3 KNOWLEDGE REPRESENTATIONS
3.1. Attributes of Knowledge
3.1.1. Types
procedural
knowing how to do something
how to boil a pot of water
declarative
knowing that something is true or false
statement such as “get burned if you put fingers in
a pot of
boiling water”
control
knowing which rules to use to solve problems
choice of pot/stove
3.1.2. Levels of knowledge
shallow
surface level information that can be used to deal with
specific situation
is described by common words and sentences
deep
information that reveal internal and causal structure of a
system which can be applied to different situations
is described by words and sentences of more technical
meanings
Notes:
1.
qualitative terms, no measure regarding depth of knowledge
2.
in some
circumstances, shallow knowledge may suffice
3.
level of knowledge to be used may determine level of
performance
3.1.3. Hierarchy of knowledge
noise
items of no interest
data
values actually stored in a database that are of potential interest
informat
ion
meanings of those values as understood by some users
(processed data)
knowledge
specialized information about the world that allows somebody
to make decision
metaknowledge
knowledge about knowledge
expertise
specialized operative knowledge that is
i
nherently
task

specific
and
relatively inflexible
intelligence
the capability to
acquire
and
apply
knowledge
3.1.4. Pragmatic aspects
naming
ways to denote objects by name
describing
ways to specify properties objects have
organizing
ways to categ
orize objects into hierarchy or classes
relating
ways to describe relationships among objects
constraining
ways to limit ranges of values, relationships and organizational
structures for attributes of objects
3.2. What Is Knowledge Representation (K
R)?
3.2.1. A KR is a surrogate
a KR functions as a surrogate inside the reasoner, a stand

in
for the things that exist in the world
the only completely accurate representation of an object is the
object itself, all other representations are inaccurate
, they
contain simplifying assumptions and artifacts
consequence of inevitability of imperfect surrogates: in
describing natural objects in the world, we must lie by
* omitting some of the limitless complexity of natural
world
* introducing artif
acts not present in natural world
3.2.2. A KR is a set of ontological commitments
ontology: concerned with what exists in the world
selecting a representation means making a set of ontological
commitments which are, in effect, a strong pair of glasses
that
determine what we can see
3.2.3. A KR is a fragmentary theory of intelligent
reasoning (IR)
representation’s fundamental conception of IR
mathematic logic: IR is some variety of formal calculation,
typically, deduction
psychology: IR is s
een as characteristic human behavior
set of inferences that representation sanctions
logic: sanctions sound inferences, those encompassed by
logical entailment, in which every model for the axiom set is
also a model for the conclusion
rule

based: captur
e guesses of the sort that a human expert
makes, guesses that are not necessarily either sound or true in
any model
set of inferences that representation recommends
representation and reasoning are intertwined
different representations recommend differen
t inferences
3.2.4. A KR is a medium for efficient computation
a KR offers a set of ideas about how to organize information
in ways that facilitate making inferences
computational efficiency central to notion of representation
3.2.5. A KR is a me
dium of human expression
medium of expression and communication in which we tell
machine and one another about the world
is the language in which we communicate, hence, we must be
able to speak it without heroic effort
3.2.6. Some guidelines
make a con
scious effort in selecting a KR for tasks at hand
avoid using a KR for unintended purposes
cannot take the singular role of representation to be
conveying knowledge contents
when combining representations, have to determine how two
theories of intelligent
reasoning might work together
evaluation criteria
* quality of basic knowledge structure, storage and
retrieval mechanisms
* quality of KR environment
3.3. Production Rules
3.3.1. General idea
based on the notion of condition

action pai
rs
if
condition
then
action
components
* rule base: set of production rules
* global database: contains problem states
* control system: determine which rules to apply and
termination of deduction
8

puzzle example
* basic elements o
f a problem definition: states and actions
* the initial state
* set of possible actions (operators)
* state space: set of all states reachable from the initial
state by any sequence of actions
* path in the state space: any sequence of action
s leading
from one state to another
* goal test (state that satisfies goal test will be a goal state)
* path cost: function that assigns a cost to a path
* solution: a path from the initial state to a state that
satisfies the goal test
3
.3.2. Objects and their attributes/values, and clauses
building blocks of condition/action: AV

