-sense pre-scientific stage.  In
this stage, it is decided or just taken for granted what
phenomena are to be covered and what is the relation between
certain formal terms of the theory and the common-sense world.
Thus in classical mechanics it is decided what kinds of bodies
and forces are to be used before the differential equations are
written down.  In probabilistic theories, the sample space is
determined.  In theories expressed in first order logic, the
predicate and function symbols are decided upon.  The axiomatic
reasoning techniques used in mathematical and logical theories
depend on this having been done.  However, a robot or computer
program with human-level intelligence will have to do this for
itself.  To use science, common sense is required.

	Once developed, a scientific theory remains imbedded
in common sense.  To apply the theory to a specific problem,
common-sense descriptions must be matched to the terms of the theory.
For example, $d = {1\over 2} gt↑2$ does not in itself identify
$d$ as the distance a body falls in time $t$ and identify $g$
as the acceleration due to gravity.  
(McCarthy and Hayes 1969) uses the {\it situation
calculus} introduced in that paper to imbed the above formula
in a formula describing the common-sense situation, for example
%
%$$\eqalign{
%&dropped(x,s)\wedge height(x,s) = h\wedge d = {1\over 2}gt↑2 \wedge d < h\cr
%\supset  &\exists s'(F(s,s') \wedge time(s') = time(s)+t
% \wedge  height(x,s') = h - d).}$$
%
\first{dropped(x,s) \wedge  height(x,s) = h \wedge  d = 
{1\over 2}gt↑2 \wedge  d < h \supset}{}
\next{\exists s'(F(s,s') \wedge time(s') = time(s)+t \;\wedge}
\last{\wedge\; height(x,s') = h - d).}
%

\vspace{3pt}%\smallskip

Here $x$ is the falling body, and we are presuming a language
in which the functions $height$, $time$, etc. are formalized
in a way that corresponds to what the English words suggest.
$s$ and $s'$ denote {\it situations} as discussed in that paper,
and $F(s,s')$ asserts that the situation $s'$ is in the future
of the situation $s$.

	(2) Common-sense reasoning is required for solving problems in
the common-sense world.  From the problem solving or goal-achieving
point of view, the common-sense world is characterized by a different
{\it informatic situation} than that {\it within} any formal
scientific theory.  In the typical common-sense informatic situation,
the reasoner doesn't know what facts are relevant to solving his
problem.  Unanticipated obstacles may arise that involve using parts
of his knowledge not previously thought to be relevant.

	(3) Finally, the informal metatheory of any scientific
theory has a common-sense informatic character.  By this I mean
the thinking about the structure of the theory in general and the
research problems it presents.  Mathematicians invented the
concept of a group in order to make previously vague parallels
between different domains into a precise notion.  The thinking
about how to do this had a common-sense character.

	It might be supposed that the common-sense world would admit a
conventional scientific theory, e.g. a probabilistic theory.  But no
one has yet developed such a theory, and AI has taken a somewhat
different course that
involves nonmonotonic extensions to the kind of reasoning used in
formal scientific theories.  This seems likely to work better.

	Aristotle, Leibniz, Boole and Frege all included common-sense
knowledge when they discussed formal logic.  However,
formalizing much of common-sense knowledge and reasoning proved
elusive, and the twentieth century emphasis has been on formalizing
mathematics.  Some important philosophers, e.g. Wittgenstein, have
claimed that common-sense knowledge is unformalizable or mathematical
logic is inappropriate for doing it.  Though it is possible to give a
kind of plausibility to views of this sort, it is much less easy to
make a case for them that is well supported and carefully worked out.
If a common-sense reasoning problem is well presented, one is well on
the way to formalizing it.  The examples that are presented for this
negative view borrow much of their plausibility from the inadequacy of
the specific collections of predicates and functions they take into
consideration.  Some of their force comes from not formalizing
nonmonotonic reasoning, and some may be due to lack of logical tools
still to be discovered.  While I acknowledge this opinion, I haven't
the time or the scholarship to deal with the full range of such
arguments.  Instead I will present the positive case, the problems that
have arisen, what has been done and the problems that can be foreseen.
These problems are often more interesting than the ones suggested by
philosophers trying to show the futility of formalizing common sense, and
they suggest productive research programs for both AI and philosophy.

	In so far as the arguments against the formalizability of
common-sense attempt to make precise intuitions of their authors,
they can be helpful in identifying problems that have to be solved.
For example, Hubert Dreyfus (1972) said that computers couldn't have
``ambiguity tolerance'' but didn't offer much explanation of the
concept.  With the development of nonmonotonic reasoning, it became
possible to define some forms of {\it ambiguity tolerance} and show
how they can and must be incorporated in computer systems.  For
example, it is possible to make a system that doesn't know about
possible {\it de re}/{\it de dicto} ambiguities and has a
default assumption that amounts to saying that a reference holds
both {\it de re} and {\it de dicto}.  When this assumption
leads to inconsistency, the ambiguity can be discovered and
treated, usually by splitting a concept into two or more.

	If a computer is to store facts about the world and reason
with them, it needs a precise language, and the program has to embody
a precise idea of what reasoning is allowed, i.e. of how new formulas
may be derived from old.  Therefore, it was natural to try to use
mathematical logical languages to express what an intelligent computer
program knows that is relevant to the problems we want it to solve and
to make the program use logical inference in order to decide what to
do.  (McCarthy 1959) contains the first proposals to use logic in AI
for expressing what a program knows and how it should reason.
(Proving logical formulas as a domain for AI had already been
studied by several authors).

	The 1959 paper said:

%\begingroup\narrower\narrower
% COMMON.TEX[E80,JMC] TeX version Programs with Common Sense
%

\medskip

\noindent\hspace*{.6cm}\parbox[t]{9.4cm}{ \parindent=20pt
The {\it advice taker} is a proposed program for solving problems by
manipulating sentences in formal languages.  The main difference
between it and other programs or proposed programs for manipulating
formal languages (the {\it Logic Theory Machine} of Newell, Simon and
Shaw and the Geometry Program of Gelernter) is that in the previous
programs the formal system was the subject matter but the heuristics
were all embodied in the program.  In this program the procedures will
be described as much as possible in the language itself and, in
particular, the heuristics are all so described.

	The main advantages we expect the {\it advice taker} to have
is that its behavior will be improvable merely by making statements to
it, telling it about its symbolic environment and what is wanted from
it.  To make these statements will require little if any knowledge of
the program or the previous knowledge of the {\it advice taker}.  One
will be able to assume that the {\it advice taker} will have available
to it a fairly wide class of immediate logical consequences of anything
it is told and its previous knowledge.  This property is expected to
have much in common with what makes us describe certain humans as
having {\it common sense}.  We shall therefore say that {\it a program
has common sense if it automatically deduces for itself a sufficiently
wide class of immediate consequences of anything it is told and what
it already knows.}
%\par\endgroup
}

\medskip

	The main reasons for using logical sentences extensively in AI
are better understood by researchers today than in 1959.  Expressing
information in declarative sentences is far more modular than
expressing it in segments of computer program or in tables.  Sentences
can be true in much wider contexts than specific programs can be
useful.  The supplier of a fact does not have to understand much about
how the receiver functions, or how or whether the receiver will use it.
The same fact can be used for many purposes, because the logical
consequences of collections of facts can be available.

	The {\it advice taker} prospectus was ambitious in 1959, would
be considered ambitious today and is still far from being immediately
realizable.  This is especially true of the goal of expressing the
heuristics guiding the search for a way to achieve the goal in the
language itself.  The rest of this paper is largely concerned with
describing what progress has been made, what the obstacles are, and
how the prospectus has been modified in the light of what has been
discovered.

	The formalisms of logic have been used to differing
extents in AI.  Most of the uses are much less ambitious than
the proposals of (McCarthy 1959).  We can distinguish four
levels of use of logic.

\medskip

	1. A machine may use no logical sentences---all its
``beliefs'' being implicit in its state.  Nevertheless, it is often
appropriate to ascribe beliefs and goals to the program, i.e. to
remove the above sanitary quotes, and to use a principle of
rationality---{\it It does what it thinks will achieve its goals}.
Such ascription is discussed from somewhat different points of view
 in (Dennett 1971), (McCarthy 1979a) and
(Newell 1981).  The advantage is that the intent of the machine's
designers and the way it can be expected to behave may be more readily
described {\it intentionally} than by a purely physical description.

