Minds and Computers : An Introduction to the Philosophy of Artificial Intelligence

patterns from environmental stimulus and recognising when these
patterns obtain again, even when they only partially obtain, or when
there is some variation in the pattern.
This is an important insight and one which we will return to discuss
at great length in Chapter 19. For the moment, note that this is not
ipso facto an argument against computationalism, but it does place an
explanatory burden on the computationalist – the burden being to
give a computational account of this cognitive capacity.
Now that we have compared, at least in rudimentary fashion, the way
humans play complex games with the way computers can be pro-
grammed to play these games, it is time to turn our attention to the
human rational and linguistic capacities.
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C H A P T E R 1 3
MACHINE REASONING
In this chapter we are going to begin to investigate the rational cap-
acity – the ability to reason. A thorough survey of automated rea-
soning methods would require dedicated volumes. We’re going to
concentrate on one kind of automated reasoning project which suits
our purposes well – the design of expert systems.
We’re going to see how we might recreate, with the use of formal
systems, the reasoning processes of a human expert in a particular
domain.
Before we do so, we will first need to make clear some concepts and
terminology involved in the study of logic.
13.1 LOGIC AND DEDUCTION
The first thing to appreciate is that there is a distinction between logic
and logics. Logic is a research tradition whose objects of investigation
are logics. These logics are formal systems and there are very many of
them.
The aim of logics is to formally encode relations of entailment or
logical consequence. In other words, logics are formal systems which
provide methods for determining what follows from what as a matter
of logical form.
Another important point is that, like all formal systems, logics are
concerned only with formal properties. While it is the case that elem-
ents of logics are interpretable as meaning something, issues of
meaning never have any bearing on determinations of logical conse-
quences. In other words, whether or not something follows logically
from some other things is entirely a question of their respective logical
forms. The relevance of this will become apparent in exercises later in
this chapter.
I don’t expect you to yet have an understanding of precisely what
logical form is or how to discern logical forms. I don’t intend this to
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be a fully fledged introduction to logic so I’ll reserve further discus-
sion concerning this for the next section where we’ll see some simple
examples.
Given that logics are formal systems, you should be wondering
what the states are and what the rules are. For our purposes, states can
be thought of as sets of statements. Rules of logics are such that given
an input state containing some statements of a certain form, we can
derive new statements of a certain form to add to the output state.
This process of applying logical rules to sets of statements to gen-
erate novel statements is the process of deduction.
While we will be concentrating on deduction in this chapter, it is
important to realise that there are other distinct kinds of reasoning.
We’ll revisit this issue at length in Chapter 15 and again in Chapter 19
but for the moment let’s just briefly consider the distinction between
deduction and induction.
Induction is the form of reasoning employed by empirical science.
Inductive proof is rather a di
fferent thing from deductive proof. A
deductive proof is a demonstration – of the kind we will see in the fol-
lowing section – that certain statement forms can be derived from
other statement forms according to certain logical rules. A typical