Transcript Knowledge representation 1

KNOWLEDGE
REPRESENTATION
22C:145 ARTIFICIAL INTELLIGENCE
THE UNIVERSITY OF IOWA
THE IMPORTANCE OF KNOWLEDGE
REPRESENTATION
Contrary to the beliefs of early workers in AI,
experience has shown that Intelligent Systems
cannot achieve anything useful unless they
contain a large amount of real-world - probably
domain-specific - knowledge.
 Humans almost always tackle difficult realworld problems by using their resources of
knowledge - "experience", "training" etc.

KNOWLEDGE REP. FORMALISMS
Production rules
 Formal logic, and languages based on it (e.g.
PROLOG)
 Structured objects:
Semantic nets (or networks)
Frames, and object-orientated programming,
which was derived from frames
Other similar objects, such as Scripts

KNOWLEDGE REPRESENTATION USING
STRUCTURED OBJECTS

Structured objects are:
 knowledge
representation formalisms whose
components are essentially similar to the nodes
and arcs found in graphs.
 in contrast to production rules and formal logic.
 an attempt to incorporate certain desirable
features of human memory organisation into
knowledge representations.
TAXONOMIC KNOWLEDGE
The entities with which we reason can be
grouped into categories.
 Categories may be divided into sub-categories.
 The hierarchical structure of these categories is
called taxonomy.
 Taxonomic knowledge can be represented by
first-order logic, or more conveniently by
semantic nets.

SEMANTIC NETS
Devised by Quillian in 1968, as a model of
human memory.
 The technique offered the possibility that
computers might be made to use words in
something like the way humans did, following
the failure of early machine-translators.
 Organisation of semantic nets.

c o v e re d _ b y
a n im a l
s k in
tr a v e ls _ b y
fly in g
is a
is a
tr a v e ls _ b y
b ir d
fe a th e r s
fis h
c o v e re d _ b y
is a
o s tr ic h
s w im m in g
is a
p e n g u in
is a
is a
c a n a ry
r o b in
tr a v e ls _ b y
c o lo u r
c o lo u r
w a lk in g
y e llo w
tr a v e ls _ b y
re d
in s ta n c e _ o f
O pus
in s ta n c e _ o f
T w e e ty
c o lo u r
w h ite
SEMANTIC NETS

knowledge is represented as a collection of
concepts, represented by nodes (shown as
boxes in the diagram), connected together by
relationships, represented by arcs (shown as
arrows in the diagram).
SEMANTIC NETS
certain arcs - particularly isa arcs - allow
inheritance of properties.
 This permits the system to "know" that a Ford
Escort has four wheels because it is a type of
car, and cars have four wheels.

SEMANTIC NETS


inheritance provides cognitive economy, but
there is a storage-space / processing-time
trade-off.
This means that, if you adopt this technique,
you will use less storage space than if you
don't, but your system will take longer to find
the answers to questions.
SEMANTIC NETS

a semantic net should make a distinction
between types and tokens. This is why the
diagram above uses “instance_of” arcs as well
as “isa” arcs.
 Individual
instances of objects have a token node.
 Categories of objects have a type node.
 There is always at least one type node above a
token node. The information needed to define an
item is (normally) found attached to the type nodes
above it.
SEMANTIC NETS