	The relation between the physical and the {\it intentional}
descriptions is most readily understood in simple systems that admit
readily understood descriptions of both kinds, e.g. thermostats.  Some
finicky philosophers object to this, contending that unless a system
has a full human mind, it shouldn't be regarded as having any mental
qualities at all.  This is like omitting the numbers 0 and 1 from the
number system on the grounds that numbers aren't required to count
sets with no elements or one element.
Indeed if your main interest is the null set or unit sets, numbers
{\it are} irrelevant.  However, if your interest is the number system
you lose clarity and uniformity
if you omit 0 and 1.  Likewise, when one studies phenomena like belief,
e.g. because one wants a machine with beliefs and which reasons about
beliefs, it works better not to exclude simple cases from the formalism.
One battle has been over whether it should be forbidden to ascribe to a simple
thermostat the belief that the room is too cold.
(McCarthy 1979a) says much more about ascribing mental qualities
to machines, but that's not where the main action is in AI.

\medskip

	2. The next level of use of logic involves computer programs
that use sentences in machine memory to represent their beliefs but
use other rules than ordinary logical inference to reach conclusions.
New sentences are often obtained from the old ones by ad hoc programs.
Moreover, the sentences that appear in memory belong to a
program-dependent subset of the logical language being used.  Adding
certain true sentences in the language may even spoil the functioning
of the program.  The languages used are often rather unexpressive
compared to first order logic, for example they may not admit
quantified sentences, or they may use a
different notation from that used for ordinary facts to represent
``rules'', i.e.  certain universally quantified implication sentences.
Most often, conditional rules are used in just one
direction, i.e. contrapositive reasoning is not used.  
Usually the program cannot infer new rules; rules
must have all been put in by the ``knowledge engineer''.  Sometimes
programs have this form through mere ignorance, but the usual
reason for the restriction is the practical desire to make the program
run fast and deduce just the kinds of conclusions its designer
anticipates.
  We
believe the need for such specialized inference will turn out to be
temporary and will be reduced or eliminated by improved ways of
controlling general inference, e.g. by allowing the heuristic rules to
be also expressed as sentences as promised in the above extract from
the 1959 paper.

\medskip

	3. The third level uses first order logic and also logical
deduction.  Typically the sentences are represented as clauses, and the
deduction methods are based on J. Allen Robinson's (1965) method of
resolution.  It is common to use a theorem prover as a problem solver,
i.e.  to determine an $x$ such that $P(x)$ as a byproduct of a proof of
the formula $\exists xP(x)$.
This level is less used for practical
purposes than level two, because techniques for controlling the
reasoning are still insufficiently developed, and it is common for the
program to generate many useless conclusions before reaching the desired
solution.  Indeed, unsuccessful experience (Green 1969) with this method
led to more restricted uses of logic, e.g. the STRIPS system of (Nilsson
and Fikes 1971).
%The promise of (McCarthy 1959) to express the
%heuristic facts that should be used to guide the search as logical
%sentences has not yet been realized by anyone.

	The commercial ``expert system shells'', e.g. ART, KEE and
OPS-5, use logical representation of facts, usually ground facts only,
and separate facts from rules.  They provide elaborate but not always
adequate ways of controlling inference.

	In this connection it is important to mention logic programming,
first introduced in Microplanner (Sussman et al., 1971) 
and from different points of view by Robert Kowalski (1979) and Alain
Colmerauer in the early 1970s.
A recent text is (Sterling and Shapiro 1986).  Microplanner
was a rather unsystematic collection of tools, whereas Prolog relies
almost entirely on one kind of logic programming, but the main idea
is the same.  If one uses a restricted class of sentences, the so-called
Horn clauses, then it is possible to use a restricted form of logical
deduction.  The control problem is then much eased, and it is possible
for the programmer to anticipate the course the deduction will take.
The price paid is that only certain kinds of facts are conveniently
expressed as Horn clauses, and the depth first search built into
Prolog is not always appropriate for the problem.


	Even when the relevant facts can be expressed as Horn
clauses supplemented by negation as failure, the reasoning
carried out by a Prolog program may not be appropriate.  For
example, the fact that a sealed container is sterile if all the
bacteria in it are dead and the fact that heating a can kills a
bacterium in the can are both expressible as Prolog clauses.
However, the resulting program for sterilizing a container will
kill each bacterium individually, because it will have to index
over the bacteria.  It won't reason that heating the can kills
all the bacteria at once, because it doesn't do universal
generalization.

	Here's a Prolog program for testing whether a container
is sterile.  The predicate symbols have obvious meanings.

\newpage
{\small\tt \obeyspaces\obeylines

not(P) :- P, !, fail.
not(P).

sterile(X) :- not(nonsterile(X)).
nonsterile(X) :- 
\hspace*{5ex}bacterium(Y), in(Y,X), not(dead(Y)).
hot(Y) :- in(Y,X), hot(X).
dead(Y) :- bacterium(Y), hot(Y).
bacterium(b1).
bacterium(b2).
bacterium(b3).
bacterium(b4).
in(b1,c1).
in(b2,c1).
in(b3,c2).
in(b4,c2).
hot(c1).}

\medskip

Giving Prolog the goal $sterile(c1)$ and $sterile(c2)$ gives
the answers $yes$ and $no$ respectively.  However, Prolog has
indexed over the bacteria in the containers.

	The following is a Prolog program that can verify whether
a sequence of actions, actually just heating it, will sterilize
a container.  It involves introducing situations analogous to
those discussed in (McCarthy and Hayes 1969).

\medskip

{\small \tt\obeyspaces\obeylines
not(P) :- P, !, fail.
not(P).

sterile(X,S) :- not(nonsterile(X,S)).
nonsterile(X,S) :- 
\hspace*{5ex}bacterium(Y), in(Y,X), not(dead(Y,S)).
hot(Y,S) :- in(Y,X), hot(X,S).
dead(Y,S) :- bacterium(Y), hot(Y,S).
bacterium(b1).
bacterium(b2).
bacterium(b3).
bacterium(b4).
in(b1,c1).
in(b2,c1).
in(b3,c2).
in(b4,c2).
hot(C,result(heat(C),S)).}

\medskip

	When the program is given the goals $sterile(c1,heat(c1,s0))$
\newpage\noindent
and $sterile(c2,heat(c1,s0))$ it answers $yes$ and $no$ respectively.
However, if it is given the goal $sterile(c1,s)$, it will fail because
Prolog lacks what logic programmers call ``constructive negation''.

	The same facts as are used in the first Prolog program can be 
expressed in in a first order language as follows.
%
$$(\forall X)(sterile(X) \equiv  (\forall Y)(bacterium(Y) \wedge  in(Y,X) \supset  dead(Y))),$$

\vspace*{-2ex}


$$(\forall X Y)(hot(X) \wedge  in(Y,X) \supset  hot(Y)),$$

\vspace*{-2ex}

$$(\forall Y)(bacterium(Y) \wedge  hot(Y) \supset  dead(Y)),$$
%
and
%
$$hot(a).$$
%
However, from them we can prove $sterile(a)$ without having
to index over the bacteria.

	Expressibility in Horn clauses, whether supplemented by
negation as failure or not, is an important property of a set of
facts and logic programming has been successfully used for many
applications.  However, it seems unlikely to dominate AI
programming as some of its advocates hope.

	Although  third level systems express both facts and rules
as logical sentences, they are still rather specialized.  The axioms
with which the programs begin are not general truths about the world
but are sentences whose meaning and truth is limited to the narrow
domain in which the program has to act.  For this reason, the ``facts''
of one program usually cannot be used in a database for other programs.

\medskip

	4. The fourth level is still a goal.  It involves representing
general facts about the world as logical sentences.  Once put in
a database, the facts can be used by any program.  The facts would
have the neutrality of purpose characteristic of much human information.
The supplier of information would not have to understand
the goals of the potential user or how his mind works.  The present
ways of ``teaching'' computer programs by modifying them or
directly modifying their databases amount to ``education
by brain surgery''.

