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Introduction to Artificial Intelligence & Expert Systems

Notes
Example: Consider a stereotypical situation, such as going to hear a lecture. One’s
knowledge of what might go on during such an event is based on assumptions. For instance, it
can be assumed that the person who actually delivers the lecture is likely to be identical with the
person advertised; that the lecturer’s actual time of arrival is not more than a few minutes after
the advertised start; that the duration of the lecture is unlikely to exceed an hour and a half at the
maximum; and so on. These and other expectations can be encoded in a generic ‘lecture frame’ to
be modified by what actually occurs during a specific lecture. This frame will include various
slots, where specific values can be entered to describe the occasion under discussion. For example,
a lecture frame may include slots for ‘room location’, ‘start time’, ‘finish time’, and so on.

Scripts were developed in the early AI work by Roger Schank, Robert P. Abelson and their
research group, and are a method of representing procedural knowledge. They are very much
like frames, except the values that fill the slots must be ordered. A script is a structured
representation describing a stereotyped sequence of events in a particular context. Scripts are
used in natural language understanding systems to organize a knowledge base in terms of the
situations that the system should understand.

3.1.3 Logic

Propositional Logic

The following is a brief summary of propositional logic, intended only as a reminder to those
who have taken a course in elementary logic.

Language

Propositional logic is the logic of propositional formulas. Propositional formulas are constructed
from a set var of elementary or ‘atomic’ propositional variables p, q, and so on, with the
connectives:

(negation, ‘not’), ^ (conjunction, ‘and’), _ (disjunction, ‘or’), ! (implication, ‘if . . . then’), and $
(equivalence, ‘if and only if’). If ‘ and are formulas, then so are:’ and:, (‘^), (‘_), (‘ !), and (‘ $). So p
is a formula,:(p ^ q) and q _ (q ^:(r !:p)) are formulas, but pq is not a formula, and neither are p ^
q ! and p: _ r. We add the simple symbol ? which is called the falsum. We write this definition in
Backus-Naur Form (BNF) notation, as follows:
[Lprop] ‘::= p j ? j:’ j (‘ ^ ‘) j (‘ _ ‘) j (‘ ! ‘) j (‘ $ ‘)
This means that a formula ‘ can be an atom p, the falsum ?, or a complex expression of the other
forms, whereby its sub-expressions themselves must be formulas. The language of propositional
logic is called Lprop.
Brackets are important to ensure that formulas are unambiguous. The sentence p _ q ^ r could be
understood to mean either (p _ q) ^ r or p _ (q ^ r), which are quite different insofar as their
meaning is concerned. We omit the outside brackets, so we do not write ((p _ q) ^ r).

The symbols ‘;; _;::: are formula variables. So, if it is claimed that the formula ‘ _:’ is a tautology,
it means that every propositional formula of that form is a tautology. This includes p _:p, (p !:q)
_:(p !:q) and any other such formula. In a similar way, we formulate axiom schemata and inference
rules by means of formula variables. If ‘ ! (! ‘) is an axiom scheme, then every formula of that
form is an axiom, such as (p ^ q) ! (:q ! (p ^ q)). And an inference rule that allows us to infer
‘ _ from ‘ allows us to infer p _ (q $ r) from p, and so on.

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