pairs
attributes have:
* name and type
* prompt
* legal values
* confidence factors
AV

pair table
clauses
3.3.3. Rules
properties: name, priori
ty, cost, confidence factor
rule status
rule organization: disjunctive premise, multiple conclusions,
grouping and ordering
commutative rules
3.3.4. Control system
chaining
forward (data

driven)
backward (problem

reduction)
bi

directional
strategies
irrevocable:
backtracking
graph search
decomposability
database
goals
3.3.5. Rules as a KR
ontological commitment: view the world in terms of object

attribute

value triple, and rules of plausible inference that
connect them
inference recommended:
plausible inferences which are
modeled after behavior of human expert (rather than an
abstract formal model)
facilitate plausible inferences by supplying indexes from facts
(goals) to rules
3.4. Semantic Networks
3.4.1. Components
a graphical re
presentation in which
* nodes: objects, events, concepts, or situations
* links: relationships among them
relationships
* IS

A: an instance in a set
* AKO: subset in a set
* HAS

A: part in an object
* EQ: function applied to tail node yie
lds head node
examples
* from
Principles of AI
, Nils Nilsson, Morgan Kaufman
3.4.2. Representing knowledge
representing connectives
* use of enclosure, a closed dashed line
asserting properties
* use of sorted

variable nodes
property inheritanc
e
3.4.3. Reasoning
through matching
* given: fact network and goal network
* find a match between the two
syntactic matching
semantic matching
matching involving variables
3.4.4. Semantic networks as a KR
ontological commitment: view the w
orld in terms of objects
and certain relationships that connect them
inference recommended: matching process (bi

directional
propagation through the networks
appropriate set of links to facilitate bi

directional propagation
introduced concept such as prop
erty inheritance
3.5. Frames
3.5.1. Structure
name
: identification for frames
parent
: property inheritance via hierarchical structure
slot
/
value
pairs: attributes describing objects
predicate
conditions for slots: monitor update/retrieval of
info
rmation in frame

based systems
*
if

needed
predicates
*
if

added
predicates
*
if

removed
predicate
3.5.2. Property inheritance
frames are organized into a hierarchy with each element at a
lower level inheriting the properties of its ancestors
eac
h frame may include all the slots of its ancestors
slot value inheritance
(retrieval): a frame may inherit the
value of an inherited slot without explicitly containing the
slot
slot name inheritance (updating): a frame may inherit the
name of an inherited
slot by explicitly adding it (any attached
predicate will also be inherited)
3.5.3. Exceptions and defaults
objects/events usually have
* regular (default) behavior, and
* exceptional behavior
static situation
: exception handling is provided thr
ough
redefinition of the value of an inherited slot at a lower level in
the hierarchy of inheritance
dynamic situation
: by dynamically changing the frame where
exception occurs
* slot name explicitly inherited
* a different value is assigned
3.5.4.
Attached predicates
purposes:
* maintain integrity of KB
* provide for dynamic information management
* associate rules with frames
usage: predicates used to
restrict access
, offer
controlled
updating
, guarantee
data
integrity
, compute
dynamic dat
a
processing procedures
*
if

needed
predicates
*
if

added
predicates
3.5.5. Logical operations on frames
can define a set of built

in predicates that operate on frames
new_frame(frame_name, parent)
delete_frame(frame_name)
add_slot(frame_name, sl
ot_name)
delete_n_frame: delete all new frames created during
execution
is_a(x, y): check if frame x is an instance of frame y
has_a(x, y): check if frame x has a slot y
has_parent(x, y): check if frame x has frame y as its parent
has_value(frame_name,
slot_name): check if slot has a value
3.5.6. Combining rules with frames
rules that act on frames
frames that trigger rules (through attached predicates)
frames, rules and relational databases
3.5.7. Frames as a KR
based on insights about human
cognition and organization of
knowledge in memory
ontological commitment:
* to view the world in terms of stereotypical descriptions
* to link frames into systems to capture perspective shifts
theory of IR
* reasoning is based on recognition (matchin
g stereotypes
against individual instances)
* inferences sanctioned are based on good matches,
expectations, or defaults, which are unsound
* recommended inference is anticipatory matching
medium for efficient computation
* triggers and pro
cedural attachment
* taxonomic hierarchies
medium of expression
* useful for describing concepts in natural world
* need some way of indicating what properties an object
typically has, without committing to statements about
what is always t
rue
3.6. First Order Predicate Logic
FOP calculus consists of:
first order language (set of well