	A key problem for achieving the fourth level is to develop
a language for a general common-sense database.  This is difficult,
because the {\it common-sense informatic situation} is complex.
Here is a preliminary list of features and
considerations.

\medskip

	1. Entities of interest are known only partially, and the
information about entities and their relations that may be relevant
to achieving goals cannot be permanently separated from irrelevant
information.  
%
(Contrast this with the situation in gravitational
astronomy in which it is stated in the informal introduction to
a lecture or textbook that
the chemical composition and shape of a body are irrelevant to the
theory; all that counts is the body's mass, and its initial position
and velocity.)

	Even within gravitational astronomy, non-equational theories arise
and relevant information may be difficult to determine.  For example, it was
recently proposed that periodic extinctions discovered in the
paleontological record are caused by showers of comets induced by a
companion star to the sun that encounters and disrupts the Oort cloud of
comets every time it comes to perihelion.  This theory is qualitative
because neither the orbit of the hypothetical star nor those of the comets
is available.

\medskip

	2. The formalism has to be {\it epistemologically adequate},
a notion introduced in (McCarthy and Hayes 1969).  This means that
the formalism must be capable of representing the information that
is actually available, not merely capable of representing actual
complete states of affairs.

	For example, it is insufficient to have a formalism that
can represent the positions and velocities of the particles in a
gas.  We can't obtain that information, our largest computers don't
have the memory to store it even if it were available, and our
fastest computers couldn't use the information to make predictions even
if we could store it.

	As a second example, suppose we need to be able to predict
someone's behavior.  The simplest example is a clerk in a store.
The clerk is a complex individual about whom a customer may know
little.  However, the clerk can usually be counted on to accept
money for articles brought to the counter, wrap them as appropriate
and not protest when the customer then takes the articles from the store.
The clerk can also be counted on to object if the customer attempts
to take the articles without paying the appropriate price.  Describing
this requires a formalism capable of representing information about
human social institutions.  Moreover, the formalism must be capable
of representing partial information about the institution, such as
a three year old's knowledge of store clerks.  For example, a three
year old doesn't know the clerk is an employee or even what that
means.  He doesn't require detailed information about the clerk's
psychology, and anyway this information is not ordinarily available.

	The following sections deal mainly with the advances we see
as required to achieve the fourth level of use of logic in AI.

\smallskip

\begin{center}   %\jplsection{Formalized Nonmonotonic Reasoning}
{\footnotesize 2. FORMALIZED NONMONOTONIC REASONING} 
\end{center}

\vspace*{-.1cm}

	It seems that fourth level systems require extensions
to mathematical logic.  One kind of extension is formalized {\it nonmonotonic
reasoning}, first proposed in the late 1970s (McCarthy 1977, 1980, 1986),
(Reiter 1980), (McDermott and Doyle 1980), (Lifschitz 1989a).
Mathematical logic has been monotonic
in the following sense.  If we have $A \vdash p$ and $A ⊂ B$, then we also
have $B \vdash p$.

	If the inference is logical deduction, then exactly the same
proof that proves $p$ from $A$ will serve as a proof from $B$. If the
inference is model-theoretic, i.e.  $p$ is true in all models of $A$,
then $p$ will be true in all models of $B$, because the models of $B$
will be a subset of the models of $A$.  So we see that the monotonic
character of traditional logic doesn't depend on the details of the
logical system but is quite fundamental.

	While much human reasoning is monotonic,
some important human common-sense reasoning is not.  We
reach conclusions from certain premisses that we would not reach if
certain other sentences were included in our premisses.  For example,
if I hire you to build me a bird cage, you conclude that it is appropriate
to put a top on it, but when you learn the further
fact that my bird is a penguin  you no longer draw that
conclusion.  Some people think it is possible to try to save
monotonicity by saying that what was in your mind was not a general rule
about birds flying but a probabilistic rule.  So
far these people have not worked out any detailed
epistemology for this approach, i.e.  exactly what probabilistic
sentences should be used.  Instead AI has moved to directly formalizing
nonmonotonic logical reasoning.  Indeed it seems to me that
when probabilistic reasoning (and not just the axiomatic
basis of probability theory) has been fully formalized, it will
be formally nonmonotonic.

	Nonmonotonic reasoning is an active field of study.
Progress is often driven by examples, e.g. the Yale shooting
problem (Hanks and McDermott 1986), in which obvious
axiomatizations used with the available reasoning formalisms
don't seem to give the answers intuition suggests.  One direction
being explored (Moore 1985, Gelfond 1987, Lifschitz 1989a)
involves putting facts about belief and knowledge explicitly in
the axioms\linebreak{}---even when the axioms concern nonmental domains.
Moore's classical example (now 4 years old) is ``If I had an elder
brother I'd know it.''

	Kraus and Perlis (1988) have proposed to divide much nonmonotonic
reasoning into two steps.  The first step uses Perlis's (1988)
autocircumscription to get a second order formula characterizing
what is possible.  The second step involves default reasoning to
choose what is normally to be expected out of the previously established
possibilities.  This seems to be a promising approach.

(Ginsberg 1987) collects the main papers up to 1986.  Lifschitz (1989c)
summarizes some example research problems of nonmonotonic reasoning.

\smallskip

\begin{center}  %\jplsection{Some Formalizations and their Problems}
{\footnotesize 3. SOME FORMALIZATIONS AND THEIR PROBLEMS} 
\end{center}


\vspace*{-.1cm}


	(McCarthy 1986) discusses several formalizations, proposing
those based on nonmonotonic reasoning as improvements of earlier
ones.  Here are some.

\medskip

	1. Inheritance with exceptions.  Birds normally fly, but there
are exceptions, e.g. ostriches and birds whose feet are encased in
concrete.  The first exception might be listed in advance, but the
second has to be derived or verified when mentioned on the basis of
information about the mechanism of flying and the properties of
concrete.

	There are many ways of nonmonotonically axiomatizing the
facts about which birds can fly.  The following axioms using
a predicate $ab$ standing for ``abnormal'' seem
to me quite straightforward.
%\leql{a4a:}
%$$(\forall x)(\neg ab(aspect1(x)) \supset  \neg flies(x)).\leql{aiva}$$
%
%

\medskip

\noindent $(1)\hfil(\forall x)(\neg ab(aspect1(x)) \supset  \neg flies(x))\hfil$

\medskip

%
Unless an object is abnormal in $aspect1$, it can't fly.

	It wouldn't work to write $ab(x)$ instead of $ab(aspect1(x))$,
because we don't want a bird that is abnormal with respect to its ability
to fly to be automatically abnormal in other respects.  Using aspects limits
the effects of proofs of abnormality.
%leql{a5:}
%$$(\forall x)(bird(x) \supset  ab(aspect1(x))).\leql{av}$$
%leql{a6:}
%

\medskip

\noindent $(2)\hfil(\forall x)(bird(x) \supset  ab(aspect1(x))).\hfil$

%
%
%$$(\forall x)(bird(x) \wedge\neg ab(aspect2(x)) \supset flies(x))\leql{avi}$$
%
%

\smallskip

\noindent $(3)\hfil(\forall x)(bird(x) \wedge
\neg ab(aspect2(x)) \supset flies(x)).\hfil$

\medskip

%
Unless a bird is abnormal in $aspect2$, it can fly.

	When these axioms are combined with other facts about the
problem, the predicate $ab$ is then to be {\it circumscribed}, i.e.
given its minimal extent compatible with the facts being taken
into account.  This has the effect that a bird will be considered
to fly unless other axioms imply that it is abnormal in
%$aspect2$. (\eqref{av}) is called a cancellation of inheritance
$aspect2$. (2) is called a cancellation of inheritance
axiom, because it explicitly cancels the general presumption that
objects don't fly.  This approach works fine when the inheritance
hierarchy is given explicitly.  More elaborate approaches, some
of which are introduced in (McCarthy 1986) and improved in (Haugh
1988), are required when hierarchies with indefinite numbers of
sorts are considered.

