Chapter 1 What to do in an emergency
Imagine you
are travelling on the
Emergencies
Press the alarm signal button
to alert the driver.
The driver will stop
if any part of the train is in a station.
If not, the train will continue to the next station,
where help can more easily be given.
There is a 50 pound penalty
for improper use.
The
The purpose of the Emergency Notice is to regulate the
behaviour of passengers in an emergency. In this
respect, it functions as a program, not to control the behaviour
of a computer, but to control the behaviour of
people.
To fulfill its purpose, the Notice needs to be unambiguous,
so there is no misunderstanding about its intended meaning; and it needs to be
easy to understand, so that readers can extract that meaning with as little
effort as possible. Like a computer program, it should also be efficient, so
that it achieves its purpose (to get help) as quickly as possible.
The computational nature of the emergency notice is
most obvious in the first sentence:
Press the alarm signal button
to alert the driver.
This has the form of a goal-reduction procedure:
Reduce the goal of alerting the driver
to the sub-goal of pressing the alarm
signal button.
In general, much of our human communication can be
understood in such computational terms, as one human attempting to program
another, to elicit a desired response. In this case, the management of the
Underground is attempting to program passengers to behave effectively and
efficiently in an emergency.
This computational view of human communication may be
offensive at first sight, because it suggests the view that people are merely
machines. That is not my intention.
I intend only to propose that thinking of people as
computing agents can sometimes help us to formulate our communications with
them in more effective and more efficient terms. More effective, because our
“programs” will better accomplish our intentions; and more efficient, because
the recipient can compile and execute the programs with less effort.
The Logic of the second and third
sentences of the Emergency Notice
But human communication can also be understood in
logical terms. Understood in this logical way, communications are collections
of sentences having an underlying logical form, which constitutes their
meaning. To understand an input natural language sentence, a reader or listener
needs to decipher its surface structure to extract its meaning. She then needs
to assimilate that meaning into the web of her beliefs. These beliefs include both
general background beliefs and any meanings extracted from earlier sentences in
the same communication.
After extracting such a collection of meanings, the
recipient of the communication can apply these meanings to any relevant problems
that might arise in her environment. In this respect, natural language sentences
are like a computer program. The process of extracting the logical meanings of
the sentences is like compiling a program from external into internal form, and
the process of applying these meanings to problems in the environment is like executing
the resulting compiled program.
In the example of the emergency notice, the
relationship between the external form of the English sentences and their
internal, logical form is most obvious in the case of the second and third
sentences of the Notice, especially with their use of such obviously logical terms
as “if”, “any”, and “if not”.
It is tempting to argue that the Notice is easy to
understand just because the surface structure of its external form is so close
to the internal form of its intended meaning. In fact, the second and third
sentences are more ambiguous than they may appear at first sight. In
particular, the second sentence does not explicitly state what the driver will
actually stop doing. It is unlikely, for example, that:
The driver will
stop causing the emergency
if any part of the train is in a station.
Instead, it is almost certain that:
The driver will stop the train in a station
if any part of the train is in the station.
But even this interpretation does not fully capture the
sentence’s intended meaning. Understood in the context of the first sentence,
the second sentence has an additional implicit condition, namely that the
driver has been alerted to an emergency. Therefore, the intended meaning of the
second sentence is:
The driver will stop the train in a station
if the driver is alerted to an emergency
and any part of the train is in the station.
Without the additional condition, the sentence
literally means that the driver will stop the train whenever the train is in a
station, whether or not there is an emergency. If that were the case, a train
would never leave a station once it was there. To understand the sentence, a
reader of the Notice needs both general background knowledge about the way
train drivers normally behave and specific knowledge of the context of the
earlier sentences in the Notice.
In the spirit of our interpretation of the second
sentence, it is now clear that the intended meaning of the third sentence is:
The driver will
stop the train at the next station
and help can be
given there better than between stations
if the driver is alerted to an emergency
and not any part
of the train is in a station.
In natural language, it is common to leave out such
conditions as “any part of the train is in the
station”, that are already in the context. In formal logic, however,
sentences stand on their own two feet, without relying for support on the context
around them.
Because sentences in formal logic do not rely on their
context, you can take a collection of sentences written in logical form, throw
them up in the air, like a pack of cards, and then pick them up in any order.
The resulting collection of sentences has the same meaning as the collection you
started with.
In theory, therefore, if this book were written in
purely logical form, you could read it backwards, forwards or in any other
order, and it would have the same meaning. In fact, much of the work in writing
a book like this is in trying to find an appropriate order for presenting the
ideas, so that they are as easy to understand as possible,
The first sentence
of the Emergency Notice as a Logic Program
The first sentence of the Notice is written in the form
of a procedure, which hides its underlying logical form. In general, a goal-reduction procedure of the form:
Reduce goal to sub-goals
hides a logical implication:
Goal if sub-goals.
The goal-reduction behaviour
of the procedure can be obtained from the implication by backward reasoning:
To conclude that
the goal can be solved,
show that the sub-goals
can be solved.
