Knowledge Representation
(Introduction)
Some
Representations
Elements of a Representation
•
•
•
•
Represented world: about what?
Representing world: using what?
Representing rules: how to map?
Process that uses the representation: conventions
and systems that use the representations resulting
from above.
A representation will always be missing some
property of the real world entity it is trying to
model.
Marr’s levels of description
• Computational: What is the goal of the
computation, why is it appropriate, and what is the
logic of the strategy by which it can be carried
out?
• Algorithmic: How can this computational theory
be implemented? In particular, what is the
representation for the input and output, and what
is the algorithm for the transformation?
• Implementation: How can the representation and
algorithm be realized physically?
Marr’s levels of description cont.
• Computational: a lot of cognitive psychology
• Algorithmic: a lot of cognitive science
• Implementation: neuroscience
Overview
• How knowledge representation works
– Basics of logic (connectives, model theory, meaning)
• Basics of knowledge representation
– Why use logic instead of natural language?
– Quantifiers
– Organizing large knowledge bases
• Ontology
• Microtheories
• Resource: OpenCyc, WordNet, UMLS
The CYC Project
• It now ‘knows’ a huge collection of fragments of
real-world knowledge such as:
–
–
–
–
Mothers are older than their children.
You have to be awake to eat.
You can usually know people’s noses, but not their hearts.
If you cut a lump of peanut butter in half, each half is a
lump of peanut butter, but if you cut a table in half, neither
half is a table.
The CYC Project
• The ultimate objective is to give it enough
knowledge to understand ordinary books, so that it
can read them and expand its own knowledge.
• So far, it’s got to a stage where, when asked to find
photos of “risky activities”, it located photos of
people climbing mountains and doing white-water
rafting.
How Knowledge Representation
Works
• Intelligence requires knowledge
• Computational models of intelligence require
models of knowledge
• Use formalisms to write down knowledge
– Expressive enough to capture human knowledge
– Precise enough to be understood by machines
• Separate knowledge from computational
mechanisms that process it
– Important part of cognitive model is what the organism
knows
How knowledge representations are used in
cognitive models
• Contents of
KB is part of
cognitive
model
• Some models
hypothesize
multiple
knowledge
bases.
Questions,
requests
Answers,
analyses
Inference
Mechanism(s)
Examples,
Statements
Learning
Mechanism(s)
Knowledge
Base
Expert Systems
• KBS on a domain that requires expertise (mainly rulebased, but not always)
• Rules capture “shallow” knowledge; alternative is to
reason about “first principles” or “deep” knowledge (e.g.
“Ohm’s law”)
• Handling “uncertainty” in rules
MYCIN:
“certainty factor”
Knowledge Representation: revisited
• Production Rules
if leaves are yellowed AND
soil is moist AND
small white spots on undersides of leaves
then
plant is infested with spider mites
treat with DIANTHONINE
• Predicate Calculus
color(ball, red).
• Semantic net
ball23
color
red
Semantic Net
bill
“Bill is a cat.”
inst
cat
isa
species
has-part
feline
mammal
isa
isa
animal
isa
has-part
dog
isa
hair
paw
species
has-part
foot
claw
canine
living
Knowledge Representation using
structured objects
Frames
Frames
• Devised by Marvin Minsky, 1974.
• Incorporates certain valuable human thinking
characteristics:
–
Expectations, assumptions, stereotypes. Exceptions.
Fuzzy boundaries between classes.
• The essence of this form of knowledge
representation is typicality, with exceptions, rather
than definition.
Example:
Frame
System for a
“typical”
room
How frames are organized
• A frame system is a hierarchy of frames
• Each frame has:
– a name.
– slots: these are the properties of the entity that has the
name, and they have values. A particular value may
be:
•
•
•
•
a default value
an inherited value from a higher frame
a procedure, called a daemon, to find a value
a specific value, which might represent an
exception.