\medskip

	2. (McCarthy 1986) contains a similar treatment of the
effects of actions like moving and painting blocks using the
situation calculus.  Moving and painting are axiomatized entirely
separately, and there are no axioms saying that moving a block
doesn't affect the positions of other blocks or the colors of
blocks.  A general ``common-sense law of inertia''
%
%$$(\forall  p e s)(holds(p,s) \wedge  \neg ab(aspect1(p,e,s)) 
%\supset  holds(p,result(e,s))),$$
%
%
\first{(\forall p e s)(holds(p,s) \wedge  \neg ab(aspect1(p,e,s)) \supset}{}
\next{holds(p,result(e,s))),}
%
asserts that a fact $p$ that holds in a situation $s$ is presumed
to hold in the situation $result(e,s)$ that results from an event
$e$ unless there is evidence to the contrary.  Unfortunately, Lifschitz
(1985 personal communication) and Hanks and McDermott (1986)
showed that simple treatments of the common-sense law of inertia
admit unintended models.  Several
 authors have given more elaborate
treatments, but in my opinion, the results are not yet entirely
satisfactory.  The best treatment so far seems to be that of
(Lifschitz 1987).

\smallskip

\begin{center}  %\jplsection{Ability, Practical Reason and Free Will}
{\footnotesize 4. ABILITY, PRACTICAL REASON AND FREE WILL} 
\end{center}


\vspace*{-.18cm}


	An AI system capable of achieving goals in the common-sense
world will have to reason about what it and other actors can and
cannot do.  For concreteness, consider a robot that must act in the
same world as people and perform tasks that people give it.  Its need
to reason about its abilities puts the traditional philosophical
problem of free will in the following form.  What view shall we build
into the robot about its own abilities, i.e. how shall we make it
reason about what it can and cannot do?  (Wishing to avoid begging
any questions, by {\it reason} we mean {\it compute} using axioms,
observation sentences, rules of inference and nonmonotonic rules of
conjecture.)

	Let $A$ be a task we want the robot to perform, and let $B$
and $C$ be alternate intermediate goals either of which would
allow the accomplishment of $A$.  We want the robot to be able
to choose between attempting $B$ and attempting $C$.  It would be
silly to program it to reason: ``I'm a robot and a deterministic
device.  Therefore, I have no choice between $B$ and $C$.  What
I will do is determined by my construction.''  Instead it must
decide in some way which of $B$ and $C$ it can accomplish.  It
should be able to conclude in some cases that it can accomplish
$B$ and not $C$, and therefore it should take $B$ as a subgoal
on the way to achieving $A$.  In other cases it should conclude
that it {\it can} accomplish either $B$ or $C$ and should choose
whichever is evaluated as better according to the criteria we
provide it.

	(McCarthy and Hayes 1969) proposes conditions on the
semantics of any formalism within which the robot should reason.
The essential idea is that what the robot can do is determined by
the place the robot occupies in the world---not by its internal
structure.  For example, if a certain sequence of outputs from
the robot will achieve $B$, then we conclude or it concludes that
the robot can achieve $B$ without reasoning about whether the
robot will actually produce that sequence of outputs.

	Our contention is that this is approximately how any
system, whether human or robot, must reason about its ability to
achieve goals.  The basic formalism will be the same, regardless
of whether the system is reasoning about its own abilities
or about those of other systems including people.

	The above-mentioned paper also discusses the complexities
that come up when a strategy is required to achieve the goal and
when internal inhibitions or lack of knowledge have to be taken
into account.

\begin{center}  %\jplsection{Three Approaches to Knowledge and Belief}
{\footnotesize 5. THREE APPROACHES TO KNOWLEDGE AND BELIEF} 
\end{center}

\vspace*{-.18cm}

	Our robot will also have to reason about its own knowledge
and that of other robots and people.

	This section contrasts the approaches to knowledge and
belief characteristic of philosophy, philosophical logic and
artificial intelligence.  Knowledge and belief have long been
studied in epistemology, philosophy of mind and in philosophical
logic.  Since about 1960, knowledge and belief have also been
studied in AI.  (Halpern 1986) and (Vardi 1988) contain recent
work, mostly oriented to computer science including AI.

	It seems to me that philosophers have generally treated
knowledge and belief as {\it complete natural kinds}.  According
to this view there is a fact to be discovered about what
beliefs are.  Moreover, once it is decided what the objects of
belief are (e.g. sentences or propositions), the definitions of
belief ought to determine for each such object $p$ whether the
person believes it or not.  This last is the completeness mentioned
above.  Of course, only human and sometimes animal beliefs have
mainly been considered.  Philosophers have differed about whether
machines can ever be said to have beliefs, but even those who admit
the possibility of machine belief consider that what beliefs are
is to be determined by examining human belief.

	The formalization of knowledge and belief has been studied
as part of philosophical logic, certainly since Hintikka's book (1964),
but much of the earlier work in modal logic can be seen as applicable.
Different logics and axioms systems sometimes correspond to the
distinctions that less formal philosophers make, but sometimes the
mathematics dictates different distinctions.

	AI takes a different course because of its different objectives,
but I'm inclined to recommend this course to philosophers also, partly
because we want their help but also because I think it has
philosophical advantages.

	The first question AI asks is: Why study knowledge and belief
at all?  Does a computer program solving problems and achieving goals
in the common-sense world require beliefs, and must it use sentences
about beliefs?  The answer to both questions is approximately yes.
At least there have to be data structures whose usage corresponds
closely to human usage in some cases.  For example, a robot that
could use the American air transportation system has to know that
travel agents know airline schedules, that there is a book (and now a
computer accessible database) called the OAG that contains this
information.  If it is to be able to plan a trip with intermediate
stops it has to have the general information that the departure gate
from an intermediate stop is not to be discovered when the trip is
first planned but will be available on arrival at the intermediate
stop.  If the robot has to keep secrets, it has to know about how
information can be obtained by inference from other information, i.e.
it has to have some kind of information model of the people from whom
it is to keep the secrets.

	However, none of this tells us that the notions of
knowledge and belief to be built into our computer programs must
correspond to the goals philosophers have been trying to
achieve.  For example, the difficulties involved in building a
system that knows what travel agents know about airline schedules
are not substantially connected with questions about how the
travel agents can be absolutely certain.  Its notion of knowledge
doesn't have to be complete; i.e.  it doesn't have to determine
in all cases whether a person is to be regarded as knowing a
given proposition.  For many tasks it doesn't have to have
opinions about when true belief doesn't constitute knowledge.
The designers of AI systems can try to evade philosophical
puzzles rather than solve them.

	Maybe some people would suppose that if the question of
certainty is avoided, the problems formalizing knowledge and
belief become straightforward.  That has not been our experience.

	As soon as we try to formalize the simplest puzzles involving
knowledge, we encounter difficulties that philosophers have rarely
if ever attacked.

	Consider the following puzzle of Mr.~S and Mr.~P.

\medskip

	{\it Two numbers $m$ and $n$ are chosen such that $2 \leq  m \leq  n \leq  99$.
Mr.~S is told their sum and Mr.~P is told their product.  The following
dialogue ensues:}

\begin{quote}

{\it
Mr.~P:	I don't know the numbers.\\
Mr.~S: \parbox[t]{8.5cm}{I knew you didn't know them.  I don't know
them either.}\\
Mr.~P:	Now I know the numbers.\\
Mr.~S:	Now I know them too.

\smallskip

In view of the above dialogue, what are the numbers?}

\end{quote}

	Formalizing the puzzle is discussed in (McCarthy 1989).
For the present we mention only the following aspects.

\medskip

	1. We need to formalize {\it knowing what}, i.e. knowing what
the numbers are, and not just {\it knowing that}.

\medskip

	2. We need to be able to express and prove non-knowledge as well as
knowledge.  Specifically we need to be able to express the fact that as
far as Mr.~P knows, the numbers might be any pair of factors of the known
product.

\medskip

	3. We need to express the joint knowledge of Mr.~S and Mr.~P of
the conditions of the problem.

\medskip

	4. We need to express the change of knowledge with time, e.g.
how Mr.~P's knowledge changes when he hears Mr.~S say that he knew that
Mr.~P didn't know the numbers and doesn't know them himself.
This includes inferring what Mr.~S and Mr.~P still won't know.