Thus, the first sentence of the Emergency Notice has the
hidden logical form:
You alert the
driver,
if you press the
alarm signal button.
The use of backward reasoning to turn implications
into goal-reduction procedures is called logic
programming. The implications themselves are called logic programs. Logic programming became quite popular for a while
in the 1980s, and then largely fell into disuse. One of the goals of this book
is to show that logic programming can be useful, not only for Computing, but
also for Human Reasoning.
Backward reasoning contrasts with forward reasoning, which is probably more familiar to most people.
Given an implication of the form:
If
conditions then conclusion.
and a collection of statements that match the
conditions, forward reasoning derives the conclusion as a logical consequence
of the conditions.
Whether to use backward or forward reasoning is one of
the main issues investigated in this book.[1]
The fourth sentence of the
Emergency Notice as a constraint
In natural language, implications are often hidden
below the surface, sometimes in procedural form, other times in declarative
form. For example, the last sentence of the Notice is a declarative sentence, which
has the underlying logic form:
You may get a 50
pound penalty
if you press the
alarm signal button improperly.
Backwards reasoning turns this implication into a goal-reduction
procedure:
To get a 50 pound
penalty,
press the alarm
signal button improperly.
It is very unlikely that a passenger would want to get
a 50 pound penalty, and very unlikely, therefore, the passenger would use
backward reasoning to reduce such an unlikely goal to subgoals.
More likely, the passenger would use forward reasoning instead, to derive that
using the alarm signal button improperly would have an undesirable consequence.
Thus, the sentence acts a constraint on behaviour rather
than as a generator.
Since goal-reduction procedures restrict implications
to backward reasoning, the procedural form of the sentence is not appropriate. This
explains why the sentence is written declaratively and not procedurally.
In fact, only the first sentence of the Emergency
Notice is written in procedural form, and only this one sentence of the Notice functions
as a normal program, to evoke the behaviour desired of
passengers on the underground. Indeed, the fourth sentence functions as a constraint,
to prevent undesired behaviour.
The second and third sentences, on the other hand,
describe part of a program to be executed by a different agent, namely by the
driver of the train. These sentences are written declaratively and not
procedurally precisely because they are to be executed by a different agent,
and not by the agent observing the emergency.
Programs
with purpose
It is implicit that the purpose[2]
(or goal) of the Notice is to explain to passengers how to get help in an
emergency. That is why the third sentence includes the phrase
where help can more easily be given.
This phrase explains why the driver does not stop the
train immediately when it is not in a station.
The first sentence of the Notice could be rewritten as
three sentences, to make its purpose explicit:
If there is an emergency then get help.
You get help if you alert the driver.
You alert the
driver if you press the alarm signal button.
Here, for a change, I have written the second and
third sentences as logic programs. Used to reason backwards, they behave as
procedures:
To get help, alert the driver.
To alert the
driver, press the alarm signal button.
The first sentence also has the form of an implication.
But its conclusion is imperative (get help) rather than declarative (you will
get help). It is like a condition-action
rule, but more general, because its conclusion is a goal, rather than just
an action.
Implications with imperative conclusions (including
condition-action rules) can be used to “reason forward”, like logical
implications. However, they do not have all the properties of logical implications
with declarative conclusions. Logical implications can be used to reason
forwards or backwards, but implications with imperative conclusions can only be
used forward. Declarative statements can be true or false. Imperative
statements can only be obeyed or disobeyed. We will see in later chapters how
imperative statements can be transformed into declarative form, by assigning
them the status of goals and distinguishing them from beliefs.
Where
do we go from here?
This chapter has been intended to give an overall
impression of the rest of this book. It shows through an example how English
sentences can be viewed both in computational and logical terms. It also shows
how the two views come together in logic programming, which is a special case
of computational logic, which is the topic of this book.
Computational logic has been used to develop computer
applications, especially in Artificial Intelligence. However, in this book I
focus on its potential for use by people to improve their own reasoning and
communication skills.
Traditional logic was originally developed as a model
for human reasoning, but has fallen out a favour in
recent years. Other models, such as condition-action rules have mostly taken its
place. One of the main purposes of this book, therefore, is to show how
condition-action rules and logic can be reconciled and combined.
Part of the problem with traditional logic is its lack
of concern with a number of important issues that need to be dealt with in human
reasoning. These include the need to:
- distinguish between goals and beliefs
- be open to changes in the world
- relate thinking about actions with actually performing them
- relate the use of logic for thinking with the use of probability
and utility for deciding what actions to perform.
- reason by default and with rules and exceptions
- combine arguments both for and against a given conclusion.
We will see how computational logic addresses these
issues in the following chapters.
In addition, we will compare and attempt to reconcile
computational logic with rival views of human reasoning. These include:
- Condition-action rules
- Search
- Mental models
- Object-orientation
- Schemata and stereotypes
- Neural networks.
Finally, we will investigate the application of
computational logic to two main areas:
- Legal reasoning
- Human communication.
The problem we address in this book can be pictured
like this:
?