So far, this is just a diagram - not a knowledge
base. But it can be converted into a knowledge
base.
SEMANTIC NETS TO PROLOG
is_a(sammy,goldfish).
is_a(goldfish,freshwater_fish).
…
has(fish,fins).
has(fish,scales).
…
Etc.
Each arrow on the semantic net becomes a Prolog clause.
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c o v e re d _ b y
a n im a l
s k in
tr a v e ls _ b y
fly in g
is a
is a
tr a v e ls _ b y
b ir d
fe a th e r s
fis h
c o v e re d _ b y
is a
o s tr ic h
s w im m in g
is a
p e n g u in
is a
is a
c a n a ry
r o b in
tr a v e ls _ b y
c o lo u r
c o lo u r
w a lk in g
y e llo w
tr a v e ls _ b y
re d
in s ta n c e _ o f
O pus
in s ta n c e _ o f
T w e e ty
c o lo u r
w h ite
A SEMANTIC NET PROGRAM WRITTEN
IN PROLOG
% defining operators.
:- op(500, xfx, isa).
:- op(500,xfx, instance_of).
:- op(500,xfx, covered_by).
:- op(500,xfx, travels_by).
:- op(500,xfx, colour).
:- op(500,xfx, travels).
:- op(500,fx, is).
:- op(600,xfx, a).
:- op(600,xfx, an).
:- op(700, xf, ?).
:- op(500,fx, what).
:- op(600, xfx, is).
A SEMANTIC NET PROGRAM WRITTEN IN
PROLOG
:- op(650, xfx, what).
:- op(650, xfx, how).
ostrich isa bird.
penguin isa bird.
canary isa bird.
robin isa bird.
bird isa animal.
fish isa animal.
opus instance_of penguin.
tweety instance_of canary.
canary colour yellow.
A SEMANTIC NET PROGRAM WRITTEN IN
PROLOG
robin colour red.
tweety colour white.
penguin travels_by walking.
ostrich travels_by walking.
bird travels_by flying.
fish travels_by swimming.
bird covered_by feathers.
animal covered_by skin.
A SEMANTIC NET PROGRAM WRITTEN IN
PROLOG
inherit(A isa C):A isa C.
inherit(A isa C):A instance_of
inherit(D isa
inherit(A isa C):A isa D,
inherit(D isa
is X a Y :- inherit(X
is X an Y:- inherit(X
D,
C).
C).
isa Y).
isa Y).
A SEMANTIC NET PROGRAM WRITTEN IN
PROLOG
inherit(A colour C):A colour C.
inherit(A colour C):(A instance_of D ; A isa D),
inherit(D colour C).
what_colour A :inherit(A colour C),
nl, write(A), write(' is '),
write(C).
A SEMANTIC NET PROGRAM WRITTEN IN
PROLOG
inherit(A covered_by C):A covered_by C.
inherit(A covered_by C):(A instance_of D ; A isa D),
inherit(D covered_by C).
A covers:inherit(A covered_by C),
nl, write(A),
write(' is covered by '),
write(C).
SEMANTIC NETS

This is a program, written in Prolog, which
contains all the knowledge represented in the
diagram above, together with a mechanism for
finding information by inheritance, and a
rudimentary natural language interface.
SEMANTIC NETS

It can answer questions like
is tweety an animal ? (it answers “yes”)
what colour is tweety ? (it answers “white”)
opus is covered_by what ? (it answers “feathers”)
and so on.
SEMANTIC NETS

It could have been written in C++ or Java
(although it would have been much harder), or
any other present-day high-level language.
SEMANTIC NETS

Problems with semantic nets
 logical
inadequacy - vagueness about what types
and tokens really mean.
 heuristic inadequacy – finding a specific piece of
information could be chronically inefficient.
 trying to establish negation is likely to lead to a
combinatorial explosion.
 "spreading activation" search is very inefficient,
because it is not knowledge-guided.
SEMANTIC NETS

Attempted improvements
building search heuristics into the network.
more sophisticated logical structure,
involving partitioning.
these improvements meant that the
formalism’s original simplicity was lost.
SEMANTIC NETS

Developments of the semantic nets idea:
psychological research into whether human
memory really was organised in this way.
 used in the knowledge bases in certain expert
systems.
 special-purpose languages have been written to
express knowledge in semantic nets.

FRAMES
The frame system mimics the human style of knowledge
organisation by creating a structure consisting of slots that
are filled with specific instances of data. For example we
could organise the information about a wooden table as
follows:
In some cases a slot may hold a default value which will
be assumed unless an alternative value is specified. In the
Table frame, the default value for the number of legs is 4,
but this could be changed (for example a larger table might
have 6 legs)
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FRAME STRUCTURE
The values stored in slots
are often pointers to other
frames
Frames allow facts to be
retrieved directly
Frames may be linked to
form a hierarchy that
allows properties to be
inherited
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SEMANTIC NET VS FRAMES
Terminology:
Subclass and has-part are called slots.
Animal and head are the slot values.
As Nellie is an instance of elephant, she inherits the properties
of elephants, so we can also say that Nellie is large and grey.
Elephants, in turn, are a subclass of mammals, so we can say
that Nellie has a head, and is an animal, by a process of multiple
inheritance.
We could represent the same knowledge in the form of frames, as
above: (note: these 3 frames represent only parts of the semantic net)
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MONOTONIC LOGIC