\medskip

	The first order language used to express the facts of this
problem involves an accessibility relation $A(w1,w2,p,t)$,
modeled on Kripke's semantics for modal logic.  However, the
accessibility relation here is in the language itself rather than
in a metalanguage.  Here $w1$ and $w2$ are possible worlds, $p$
is a person and $t$ is an integer time.  The use of possible
worlds makes it convenient to express non-knowledge.  Assertions
of non-knowledge are expressed as the existence of accessible
worlds satisfying appropriate conditions.

	The problem was successfully expressed in the language
in the sense that an arithmetic condition determining the values
of the two numbers can be deduced from the statement.  However, this
is not good enough for AI.  Namely, we would like to include facts
about knowledge in a general purpose common-sense database.  Instead
of an {\it ad hoc} formalization of Mr.~S and Mr.~P, the problem
should be solvable from the same general facts about knowledge that
might be used to reason about the knowledge possessed by travel agents
supplemented only by the facts about the dialogue.  Moreover, the
language of the general purpose database should accommodate all
the modalities that might be wanted and not just knowledge.  This
suggests using ordinary logic, e.g. first order logic, rather than
modal logic, so that the modalities can be ordinary functions or
predicates rather than modal operators.

	Suppose we are successful in developing a ``knowledge formalism''
for our common-sense database that enables the program controlling
a robot to solve puzzles and plan trips and do the other tasks that
arise in the common-sense environment requiring reasoning about knowledge.
It will surely be asked whether it is really {\it knowledge} that
has been formalized.  I doubt that the question has an answer.
This is perhaps the question of whether knowledge is a natural kind.

	I suppose some philosophers would say that such problems are
not of philosophical interest.  It would be unfortunate, however, if
philosophers were to abandon such a substantial part of epistemology
to computer science.  This is because the analytic skills that
philosophers have acquired are relevant to the problems.

\newpage

\begin{center}
{ \footnotesize 6. REIFYING CONTEXT} %\jplsection{Reifying Context}
\end{center}

%contex[w89,jmc]		Reifying context - for paper for Thomason

\vspace*{-.2cm}

	We propose the formula $\mbox{\em holds}(p,c)$ to assert that the
proposition $p$ holds in context $c$.  It expresses explicitly
how the truth of an assertion depends on context.  The relation
$c1 \leq c2$ asserts that the context $c2$ is more general than
the context $c1$.

	Formalizing common-sense reasoning needs contexts as objects,
in order to match human ability to consider context
explicitly.  The proposed database of general common-sense knowledge
will make assertions in a general context called $C0$.  However, $C0$
cannot be maximally general, because it will surely involve unstated
presuppositions.  Indeed we claim that there can be no
maximally general context.  Every context involves unstated presuppositions,
both linguistic and factual.

	Sometimes the reasoning system will
have to transcend $C0$, and tools will have to be provided to do
this.  For example, if Boyle's law of the dependence of the volume
of a sample of gas on pressure were built into $C0$, discovery of
its dependence on temperature would have to trigger a process of 
generalization
that might lead to the perfect gas law.

	The following ideas about how the formalization might
proceed are tentative.  Moreover, they appeal to recent logical
innovations in the formalization of nonmonotonic reasoning. In
particular, there
will be nonmonotonic ``inheritance rules'' that allow default
inference from $\mbox{\em holds}(p,c)$ to $\mbox{\em holds}(p,c')$, where $c'$ is
either more general or less general than $c$.

	Almost all previous discussion of context has been in
connection with natural language, and the present paper
relies heavily on examples from natural language.  However, I
believe the main AI uses of formalized context will not be in
connection with communication but in connection with reasoning
about the effects of actions directed to achieving goals.  It's
just that natural language examples come to mind more readily.

	As an example of intended usage, consider
%
$$\mbox{\em holds}(\mbox{\em at}(\mbox{\em he},\mbox{\em
inside}(\mbox{\em car})),c17).$$
%
Suppose that this sentence is intended to assert that a
particular person is in a particular car on a particular occasion,
i.e. the sentence is not just being used as a
linguistic example but is meant seriously.  A corresponding
English sentence is ``He's in the car'' where who he is and which
car and when is determined by the context in which the sentence
is uttered.  Suppose, for simplicity, that the sentence is said
by one person to another in a situation in which the car is
visible to the speaker but not to the hearer and the time at
which the the subject is asserted to be in the car is the same
time at which the sentence is uttered.

	In our formal language $c17$ has to carry the information about
who he is, which car and when.

	Now suppose that the same fact is to be conveyed as in
example 1, but the context is a certain Stanford Computer Science
Department 1980s context.  Thus familiarity with cars is
presupposed, but no particular person, car or occasion is
presupposed.  The meanings of certain names is presupposed, however.
We can call that context (say) $c5$.  This more general context requires
a more explicit proposition; thus, we would have
%
%$$\mbox{\em holds}(at(``Timothy McCarthy'',inside((\iota x)(iscar(x)\wedge 
%belongs(x,``John McCarthy'')))),c5).$$
%
\first{\mbox{\em holds}(\mbox{\em at}(\mbox{\em ``Timothy
McCarthy''},\mbox{\em inside}((\iota x)(\mbox{\em iscar}(x)\;\wedge }{}
\next{\wedge\; \mbox{\em belongs}(x,\mbox{\em ``John McCarthy''})))),c5).}
%
	A yet more general context might not identify a
specific John McCarthy, so that even this more explicit sentence would need
more information.  What would constitute an adequate identification
might also be context dependent.

	Here are some of the properties formalized contexts might have.

\medskip

	1. In the above example, we will have $c17 \leq  c5$, i.e. $c5$ is
more general than $c17$.
There will be nonmonotonic rules like
%
%$$(\forall  c1\ c2\ p)(c1 \leq  c2) \wedge  \mbox{\em holds}(p,c1) \wedge  
%\neg ab1(p,c1,c2) \supset  \mbox{\em holds}(p,c2)$$
%
\first{(\forall c1\ c2\ p)(c1 \leq  c2) \wedge  
\mbox{\em holds}(p,c1) \wedge  \neg ab1(p,c1,c2) \supset}{}
\next{  \mbox{\em holds}(p,c2)}
%
and
%
%$$(\forall  c1\ c2\ p)(c1 \leq  c2) \wedge  \mbox{\em holds}(p,c2) \wedge
%\neg ab2(p,c1,c2) \supset  \mbox{\em holds}(p,c1).$$
%
% VLADIMIR SUGGESTS THAT THESE ARE INSUFFIENTLY GENERAL
%
\first{(\forall  c1\ c2\ p)(c1 \leq  c2) \wedge  \mbox{\em holds}(p,c2) 
\wedge\neg ab2(p,c1,c2)\supset  }{}
\next{\mbox{\em holds}(p,c1).}
%
Thus there is nonmonotonic inheritance both up and down in the generality
hierarchy.

\medskip

	2. There are functions forming new contexts by specialization.
We could have something like
%
%$$c19 = specialize({he = Timothy McCarthy,belongs(car, John McCarthy)},c5).$$

\first{c19 = \mbox{\em specialize}(\mbox{\em he} = \mbox{\em Timothy
McCarthy},}{} 
\next{\mbox{\em belongs}(\mbox{\em car}, \mbox{\em John McCarthy}),c5).}

We will have $c19 \leq  c5$.

\medskip

	3. Besides $\mbox{\em holds}(p,c)$, we may have $\mbox{\em
value}(\mbox{\em term},c)$, where $\mbox{\em term}$ is a term.  The domain in
which $\mbox{\em term}$ takes values is defined in some outer context.

\medskip

	4. Some presuppositions of a context are linguistic and some
are factual.  In the above example, it is a linguistic matter who the
names refer to.  The properties of people and cars are factual, e.g.
it is presumed that people fit into cars.

