Download Lecture02_3337_2009

EXPERT SYSTEMS
Chapter 02
Knowledge Representation
Techniques
Types of Knowledge
• a priori knowledge
– comes before knowledge perceived through senses
– considered to be universally true
• a posteriori knowledge
– knowledge verifiable through the senses
– may not always be reliable
• procedural knowledge
– knowing how to do something
• declarative knowledge
– knowing that something is true or false
• tacit knowledge
– knowledge not easily expressed by language
Knowledge Representation
Methods
Production Rules
Semantic Networks
Schemata and Frames
Propositional Logic
Predicate Calculus
Advantages of Production Rules
• simple and easy to understand
• straightforward implementation in
computers possible
• formal foundations for some variants
Problems with Production Rules
• simple implementations are very inefficient
• some types of knowledge are not easily
expressed in such rules
• large sets of rules become difficult to
understand and maintain
Semantic Networks
• graphical representation for propositional
information
• originally developed by M. R. Quillian as a model
for human memory
• labeled, directed graph
• nodes represent objects, concepts, or situations
• labels indicate the name
• links represent relationships
• the label indicates the type of the relationship
Frame
represents related knowledge about a subject
provides default values for most slots
frames are organized hierarchically
allows the use of inheritance
knowledge is usually organized according to
cause and effect relationships
slots can contain all kinds of items
rules, facts, images, video, comments,
debugging info, questions, hypotheses,
other frames
Frame Advantages
• fairly intuitive for many applications
– similar to human knowledge organization
– suitable for causal knowledge
– easier to understand than logic or rules
• very flexible
Propositional logic
• In general a logic is defined by
– syntax: what expressions are allowed in the
language.
– Semantics: what they mean, in terms of a
mapping to real world
– proof theory: how we can draw new
conclusions from existing statements in the
logic.
• Propositional logic is the simplest.
Propositional Logic: Syntax
• Symbols (e.g., letters, words) are used to represent facts
about the world, e.g.,
– “P” represents the fact “Andrew likes chocolate”
– “Q” represents the fact “Andrew has chocolate”
• These are called atomic propositions
• Logical connectives are used to represent and: , or:  , ifthen: , not: .
• Statements or sentences in the language are constructed
from atomic propositions and logical connectives.
– P  Q “Andrew likes chocolate and he doesn’t have
any.”
– P Q “If Andrew likes chocolate then Andrew has
chocolate”
Propositional Logic: Semantics
• Sentences in propositional logic tell you about what is
true or false.
– P  Q means that both P and Q are true.
– P  Q means that either P or Q is true (or both)
– P  Q means that if P is true, so is Q.
• This is all formally defined using truth tables.
XY XvY
TT T
TF T
FT T
FF
F
We now know exactly what is meant in
terms of the truth of the elementary
propositions when we get a sentence in
the language (e.g., P => Q v R).
Proof Theory
• For propositional logic useful one is modus
ponens:
• If A is true and A=> B is true, then conclude B is
true.
A, A B
—————————
B
LOGICAL EXPRESSIONS
Predicate Calculus
• includes a wider range of entities
• permits the description of relations and the
use of variables.
• It also requires an understanding of
quantification
Predicate Logic
• Propositional logic isn’t powerful enough as a general
knowledge representation language.
• In predicate logic the basic unit is a predicate/ argument
structure called an atomic sentence:
– likes(alison, chocolate)
– Tall (fred)
• Arguments can be any of:
– constant symbol, such as ‘Richard’
– variable symbol, such as X
– function expression, e.g., likes
• So we can have:
– likes(X, Richard)
– friends(motherof(joe), motherof(jim))
Proof and Inference
• What can we conclude from the
following?
–  X tall(X)  strong(X)
– tall(john)
–  X strong(X)  loves(mary, X)