Frames: some examples
• We will start with a simple piece of information:
there is a category of things called cars.
• Given this information, we can start to build a
frame:
Name: car
Subclass of:
thing
• More information: a car has 4 wheels, is moved by
an engine, and runs on petrol or diesel.
• We can now add three slots to the frame.
• The last of these has a restriction rather than a
specific value.
“a car has 4 wheels, is moved by an engine,
and runs on petrol or diesel.”
Name: car
Subclass of:
thing
Slots:
Name:
Value:
wheels
4
moved by
engine
fuel
?
Restrictions:
petrol or diesel
car subclass_of
thing
with
wheels: 4,
moved_by:
engine,
fuel:
[value:
unknown,
type:
[petrol,diesel]].
• More information: there is a particular type of car
called a VW, manufactured in Germany.
• We can add a second frame to our system, with
one slot. We don’t need to repeat the slots and
values in the previous frame: they will be
inherited.
“there is a particular type of car called a VW,
manufactured in Germany.”
Name: VW
Subclass of:
car
Slots:
Name:
made in
Value:
Germany
Restrictions:
‘VW’ subclass_of
car
with
made_in:
‘Germany’.
• More information: there is a particular type of VW
called a Golf, which has a sun-roof.
• We can add a third frame to our system, with one
slot. Once again, we don’t repeat the slots in the
previous frames, because they will be inherited.
“there is a particular type of VW called a Golf,
which has a sunroof.”
Name: Golf
Subclass of: VW
Slots:
Name:
top
Value:
sunroof
Restrictions:
‘Golf’ subclass_of
VW
with
top: sunroof.
• More information: there is a particular type of
Golf called a TDi, which runs on diesel. A TDi
has 4 cylinders, and an engine capacity of 1.8
litres.
• We can add a fourth frame to our system, with
three slots. One of the slots (fuel) was already in
the system, but appears here because it now has a
specific value rather than a restriction.
“there is a particular type of Golf called a TDi,
which runs on diesel, has 4 cylinders, and has a 1.8
litre engine.”
Name: TDi
Subclass of:
Golf
Slots:
Name:
Value:
fuel
diesel
engine
capacity
1.8 litres
cylinders
4
Restrictions:
‘TDi’ subclass_of
‘Golf’
with
fuel: diesel,
engine_capacity:
1.8,
cylinders: 4.
Scripts
• Knowledge representation researchers particularly Roger Schank and his associates devised some interesting variations on the theme
of structured objects.
• In particular, they invented the idea of scripts
(1973).
• A script is a description of a class of events in
terms of contexts, participants, and sub-events.
Plans and Scripts
Roger Schank
Example:
Restaurant Script
“John went to a
restaurant. He
ordered lobster. He
paid the bill and left.”
What did John eat?
Scripts
• Rather similar to frames: uses inheritance and slots;
describes stereotypical knowledge, (i.e. if the system
isn't told some detail of what's going on, it assumes
the "default" information is true), but concerned with
events.
• Somewhat out of the mainstream of expert systems
work. More a development of natural-languageprocessing research.
Scripts
• Why represent knowledge in this way?
–
Because real-world events do follow stereotyped patterns.
Human beings use previous experiences to understand
verbal accounts; computers can use scripts instead.
–
Because people, when relating events, do leave large
amounts of assumed detail out of their accounts. People
don't find it easy to converse with a system that can't fill in
missing conversational detail.
Scripts
• Scripts predict unobserved events.
• Scripts can build a coherent account from disjointed
observations.
Scripts
• Commercial applications of script-like structured
objects: work on the basis that a conversation between
two people on a pre-defined subject will follow a
predictable course.
• Certain items of information need to be exchanged.
–
Others can be left unsaid (because both people know what the
usual answer would be, or can deduce it from what's been said
already), unless (on this occasion) it's an unusual answer.
What’s in a knowledge base?