\medskip

	5. We may want meanings as abstract objects.  Thus we might
have
%
$$\mbox{\em meaning}(\mbox{\em he},c17) = \mbox{\em
meaning}(\mbox{\em ``Timothy McCarthy''},c5).$$

\medskip

	6. Contexts are ``rich'' entities not to be fully described.
Thus the ``normal English language context'' contains factual assumptions
and linguistic conventions that a particular English speaker may not
know.  Moreover, even assumptions and conventions in a context that
may be individually accessible cannot be exhaustively listed.  A person
or machine may know facts about a context without ``knowing the context''.

	7. Contexts should not be confused with the situations of the
situation calculus of (McCarthy and Hayes 1969).  Propositions about
situations can hold in a context.  For example, we may have
%
%$$\mbox{\em holds}(\mbox{\em Holds}1(at(I,airport),
%result(drive-to(airport,result(walk-to(car),S0))),c1).$$
%
\first{\mbox{\em holds}(\mbox{\em Holds}1(at(I,\mbox{\em airport}),
\mbox{\em result}(\mbox{\em drive-to}(\mbox{\em airport},}{}
\next{\mbox{\em result}(\mbox{\em walk-to}(car),S0))),c1).}
%
This can be interpreted as asserting that under the assumptions embodied
in context $c1$, a plan of walking to the car and then driving to the airport
would get the robot to the airport starting in situation $S0$.

\medskip

	8. The context language can be made more like natural
language and more extensible if we introduce notions of entering
and leaving a context.  These will be analogous to the notions
of making and discharging assumptions in natural deduction systems,
but the notion seems to be more general.  Suppose we have $\mbox{\em holds}(p,c)$.
We then write

\medskip

\noindent $\mbox{\em enter c}$.

\medskip

\noindent This enables us to write $p$ instead of $\mbox{\em holds}(p,c)$.
If we subsequently infer $q$, we can replace it by $\mbox{\em holds}(q,c)$
and leave the context $c$.  Then $\mbox{\em holds}(q,c)$ will itself hold in
the outer context in which $\mbox{\em holds}(p,c)$ holds.  When a context
is entered, there need to be restrictions analogous to those
that apply in natural deduction when an assumption is made.

	One way in which this notion of entering and leaving contexts
is more general than natural deduction is that formulas like
$\mbox{\em holds}(p,c1)$ and (say) $\mbox{\em holds}(\mbox{\em not}
p,c2)$ behave differently from $c1 \supset p$ and $c2 \supset \neg p$
which are their natural deduction analogs.  For example, if $c1$ is
associated with the time 5pm and $c2$ is associated with the time 6pm
and $p$ is $at(I, \mbox{\em office})$, then $\mbox{\em holds}(p,c1) \wedge
\mbox{\em holds}(not\ p,c2)$ might be used to infer that I left the
office between 5pm and 6pm.  $(c1 \supset p) \wedge (c2 \supset \neg
p)$ cannot be used in this way; in fact it is equivalent to $\neg c1
\vee \neg c2$.

\medskip

	9. The expression $\mbox{\em Holds}(p,c)$ (note the caps) represents
the proposition that $p$ holds in $c$.  Since it is a proposition,
we can assert $\mbox{\em holds}(\mbox{\em Holds}(p,c),c')$.

\medskip

	10. Propositions will be combined by functional analogs of 
the Boolean operators as discussed in (McCarthy 1979b).
Treating propositions involving quantification is
necessary, but it is difficult to determine the right formalization.

\medskip

	11. The major goals of research into formalizing context
should be to determine the rules that relate contexts to their
generalizations and specializations.  Many of these rules will
involve nonmonotonic reasoning.

\newpage %\smallskip

\begin{center}
{\footnotesize 7. REMARKS} %\jplsection{Remarks}
\end{center}


\vspace*{-.1cm}


	The project of formalizing common-sense knowledge and
reasoning raises many new considerations in epistemology and
also in extending logic.  The role that the following ideas
might play is not clear yet.

\medskip

\noindent {\em Epistemological Adequacy often Requires Approximate Partial Theories}

	(McCarthy and Hayes 1969) introduces the notion of epistemological
adequacy of a formalism.  The idea is that the formalism used by
an AI system must be adequate to represent the information that
a person or program with given opportunities to observe can actually
obtain.  Often an epistemologically adequate formalism for some
phenomenon cannot take the form of a classical scientific theory.
I suspect that some people's demand for a classical scientific
theory of certain phenomena leads them to despair about formalization.
Consider a theory of a dynamic phenomenon, i.e. one that changes
in time.  A classical scientific theory represents the state of
the phenomenon in some way and describes how it evolves with time, most
classically by differential equations.

	What can be known about common-sense phenomena usually doesn't
permit such complete theories.  Only certain states permit prediction
of the future.  The phenomenon arises in science and engineering
theories also, but I suspect that philosophy of science sweeps these
cases under the rug.  Here are some examples.

	(1) The theory of linear electrical circuits is complete
within its model of the phenomena.  The theory gives the response
of the circuit to any time varying voltage.  Of course, the theory
may not describe the actual physics, e.g. the current may overheat
the resistors.  However, the theory of sequential digital circuits
is incomplete from the beginning.  Consider a circuit built from
NAND-gates and D flipflops and timed synchronously by an appropriate
clock.  The behavior of a D flipflop is defined by the theory
when one of its inputs is 0 and the other is 1 when the inputs
are appropriately clocked.  However, the behavior is not defined
by the theory when both inputs are 0 or both are 1.  Moreover,
one can easily make circuits in such a way that both
inputs of some flipflop get 0 at some time.

	This lack of definition is not an oversight.  The actual
signals in a digital circuit are not ideal square waves but have
finite rise times and often overshoot their nominal values.
However, the circuit will behave as though the signals were
ideal provided the design rules are obeyed.  Making both
inputs to a flipflop nominally 0 creates a situation in
which no digital theory can describe what happens, because
the behavior then depends on the actual time-varying signals
and on manufacturing variations in the flipflops.

	(2) Thermodynamics is also a partial theory.  It tells
about equilibria and it tells which directions reactions go, but
it says nothing about how fast they go.

	(3) The common-sense database needs a theory of the
behavior of clerks in stores.  This theory should cover
what a clerk will do in response to bringing items to the
counter and in response to a certain class of inquiries.
How he will respond to other behaviors is not defined by
the theory.

	(4) (McCarthy 1979a) refers to a theory of skiing that
might be used by ski instructors.  This theory regards the skier
as a stick figure with movable joints.  It gives the consequences
of moving the joints as it interacts with the shape of the ski
slope, but it says nothing about what causes the joints to be
moved in a particular way.  Its partial character corresponds
to what experience teaches ski instructors.  It often assigns
truth values to counterfactual conditional assertions like, ``If
he had bent his knees more, he wouldn't have fallen''.

\medskip

\noindent {\em Meta-epistemology}
% meta[s88,jmc]		Message to AILIST on metaepistemology
% meta[e85,jmc]		Meta-epistemology
% metaep[f82,jmc]		A proposal for meta-epistemology

	If we are to program a computer to think about its own
methods for gathering information about the world, then it needs
a language for expressing assertions about the relation between
the world, the information gathering methods available to an
information seeker and what it can learn.  This leads to a subject
I like to call meta-epistemology.  Besides its potential applications
to AI, I believe it has applications to philosophy considered in
the traditional sense.

	Meta-epistemology is proposed as a mathematical theory
in analogy to metamathematics.  Metamathematics considers the
mathematical properties of mathematical theories as objects.
In particular model theory as a branch of metamathematics deals
with the relation between theories in a language and interpretations
of the non-logical symbols of the language.  These interpretations
are considered as mathematical objects, and we are only sometimes
interested in a preferred or true interpretation.

	Meta-epistemology considers the relation between the world,
languages for making assertions about the world, notions of what
assertions are considered meaningful, what are accepted as rules
of evidence and what a knowledge seeker can discover about the
world.  All these entities are considered as mathematical objects.
In particular the world is considered as a parameter.
Thus meta-epistemology has the following characteristics.

\medskip

	1. It is a purely mathematical theory.  Therefore, its
controversies, assuming there are any, will be mathematical
controversies rather than controversies about what the real world
is like.  Indeed metamathematics gave many philosophical issues
in the foundations of mathematics a technical content.  For
example, the theorem that intuitionist arithmetic and Peano
arithmetic are equi-consistent removed at least one area of
controversy between those whose mathematical intuitions support
one view of arithmetic or the other.