Standard logic is monotonic:
 once you prove something is true, it is true
forever
Monotonic Logic is not a good fit to reality
 If the wallet is in the purse, and the purse in is
the car, we can conclude that the wallet is in
the car
 But what if we take the purse out of the car?
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MONOTONIC LOGIC



Given a collection of facts D that entail some
sentence s (s is a logical conclusion of D):
For any collection of facts D’ such that DD’ ,
D’ also entails s.
In other words: s is also a logical conclusion of
any superset of D.
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NONMONOTONIC LOGIC

In a nonmonotonic system:
 the addition of new facts can reduce the set of
logical conclusions.
 S is a conclusion of D, but is not necessarily a
conclusion of D+new fact.
 Humans use nonmonotonic reasoning constantly!
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WHAT IS “NON-MONOTONIC LOGIC” ?

To understand what nonmonotonic logic means simple
consider a popular example:
"all birds fly",
"Tweety is a bird",
"Does Tweet fly?".

The obvious answer is yes,
 however what if later you learned that Tweety had a broken
wing, then the answer becomes no,
 then what if you learned that tweet was an airplane pilot,
or had a jet pack, the answer can change again.

The important point is that as new information is added the
answers change.
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NONMONOTONIC LOGIC

Facts and rules can be changed at any time


such facts and rules are said to be dynamic
Prolog uses nonmonotonic logic
 assert(...) adds a fact or rule
 retract(...) removes a fact or rule
 assert and retract are said to be extralogical
predicates.
 Negation as failure is also non-monotonic.
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INTELLIGENT REASONING



One of the characteristics associated with intelligent
systems is adaptability - the ability to deal with a
changing environment.
Adaptation requires that a system be capable of
adding and retracting beliefs as new information is
available.
This requires non-monotonic reasoning.
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UNCERTAINTY

Another characteristic of intelligent systems is
the ability to reason under conditions of
uncertainty.
 Another way of saying this: the ability to
reason with an incomplete set of facts.
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CAN WE IMPLEMENT INHERITANCE USING
PREDICATE LOGIC?







Pat is a Bat.
Bats are Mammals.
Bats can fly.
Bats have 2 legs.
Mammals cannot fly.
Mammals have 4 legs.
How many legs does Pat have?
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INHERITANCE



Reasoning about inheritance of properties from one
class to another:
Bird(x)  Flies(x)
Clearly this is not a good rule, since we know there are
exceptions.
Bird(x)  Normal(x)  Flies(x)
This provides for exceptions, although we must define
the conditions that imply Normal(x).
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NORMAL(X)




Assuming we know that:
Ostrich(x)  Bird(x)  ~Flies(x)
we can derive:
Ostrich(x)  ~Normal(x)
So an ostrich is not a normal bird.
But what about all the the other things that are birds?
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ASSUMPTIONS AND DEFAULTS



If there is no reason to believe otherwise, assume that
Normal(x) is TRUE.
The default is that everything is normal.
Now we only need to supply additional information for
exceptions.
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HOW TO SPECIFY DEFAULTS




A number of formal systems have been developed to
handle defaults.
Nonmonotonic logics formalize unsound but
reasonable patterns of reasoning with uncertain,
incomplete and inconsistent information
Default Logic: New rule of inference
Abduction: New interpretation of implication.
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AND MORE LOGICS TO THINK ABOUT!


Modal logic is useful for modeling reasoning about
knowledge, actions, time (next, eventually, forever,
never) or obligations.
Epistemic logics apply the techniques of modal logic
to reasoning about knowledge.