• Facts about the specifics of the world
– Fordham is a private university
– The first thing Andrea did at the party was talk to John.
• Rules (aka axioms) that describe ways to infer new
facts from existing facts
– All triangles have three sides
– All elephants are grey
• Facts and rules are stated in a formal language
– Generally some form of logic (aka predicate calculus)
Propositional logic
• A step towards understanding predicate calculus
• Statements are just atomic propositions, with no
structure
– Propositions can be true or false
• Statements can be made into larger statements via
logical connectives.
• Examples:
– C = “It’s cold outside” ; C is a proposition
– O = “It’s October” ; O is a proposition
– If O then C ;if it’s October then it’s cold outside
Model Theory
• Meaning of a theory = set of models that satisfy it.
– Model = set of objects and relationships
– If statement is true in KB, then the corresponding
relationship(s) hold between the corresponding objects
in the modeled world
– The objects and relationships in a model can be formal
constructs, or pieces of the physical world, or whatever
• Meaning of a predicate = set of things in the
models for that theory which correspond to it.
– E.g., above means “above”, sort of
Representations as Sculptures
• How does one make a statue of an elephant?
– Start with a marble block. Carve away everything that
does not look like an elephant.
• How does one represent a concept?
– Start with a vocabulary of predicates and other axioms.
Add axioms involving the new predicate until it fits
your intended model well.
• Knowledge representation is an evolutionary
process
– It isn’t quick, but incremental additions lead to
incremental progress
– All representations are by their nature imperfect
NL vs. Logic: Expressiveness
NL:
Jim’s injury resulted from his falling.
Jim’s falling caused his injury.
Jim’s injury was a consequence of his falling.
Jim’s falling occurred before his injury.
NL: Write the
rule for every
expression?
Logic: identify the common concepts, e.g.
the relation: x caused y
Write rules about the common concepts, e.g.
x caused y  x temporally precedes y
NL vs. Logic:
Ambiguity and Precision
NL:
Ambiguous
•x is at the bank.
•x is running.
•river bank?
•changing location?
•financial institution?
•operating?
•a candidate for office?
Logic:
Precise
x is running-InMotion  x is changing location
x is running-DeviceOperating x is operating
x is running-AsCandidate  x is a candidate
Reasoning: Figuring out what must be true, given what is
known. Requires precision of meaning.
NL vs. Logic:Calculus of Meaning
Logic: Well-understood operators enable reasoning:
Logical constants: not, and, or, all, some
Not (All men are taller than all women).
All men are taller than 12”.
Some women are taller than 12”.
Not (All A are F than all B).
All A are F than x.
Some B are F than x.
Syntax: Terms (aka Constants)
Terms denote specific individuals or collections
(relations, people, computer programs, types of cars . . . )
Each Terms is a character string prefixed by
• A sampling of some constants:
– Dog, SnowSkiing,
PhysicalAttribute
These denote collections
– BillClinton,Rover, DisneyLandTouristAttraction
– likesAsFriend, bordersOn,
objectHasColor, and, not, implies,
forAll
These denote individuals :
•Partially Tangible
Individuals
•Relations
– RedColor, Soil-Sandy
•Attribute Values
Syntax: Propositions
Propositions: a relation applied to some
arguments
Also called formulas, sentences…
• Examples:
– (isa GeorgeWBush Person)
– (likesAsFriend GeorgeWBush AlGore)
Why constraints are important
• They guide reasoning
– (performedBy PaintingTheHouse Brick2)
– (performedBy MarthaStewart CookingAPie)
• They constrain learning
Variables and Quantifiers
• General statements can be made by using variables and quantifiers
– Variables in logic are like variables in algebra
• Sentences involving concepts like “everybody,” “something,” and
“nothing” require variables and quantifiers:
Everybody loves somebody.
Nobody likes spinach.
Some people like spinach and some people like broccoli, but no one
likes them both.
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Knowledge Representation