\medskip

	2. While many modern philosophies of science assume some
relation between what is meaningful and what can be verified or
refuted, only special meta-epistemological systems will have the
corresponding mathematical property that all aspects of the world
relate to the experience of the knowledge seeker.

	This has several important consequences for the task of
programming a knowledge seeker.

	A knowledge seeker should not have a priori prejudices
(principles) about what concepts might be meaningful.  Whether
and how a proposed concept about the world might ever connect
with observation may remain in suspense for a very long time
while the concept is investigated and related to other concepts.

	We illustrate this by a literary example.  Moli\'ere's
play {\it La Malade Imaginaire} includes a doctor who explains
sleeping powders by saying that they contain a ``dormitive
virtue''.  In the play, the doctor is considered a pompous fool
for offering a concept that explains nothing.  However, suppose
the doctor had some intuition that the dormitive virtue might be
extracted and concentrated, say by shaking the powder in a
mixture of ether and water.  Suppose he thought that he would get
the same concentrate from all substances with soporific effect.
He would certainly have a fragment of scientific theory subject
to later verification.  Now suppose less---namely, he only
believes that a common component is behind all substances whose
consumption makes one sleepy but has no idea that he should try
to invent a way of verifying the conjecture.  He still has
something that, if communicated to someone more scientifically
minded, might be useful.  In the play, the doctor obviously sins
intellectually by claiming a hypothesis as certain.  Thus a
knowledge seeker must be able to form new concepts that have only
extremely tenuous relations with their previous linguistic
structure.

\medskip

\noindent {\em Rich and poor entities}

	Consider my next trip to Japan.  Considered as a plan it is
a discrete object with limited detail.  I do not yet even plan to
take a specific flight or to fly on a specific day.  Considered as
a future event, lots of questions may be asked about it.  For example,
it may be asked whether the flight will depart on time and what precisely
I will eat on the airplane.  We propose characterizing the actual trip
as a rich entity and the plan as a poor entity.  Originally, I thought
that rich events referred to the past and poor ones to the future, but
this seems to be wrong.  It's only that when one refers to the past
one is usually referring to a rich entity, while the future entities
one refers to are more often poor.  However, there is no intrinsic
association of this kind.  It seems that planning requires reasoning
about the plan (poor entity) and the event of its execution (rich
entity) and their relations.

	(McCarthy and Hayes 1969) defines situations as rich entities.
However, the actual programs that have been written to reason in
situation calculus might as well regard them as taken from a
finite or countable set of discrete states.

	Possible worlds are also examples of rich entities as
ordinarily used in philosophy.  One never prescribes a possible
world but only describes classes of possible worlds.

	Rich entities are open ended in that we can always introduce
more properties of them into our discussion.  Poor entities can often
be enumerated, e.g. we can often enumerate all the events that we
consider reasonably likely in a situation.  The passage from considering
rich entities in a given discussion to considering poor entities is
a step of nonmonotonic reasoning.

	It seems to me that it is important to get a good formalization
of the relations between corresponding rich and poor entities.
This can be regarded as formalizing the relation between the world
and a formal model of some aspect of the world, e.g. between the
world and a scientific theory.

\begin{center}
{\footnotesize 8. ACKNOWLEDGEMENTS} %\jplsection{Acknowledgements}
\end{center}

\vspace*{-.15cm}

	I am indebted to Vladimir Lifschitz and Richmond Thomason for
useful suggestions.  Some of the prose is taken from (McCarthy 1987),
but the examples are given more precisely in the present paper, since
{\it Daedalus} allows no formulas. 

	The research reported here was partially supported by the
Defense Advanced Research Projects Agency, Contract No.\linebreak
N00039-84-C-0211.

\begin{center}
{\footnotesize REFERENCES} 
\end{center} 

\vspace*{-.25cm}

\footnotesize


\smallskip

\noindent {\bf Dennett, D.C. (1971)}: ``Intentional Systems'', {\it
Journal of Philosophy,} vol. 68, No. 4, Feb. 25.

\smallskip

\noindent {\bf Dreyfus, Hubert L. (1972):} {\it What Computers Can't
Do: the Limits of Artificial Intelligence}, revised edition 1979, New
York : Harper \&{} Row.

\smallskip

\noindent {\bf Fikes, R, and Nils Nilsson, (1971)}: ``STRIPS: A New
Approach to the Application of Theorem Proving to Problem Solving'',
{\it Artificial Intelligence}, Volume 2, Numbers 3,4, January, pp.
189-208.

\smallskip

\noindent
{\bf Gelfond, M. (1987)}: ``On Stratified Autoepistemic Theories'',
 {\it AAAI-87} {\bf 1}, 207-211.

\smallskip

\noindent
{\bf Ginsberg, M. (ed.) (1987)}: {\it Readings in Nonmonotonic Reasoning},
Morgan Kaufmann, 481 pp.

\smallskip

\noindent {\bf Green, C., (1969)}: ``Application of Theorem Proving
to Problem Solving,'' {\it First International Joint Conference on
Artificial Intelligence,} pp. 219-239.

\smallskip

\noindent
{\bf Halpern, J. (ed.) (1986):}
{\it Reasoning about Knowledge}, Morgan Kaufmann,
Los Altos, CA.

\smallskip

\noindent
{\bf Hanks, S. and D. McDermott (1986)}: ``Default Reasoning, Nonmonotonic
Logics, and the Frame Problem'', AAAI-86, pp. 328-333.

\smallskip

\noindent {\bf Haugh, Brian A. (1988)}: ``Tractable Theories of
Multiple Defeasible Inheritance in Ordinary Nonmonotonic Logics'',
{\it Proceedings of the Seventh National Conference on Artificial
Intelligence (AAAI-88)}, Morgan Kaufmann.

\smallskip

\noindent
{\bf Hintikka, Jaakko (1964)}: {\it Knowledge and Belief; an Introduction
 to the Logic of the Two Notions}, Cornell Univ. Press, 179 pp.

\smallskip

\noindent
{\bf Kowalski, Robert (1979)}: {\it Logic for Problem Solving},
North-Holland, Amsterdam.

\smallskip

\noindent
{\bf Kraus, Sarit and Donald Perlis (1988)}: ``Names and Non-Monotonic\-ity'',
UMIACS-TR-88-84, CS-TR-2140, Computer Science Technical Report Series,
University of Maryland, College Park, Maryland 20742.

\smallskip

\noindent
{\bf Lifschitz, Vladimir (1987)}: ``Formal theories of action'',
{\it The Frame Problem in Artificial Intelligence,
Proceedings of the 1987 Workshop}, reprinted in (Ginsberg 1987).

\smallskip

\noindent
{\bf Lifschitz, Vladimir (1989a)}: {\it Between Circumscription and
Autoepistemic Logic,} to appear in the Proceedings of the First
International Conference on Principles of Knowledge Representation
and Reasoning, Morgan Kaufmann.

\smallskip

\noindent
{\bf Lifschitz, Vladimir (1989b)}: ``Circumscriptive Theories: A
Logic-based  Framework for Knowledge Representation,'' this collection.

\smallskip

\noindent
{\bf Lifschitz, Vladimir (1989c)}: ``Benchmark Problems for Formal
Nonmonotonic Reasoning'', {\it Non-Monotonic Reasoning}, 2nd International
Workshop, Grassau, FRG, Springer-Verlag.

\smallskip

\noindent
{\bf McCarthy, John (1959)}: ``Programs with Common Sense'', {\it
Proceedings of the Teddington Conference on the Mechanization of
Thought Processes}, Her Majesty's Stationery Office, London.
%  common[e80,jmc],
% common.tex[e80,jmc]

\smallskip

\noindent {\bf McCarthy, John and P.J. Hayes (1969)}: ``Some
Philosophical Problems from the Standpoint of Artificial
Intelligence'', D. Michie (ed.), {\it Machine Intelligence 4},
American Elsevier, New York, NY.  
% phil.tex[ess,jmc] with slight modifications

\smallskip

\noindent
{\bf McCarthy, John (1977)}:
``On The Model Theory of Knowledge'' (with M. Sato, S. Igarashi, and
T. Hayashi), {\it Proceedings of the Fifth International Joint Conference
on Artificial Intelligence}, M.I.T., Cambridge, Mass.

