Page 253 - DCAP310_INTRODUCTION_TO_ARTIFICIAL_INTELLIGENCE_AND_EXPERT_SYSTEMS

Unit 13: Expert System Architecture

inheritance. Elephants are almost always grey, except Clyde, who’s pink. It is very tedious to Notes
represent such things in first order predicate logic - you have to specify all the exceptions in the
rules, which ends up getting very complex. To avoid this special logics have been developed.
There are a variety of such logics, but all (most?) based on the same idea.
Default logics allow you to write rules which refer to whether it is consistent to believe something.
So we’d say that if X is an elephant and it’s consistent to believe that X is grey then X is grey. This
is expressed in various ways in different variants of default logic, but one is to introduce a
special operator M, so that M X means “X is consistent with everything else”. Given the following
rule and facts:
X elephant(X) M grey(X) grey(X)
grey(clyde)
elephant(nellie)
elephant(clyde)

we would conclude that Nellie was grey but we wouldn’t conclude that Clyde was grey, as it is
not consistent with everything else (ie, grey (clyde)).
If we had a hundred elephants, about ten of which were pink (or blue, or..), then we could write
the general rule, and specify the exceptions by adding facts like: grey(albert), grey(edward).. If
we bought a new elephant we’d just add a new fact of this sort. However, if we were using
ordinary predicate logic we’d have to modify the general rule itself, which might look like:
X elephant(X) name(X, clyde) name(X, albert) name(X, edward) ....
grey(X)
If we have more complex defaults then the advantages of using a default logic become more
compelling. For example, we might want to say that elephants are generally grey, circus elephants
are generally pink, but Nellie is in fact grey. Dealing with all these nested defaults and exceptions
explicitly in predicate logic gets very complex.
Default logics can be used to provide semantics. However, remember that in frame systems you
sometimes had to choose which parent class to inherit from - if Clyde is both a circus animal and
an elephant, is he likely to be tame or not? We have the same problem in default logics. There
may be alternative, inconsistent conclusions, and the logic doesn’t (usually) specify which is the
right one. If we have a default rule that says that circus animals are generally not grey, if it is
consistent to believe that they aren’t grey, then we won’t know whether our circus elephant is
grey or not. Different alternative sets of facts we could believe are referred to as different
extensions of the knowledge base.
13.5.1 Methods for Knowledge Acquisition

The aim of a probabilistic logic (also probability logic and probabilistic reasoning) is to combine
the capacity of probability theory to handle uncertainty with the capacity of deductive logic to
exploit structure. The result is a richer and more expressive formalism with a broad range of
possible application areas.

Did u know? Probabilistic logics attempt to find a natural extension of traditional logic
truth tables: the results they define are derived through probabilistic expressions instead.
A difficulty with probabilistic logics is that they tend to multiply the computational complexities
of their probabilistic and logical components. Other difficulties include the possibility of counter-
intuitive results, such as those of Dempster-Shafer theory. The need to deal with a broad variety
of contexts and issues has led to many different proposals.

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