formed formulas,
wff
);
a set of axioms;
a set of inference rules.
Notes:
1.
wff: legitimate expressions in the language
2.
syntax of wffs (construction and
derivation)
3.
semantics of wffs (interpretation)
3.6.1. First order language
Alphabet of Symbols
consists of seven classes of symbols
variables
constants
functions
predicates
connectives
conjunction
(
);
disjunction
(
);
implication
(
);
log
ical
equivalence
(
);
negation
(
)
quantifiers
universal
(
);
existential
(
)
auxiliary symbols (parentheses, commas)
Notes:
1.
last three classes are the same for every alphabet
2.
first four classes vary from alphabet to alphabet
3.
for any alphabet,
only second and third classes may be empty
4.
binding order
wffs
terms:
* a variable is a term
* a constant is a term
* if f is an n

ary function and t
1
,...,t
n
are terms, then
f(t
1
,...,t
n
) is a term
ground terms: terms not containing variables
wffs
* if p is an n

ary predicate symbol and t
1
,...,t
n
are terms,
then p(t
1
,...,t
n
) is a wff
* if F and G are wff, then so are:
F, F
G, F
G, F
G, F
G
* if F is a wff and x is a variable, then so are:
xF,
xF
atomic formulas
(atoms)
literals
Notes
: The first order language given by an alphabet consists of
the set of all wffs constructed from the symbols of the alphabet.
Syntactical Properties of wffs
the scope of
x (
x ) in
xF (
xF ) is F
bound and free variables
* an
occurrence of a variable in a wff is
bound
iff it is
within the scope of a quantifier employing the variable
* an occurrence of a variable in a wff is
free
iff it is not
bound
closed wffs (sentences): a
closed wff
is one with no free
occurrences
of any variable
ground wffs a wff with no variables is referred to as a
ground
wff
Propositions
a subset of wffs where variables are not used
useful in many simplified domains and applications
3.6.2. Semantics of wffs
Connection between Formal Lang
uage and Structures
Interpretations
Truth Values of wffs
atoms
wffs with connectives
wffs with quantifiers
Some Examples
3.6.3. Logical equivalence
Definition:
if truth values of two wffs are the same under every interetation,
then they are logi
cally equivalent.
Set of Equivalences
3.6.4. Models and validity/inconsistency of wffs
Models
Consistent wffs (satifiable wffs)
Inconsistent wffs (unsatisfiable wffs)
Valid wffs (tautology)
Invalid wffs
Notes:
1.
A wff is valid iff its negatio
n is inconsistent.
2.
A wff is inconsistent iff its negation is valid.
3.
If a wff is valid, then it is consistent, but not vice versa.
4.
If a wff is inconsistent, then it is invalid, but not vice versa.
3.6.5. Logical consequence
Definition
Given wffs F1,..
., Fn, and a wff G, G is said to be a
logical
consequence
of F1, ..., Fn (or, G
logically follows
F1, ..., Fn; or
F1, ..., Fn
logically
imply
G) iff a model of F1, ..., Fn is also a
model of G.
Theorem 1
Given wffs F1, ..., Fn, and a wff G, G is a
logic
al consequence
of F1,..., Fn iff the following wff is valid
(F1
...
Fn)
G
Theorem 2
Given wffs F1,...,Fn, and a wff G, G is a logical consequence of
F1,...,Fn iff the following wff is inconsistent
F1
...
Fn
G
3.6.6. Predicate logic as
KR
ontological commitment
* viewing the world in terms of individual entities and
relations between them
theory of IR
* reasoning is some formal calculation, typically, deduction,
that is based on an abstract formal model
* inferences sanctio
ned are sound inferences, those
encompassed by logical entailment, in which every model
for the axiom set is also a model for the conclusion
* representation itself does not provide recommended
inferences, therefore, the user must select inferences
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