COMMENT ⊗   VALID 00004 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	%nonmon[e88,jmc]		Nonmonotonic reasoning, AI and natural language
C00012 00003	\smallskip\centerline{Copyright \copyright\ \number\year\ by John McCarthy}
C00013 00004
C00014 ENDMK
C⊗;
%nonmon[e88,jmc]		Nonmonotonic reasoning, AI and natural language
\input memo.tex[let,jmc]
\title{Nonmonotonic Reasoning and Natural Language}

	The object of this article is to suggest how formalized
nonmonotonic reasoning, studied in artificial intelligence since 1977,
can shed light on the semantics and syntax of natural language.  In
particular, it offers suggestions on the role of the subjunctive and
of words like ``but'', ``although'' and ``however''.

	AI researchers began to formalize nonmonotonic reasoning
in the late 1970s when they became convinced of two propositions.

	1. Deduction in mathematical logic didn't cover enough of
the non-inductive reasoning people did or that computers would
have to do to behave intelligently.

	2. The tools of mathematical logic were appropriate for
extending it to include nonmonotonic reasoning.

	Mathematical logical deduction is monotonic in the following
sense.  Suppose a proposition $p$ is deducible from a collection $A$ of
propositions.  The standard metamathematical notation for this is
%
$$A \vdash p.$$
%
Suppose further that $A$ is included in a more extensive collection of
propositions $B$, i.e.
%
$$A ⊂ B.$$
%
We will then have
%
$$B \vdash p.$$
%
This property doesn't depend on the details of the logical system, and
it is true for first order logic, higher order logic and the various
forms of modal logic.  If we consider the model-theoretic semantics, i.e.
we assume that $p$ is true in all models of $A$ (written $A \models p$) and
again have $A ⊂ B$, we will again have $B \models p$.  Thus the set of conclusions
is a monotonic increasing function of the set of premisses.  This is
the monotonicity property of logical deduction, and we are concerned with
inference that doesn't have that property.

	Ordinary human reasoning is often nonmonotonic.  The classical
example is that if a bird is mentioned, one assumes that it can fly.
The inference is defeasible by mentioning that the bird is a penguin or 
or is dead or has its feet encased in concrete.  We give a linguistic
example.

\noindent Example 1. Birds normally fly.

	Suppose I hire you to build me a bird cage and you build it without
a top.  A judge will support my refusal to pay on the grounds that
my bird would be able to fly away.  You won't get away with saying that
I never said my bird could fly.  On the other hand if you build it with
a top and I refuse to pay full price on the grounds that my bird is
a penguin, the judge will support you.

	Our interpretation of this example is that it is a convention
of English and other natural languages of our planet that if a bird
can fly the fact needn't be mentioned even if it is important, whereas
if the bird cannot fly the fact must be mentioned if it is important.
It might be argued that it is a matter of probability rather than a
matter of convention, but it works better have a linguistic
convention.  That way, what is inferrable doesn't depend so much on
the probabilities of the particular situation.

	A number of formalizations of nonmonotonic reasoning have been
proposed, and no one of them is presently dominant.  More will be
invented.  Some of the most active at present are circumscription
(McCarthy 1977, 1980, 1986), the logic of defaults (Reiter 1980) and
autoepistemic logic (Moore 198xx).  (Ginsberg 198xx) is a collection
of papers and (Lifschitz 198xx) summarizes the various methods.

\noindent Example 2.  The word ``but''.

	Consider the sentence

\noindent (1) ``I am going to dinner now, but I will return to
the office afterwards''.

	As far as what may be deduced from the
sentence, the word ``but'' may be replaced by ``and'', but this
would sound and read awkwardly.  Why?

	Our hypothesis is as follows.  A listener or reader attempts
to understand the discourse as he receives it, phrase by phrase.
Understanding involves drawing from it such conclusions
as are warranted by what has been heard so far.  In many cases,
these are the conclusions the hearer could draw if the discourse
was interrupted by some external event, and they even more frequently
include the conclusions that the hearer could draw if the speaker
stopped voluntarily at that point.  If the speaker says something
that would be misleading if he stopped, he should indicate the
fact.  The word ``but'' indicates that a conclusion that might
be drawn from the first part of the sentence is not to be drawn.
We can see this by imagining that the speaker was interrupted
after uttering ``but'' in the above sentence.  He won't know
what conclusion he might draw that would be incorrect, but there
is one.  For example, the sentence might have been, ``I am going
to dinner now, but George will stay here and finish the work''.

	The wrong conclusions that might be drawn from the first part
of (1) result from nonmonotonic inference.  The second part of the
sentence doesn't contradict the first or anything that might be {\it
deduced} from it, but it does contradict what might be inferred
nonmonotonically from it.  My use of ``but'' in the immediately
previous sentence is needed, because you (the reader) might
nonmonotonically infer from the first part of the sentence that the
second part doesn't modify what you might infer from the first part.
English provides ``although'' for use when it is convenient to
signal that there will be a qualification in advance.  ``However''
seems to provide the same facility on a larger scale.

	We would expect any natural language to provide the same
facility, because it is needed for the communication tasks humans
have to perform.  We might also find it useful to put it into
artificial languages for communicating among computers, but some
of the human ways of doing things are consequences of human
limitations on short term memory that don't apply to computers.
It would be interesting to observe the development of words like ``but''
as pidgins are transformed into creoles.
\smallskip\centerline{Copyright \copyright\ \number\year\ by John McCarthy}
\smallskip\noindent{This draft of nonmon[e88,jmc]\ TEXed on \jmcdate\ at \theTime}
\vfill\eject\end