Both individual and group knowledge is studied. The study
of epistemic logic is relevant to communication protocols
and cooperation.
Deontic logic formalizes normative modalities.
 Deontic logic can be applied to representation of
normative (e.g. legal) knowledge.
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DEFAULT REASONING WITH NONMONOTONIC
LOGIC
Predicate logic with an extension:
 a modal operator M which means is “consistent with
everything we know”.
 Example:
x,y: Related(x,y)  M GetAlong(x,y)  WillDefend (x,y)

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DEFAULT LOGIC



New rule of inference:
A:B
C
If A is true and it is consistent to assume B, then C is
true.
Same idea, but now used as a rule of inference. The
new rule extends the knowledge base to a set of
plausible extensions, any new statement that is true
in all extensions is added.
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INHERITANCE WITH DEFAULT LOGIC


Support for inheritance
using Default Logic:
Mammal(x) : Legs(x,4)
Legs(x,4)
In the absence of
contradictory information,
we can assume anything
that is a mammal has 4 legs
(also need a rule stating that
nothing can have 2 different
numbers of legs!)
The following statements
are consistent in Default
Logic:
Pat is a Bat.
Bats are Mammals.
Bats can fly.
Bats have 2 legs.
Mammals cannot fly.
Mammals have 4 legs.
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ABDUCTION

Deduction:
Given A(x)  B(x) and A(x), we assume that B(x) is true.
 Similar to forward reasoning
 [Cf.]
reasoning from the general to the particular
(or from cause to effect)

Abduction:
Given A(x)  B(x) and B(x), we assume that A(x) is true.
 Similar to backward reasoning
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INHERITANCE DIAGRAMS

we can also express default reasoning using
diagrams.
Can Fly
Normal Facts
Default
Ostriches
Birds
Fred
Tweety
Default
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A PROBLEM WITH NML




x: Republican(x)  M ~ Pacifist(x)  ~ Pacifist(x)
 x: Quaker(x)  M Pacifist(x)  Pacifist(x)
Republican(Dick)
Quaker(Dick)
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NOT QUITE THIS EASY

Assuming we have some mechanism for representing defaults,
there can still be problems:
Pacifists

Is Dick a pacifist?
Republicans
Quakers
Dick
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NML DILEMMA


In general we must be prepared to deal with multiple,
possibly conflicting consequences of a set of facts.
One simple idea - rank all the assumptions and use
rank to determine which to believe.
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OTHER APPROACHES TO HANDLING
CONFLICTING ASSUMPTIONS.

Minimalist Reasoning



Assume that there are fewer true statements that
false statements in the world.
Find the smallest interpretation that satisfies all the
statements we know to be true.
Closed World Assumption: the only objects that
satisfy a predicate are those that must.

forces positive assertions to take priority over
negative assertions
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CLOSED WORLD ASSUMPTION


If we are told nothing about Tweety, other than
Tweety is a bird,
 we assume that Tweety's feet are not in concrete,
or Tweety's wings are not broken, this is the
closed world assumption.
Humans regularly make assumptions and when new
evidence appears those assumptions can be changed,
causing a different answer, thus behaving
nonmonotonicaly.
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USING PROBABILITIES

Probabilities can also be used determine which
defaults apply when contradictions arise.


Label each fact with a probability of being true.
There is a big split in the A.I. community over whether
symbolic methods or numeric methods are best for
handling these types of issues.
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SUMMARY - NONMONOTONIC LOGIC VS. PROBABILTY


Nonmonotonic logic systems may miss the importance
of probability.
 Probabilistic reasoning can also represent
uncertainty, and in a different (probabilistic) way.
These systems exhibit a different set of properties,
with which non-monotonic logic can not effectively
deal with.
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NONMONOTONIC VS. CLASSICAL LOGIC

Nonmonotonic logic does not have many essential
properties of classical first order logic, specifically
semi-decidability.
 In classical logic, it is possible for a system to halt
(be stuck in an infinite loop) trying to prove the
negation of something for which there is
insufficient information.
 In nonmonotonic default logic, rather than return
with no answer, the process returns with a wrong
(default answer).
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SUMMARY - NONMONOTONIC VS. CLASSICAL LOGIC


First order logic although descriptively universal, is
not effective at handling large classes of problems.
 If computers are going to handle common sense we
need to be able to have some form of default
reasoning.
Nonmonotonic logic can be used in many domains
where classical logic falls short:
 such as in the areas of default diagnosis, diagnosis,
action, and temporal logic.
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