Page 140 - DCAP310_INTRODUCTION_TO_ARTIFICIAL_INTELLIGENCE_AND_EXPERT_SYSTEMS

Introduction to Artificial Intelligence & Expert Systems

Notes In the electrical environment, a possible world specifies the position of every switch and the
status of every component.
Possible worlds are described by algebraic variables. An algebraic variable is a symbol used to
denote features of possible worlds. Algebraic variables will be written starting with an uppercase
letter. Each algebraic variable V has an associated domain, dom(V), which is the set of values the
variable can take on.

7.1.6 Inference with a Bayesian Belief Network

Internal to a computer, a symbol is just a sequence of bits that can be distinguished from other
symbols. Some symbols have a fixed interpretation, for example, symbols that represent numbers
and symbols that represent characters. Symbols that do not have fixed meaning appear in many
programming languages. In Java, starting from Java 1.5, they are called enumeration types. Lisp
refers to them as atoms. Usually, they are implemented as indexes into a symbol table that gives
the name to print out. The only operation performed on these symbols is equality to determine
if two symbols are the same or not. To a user of a computer, symbols have meanings. A person
who inputs constraints or interprets the output associates meanings with the symbols that make
up the constraints or the outputs. He or she associates a symbol with some concept or object in
the world. For example, the variable Harry’s Height to the computer, is just a sequence of bits.
It has no relationship to Harry’s Weight or Sue’s Height. To a person, this variable may mean the
height, in particular units, of a particular person at a particular time.

The meaning associated with a variable-value pair must satisfy the clarity principle: an omniscient
agent - a fictitious agent who knows the truth and the meanings associated with all of the
symbols - should be able to determine the value of each variable.

Example: The height of Harry only satisfies the clarity principle if the particular person
being referred to and the particular time are specified as well as the units. For example, we may
want to reason about the height, in centimeters, of Harry Potter at the start of the second movie
of J. K. Rowling’s book. This is different from the height, in inches, of Harry Potter at the end of
the same movie (although they are, of course, related). If you want to refer to Harry’s height at
two different times, you must have two different variables. You should have a consistent meaning.
When stating constraints, you must have the same meaning for the same variable and the same
values, and you can use this meaning to interpret the output.
The bottom line is that symbols can have meanings because we give them meanings. For this
unit, assume that the computer does not know what the symbols mean. A computer can only
know what a symbol means if it can perceive and manipulate the environment.

Self Assessment

State whether the following statements are true or false:
1. Bayesian updating is widely used and computationally convenient.
2. The term “Bayesian” refers to the 20th century mathematician and theologian Thomas
Bayes.
3. There are four views on Bayesian probability that interpret the probability concept in
different ways.

4. A decision-theoretic justification of the use of Bayesian inference (and hence of Bayesian
probabilities) was given by Richard T. Cox.

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