\smallskip

\noindent
{\bf McCarthy, John (1977)}:
``Epistemological Problems of Artificial Intelligence'', {\it Proceedings
of the Fifth International Joint Conference on Artificial 
Intelligence}, M.I.T., Cambridge, Mass.
%  ijcai.c[e77,jmc]

\smallskip

\noindent
{\bf McCarthy, John (1979a)}:
``Ascribing Mental Qualities to Machines'', {\it Philosophical Perspectives 
in Artificial Intelligence}, Ringle, Martin (ed.), Harvester Press, July 1979.
%  .<<aim 326, MENTAL[F76,JMC],
% mental.tex[f76,jmc]>>

\smallskip

\noindent
{\bf McCarthy, John (1979b)}: 
``First Order Theories of Individual Concepts and Propositions'', 
Michie, Donald (ed.), {\it Machine Intelligence 9}, (University of
Edinburgh Press, Edinburgh).
%  .<<aim 325, concep.tex[e76,jmc]>>

\smallskip

\noindent
{\bf McCarthy, John (1980)}: 
``Circumscription---A Form of Non-Monotonic Reasoning'', {\it Artificial
Intelligence}, Volume 13, Numbers 1,2, April.
%  .<<aim 334, circum.new[s79,jmc], cirnew.tex[s79,jmc]>>

\smallskip

\noindent
{\bf McCarthy, John (1983)}: ``Some Expert Systems Need Common Sense'',
{\it Computer Culture: The Scientific, Intellectual and Social Impact
of the Computer}, Heinz Pagels (ed.), vol. 426, Annals of the New York 
Academy of Sciences.
%paper
%presented at New York Academy of Sciences Symposium.
%  common[e83,jmc]
%common.tex[e83,jmc]

\smallskip

\noindent
{\bf McCarthy, John (1986)}:
``Applications of Circumscription to Formalizing Common Sense Knowledge'',
{\it Artificial Intelligence}, April 1986.
%  circum.tex[f83,jmc]

\smallskip

\noindent {\bf McCarthy, John (1987)}: ``Mathematical Logic in
Artificial Intelligence'', {\it Daedalus}, vol. 117, No. 1,
American Academy of Arts and Sciences, Winter 1988.  
%  logic.2[w87,jmc]

\smallskip

\noindent
{\bf McCarthy, John (1989)}: ``Two Puzzles Involving Knowledge'',
{\it Formalizing Common Sense,} Ablex 1989.


\smallskip

\noindent {\bf McDermott, D. and J. Doyle, (1980)}: ``Non-Monotonic
Logic I'', {\it Artificial Intelligence\/}, Vol. 13, N. 1

\smallskip

\noindent
{\bf Moore, R. (1985)}: ``Semantical Considerations on Nonmonotonic Logic'',
 {\it Artificial Intelligence} {\bf 25} (1), pp.~75-94.

\smallskip

\noindent {\bf Newell, Allen (1981)}: ``The Knowledge Level''. {\it
AI Magazine\/}, Vol. 2, No. 2.

\smallskip

\noindent {\bf Perlis, D. (1988)}: ``Autocircumscription'', {\it
Artificial Intelligence}, {\bf 36} pp.~223-236.

\smallskip

\noindent {\bf Reiter, Raymond (1980)}: ``A Logic for Default
Reasoning'', {\it Artificial Intelligence}, Volume 13, Numbers 1,2,
April.

\smallskip

\noindent
{\bf Russell, Bertrand (1913)}: ``On the Notion of Cause'',
{\it Proceedings of the Aristotelian  Society}, 13, pp.~1-26.

\smallskip

\noindent {\bf Robinson, J. Allen (1965)}: ``A Machine-oriented Logic
Based on the Resolution Principle'', {\it JACM}, 12(1), pp.~23-41.

\smallskip

\noindent {\bf Sterling, Leon and Ehud Shapiro (1986)}: {\it The Art
of Prolog}, MIT Press.

\smallskip

\noindent {\bf Sussman, Gerald J., Terry Winograd, and Eugene
Charniak (1971)}: ``Micro-planner Reference Manual'', Report
AIM-203A, Artificial Intelligence Laboratory, Massachusetts Institute
of Technology, Cambridge.

\smallskip

\noindent {\bf Vardi, Moshe (1988)}: {\it Conference on Theoretical
Aspects of Reasoning about Knowledge}, Morgan Kaufmann, Los Altos,
CA.

\vskip .2in

{\normalsize \it
\noindent Department of Computer Science\\
\noindent Stanford University\\
\noindent Stanford, CA 94305
}

\end{document}


%\vfill\eject\end{document}

\smallskip\centerline{Copyright \copyright\ 1989 by John McCarthy}
\smallskip\noindent{This draft of thomas[f88,jmc]\ TEXed on \jmcdate\ at \theTime}


	We begin with a simpler example than the rule for using
boats.  Suppose that the sentence ``The library has the book''
is being used for communication, i.e. not just being considered
as a sample sentence.  It is being used in a context that
has a time associated with it and which refers to a particular
book under discussion and a particular library.  We propose to
formalize the assertion by
%
$$\mbox{\em holds}(has(library,book),c17),$$
%
where $has$ is conceptually a predicate, but if we are using
first order logic, $has$ is a function whose value is a term
suitable to be the first argument of $holds$.  The context
constant $c17$ should give further specification of the meaning
of $has$, since the sentence could mean either that the book is
in the library at the present moment or that the book is one of
those owned by that library.  This ambiguity may be resolvable in
a language with predicate functions $has1$ and $has2$, but it
isn't obvious that there won't be additional ambiguities within
$has1$ and $has2$ that have to be resolved by context.

	Consider a general 1980s American academic common-sense
context.  Call it $c1$.  In $c1$, the phenomena of books and libraries
are ``sufficiently definite''.  The context is not necessarily associated
with the English language.  You could imagine a discussion in which
one person is speaking English and another is speaking Russian and
they are both communicating with a machine in a suitable first order
logical language.  We won't try to define ``sufficiently definite'',
but the condition would be violated if the hearer went to the wrong
library or returned with the wrong book.

	We might now have the sentence
%
$$\mbox{\em holds}(\mbox{\em time}(1988.dec.14.pst.1540,
\mbox{\em physically}(\mbox{\em has})(\mbox{\em spec}(\mbox{\em
``Stanford_Mathematics''},\mbox{\em library}),
\mbox{\em book}(\mbox{\em Author: Hintikka,Title: Knowledge and Belief}))),c1).$$
%
	Context $c17$ is a specialization of $c1$, and the two
sentences are equivalent.

dec 29 Discuss what happens when a flip-flop has to be used outside
of its specified regime.

meaning(scalpel,c19) = meaning(give(scalpel),c7)

!yet to do
jan 7
discuss at some point elaboration tolerance, epistemological adequacy
and ambiguity tolerance - note ref to dreyfus
probably under remarks

discuss reification in general
analogy with resonances in physics - weak entities

\noindent Reification in general

	A previous section discussed reification of context.  However,
natural language uses many more reifications than that, and it seems
that many of them will be useful in AI.  Here are some examples.

	1. (McCarthy 1980) mentions the missionaries-and-cannibals
problem and discusses the possibility that there is something wrong
with the boat.  In ordinary language, it is sometimes useful to say
that there are two things wrong with the boat, i.e. ``things wrong
with the boat'' can be identified and counted.  It appears that in
ordinary language a broken motor and a leak are two different things,
while the people who fix boats do not regard the boat having a leak
and having a hole as two different things.

	2. 

	Some entities used in common-sense thought and language seem
to be {\it weak entities}.  They are used, but attempts to make them
precise fail.  It is common to propose abandoning them for that reason.
I don't think AI can let itself do that.  Weak entities are useful,
and we need to understand how to treat them theoretically.

!************

sterile(X) :- not[bacterium(Y,X), alive(Y)]