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C00009 00007	thomas[e87,jmc]		Position paper for Journal of Philosophical Logic
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\title{Logical Problems Posed by Artificial Intelligence}

\noindent Abstract: One way of making intelligent computer programs
involves expressing what the program knows in a mathematical logical
language and having it decide what to do to achieve its goals
by logical inference.  This poses logical problems different from
those that have arisen in formalizing the foundations of mathematics
or from the internal development of logic.  Our object is to
explain these problems and what has been accomplished
 in the hopes that logicians will find the problems
interesting.

\noindent Abstract: The most straightforward approach to AI is to express
what the system needs to know in a first order language and have it
programmed to deduce what it should do to achieve its goals.  This
requires formalizations of common sense knowledge and reasoning.
Specifically, facts about the effects of actions must be formalized.
The approach has had to be modified to include non-monotonic
reasoning, and further modifications may be required involving the
formalization of context.  However, using logic as the basis for AI still
looks promising --- even after 30 years.

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\section{Introduction}

It is evident that Leibniz, Boole and Frege all hoped to include
common sense knowledge in the domain formalizable by mathematical
logic.  However, this has proved very difficult, and the difficulties
have not been easy to diagnose, let alone solve.  Since the successful
applications of mathematical logic have been to the foundations
of mathematics, some people have concluded that this is all it's good
for.

Since the late 1950s there have been proposals to use mathematical
logic to formalize common sense knowledge and reasoning for purposes
of artificial intelligence.  Success has been moderate, but nevertheless
logic is the main tool used today in AI systems.  Systems differ in
how much logic is used, and some use far less than the full first
order logic.  For example, many expert systems never infer new
general sentences, but only go from the general to the particular,
and this suffices for many applications.


\section{Introduction}

	The most straightforward approach to artificial intelligence
uses logic.  It was proposed in (McCarthy 1960) but is implicit in
Leibniz and Boole.  It involves the following.

1. Express the facts about the world as sentences of mathematical
logic.  These include especially the facts about the consequences
of actions.
\smallskip\centerline{Copyright \copyright\ \number\year\ by John McCarthy}
\smallskip\noindent{This draft of THOMAS[E87,JMC]
 TEXed on \jmcdate\ at \theTime}
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thomas[e87,jmc]		Position paper for Journal of Philosophical Logic
special issue on AI and Philosophical Logic, due dec. 1
msg.msg[1,jmc]/165p
e87.in[let,jmc]/165p
THOMASON@C.CS.CMU.EDU


Wittgenstein


	The use of logic in artificial intelligence is controversial
in a variety of ways.  Sometimes it's simple ignorance.

	Many AI researchers do not understand the inevitability of logic.
For example, one moderately prominent AI researcher said, ``Why do you
have this prejudice in favor of this language invented by Russell?''

	Sometimes it's some kind of existential despair.

Problems in formalizing common sense.
	1. ccntext
	2. non-monotonic reasoning
	3. arising from insufficient reification of ordinary kinds

	I am grateful for the editor's invitation to contribute a
position paper on the relation between mathematical logic and
artificial intelligence.  This paper will be light on technical
detail, but I hope the references will permit the reader to
pursue the applications.

	My position is at one end of the spectrum of opinion.  Namely,
I believe that logic is of decisive importance for AI.  Mathematical
logical languages and mathematical logical reasoning will permit
intelligent programs that express what they know in logical formulas
and decide what to do by logically inferring that certain actions
are appropriate to achieving their goals.  This approach, first
enunciated in 1958 in (McCarthy 1960) encounters many difficulties
some of which require new logical formalisms, but it is still ahead
of any other approach in generality and promise.