7/28/2019 Knowledge Representation-Part 2
1/66
First-Order Logic
Study Material:
Section 2.2-2.4,Chapter 2 in Luger, Artificial Intelligence:
Structures and StrategiesExample 3.3.5, Chapter 3 in Luger, Artificial Intelligence:Structures and Strategies, pp 115-116
1CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
2/66
Propositional Logic Simple logic in which all sentences are assertions with
truth values.
e.g. it is raining
We cannot access the components of an individualassertion
e.g. if P represents A bug is in my soup we cannot
access the bug or soup components No variables are allowed cannot create general
assertions about entities.
2CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
3/66
Example 2
Blocks WorldGoal: to create a set of expressionsthat is to represent a static snapshot ofthe blocks world.
Assumption: predicates evaluatedtop-down, and left-right.
b
da
c
17CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
4/66
Example 2
Blocks Worldblock X is on block Y
on(X, Y)
block X is on the tableon_table(X)
block X has nothing on top of it
clear(x)
the robots hand is emptyhand_empty
b
da
c
18CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
5/66
Example 2
Blocks WorldWhat is the domain of the variables X and
Y in this world for the previousexpressions?
D={a,b,c,d}
What are the possible interpretations forX and Y for on(X,Y)?
{, ,, ,,,,,,, }
Which interpretations make on(X,Y) truein this world?
{, }
b
da
c
19CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
6/66
Example 2
Blocks WorldA description of this blocks world:
on(b,a)ontable(a)
ontable(d)
on(c,d)
clear(b)clear(c)
hand_empty
b
da
c
20CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
7/66
Models and Interpretations Models are mathematical abstractions of the possible world.
Models are defined by: a set of objects.
the relations between them and the functions that can be applied to them
Interpretations map the symbols of a language to the model: constant symbols are mapped to objects
function symbols are mapped to functions
predicate symbols are mapped relations in the model. Interpretations and models together determine the truth of a
sentence.
m is a model of sentence smeans sentence s is true in m.
21CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
8/66
Interpretations If an interpretation Imakes S true, we sayIsatisfiesS.
If there is at least one interpretation Ithat makes Strue, we saySis satisfiable.
If there is no interpretation I that makes Strue, we saySis unsatisfiable:
X (p(X) p(X))
22CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
9/66
Interpretations If a sentence S is T under all interpretations, S is said
to be valid.
Examples: X (p(X) p(X))
true
The deduction theorem
For any sentences s1 and S2, S1 entails sS2 if and only ifthe sentence (S1S2) is valid.
(proof?)
23CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
10/66
Interpretations
valid: All interpretations make S
true
satisfiableThere is aninterpretation
that makes S true
unsatisfiable
Nointerpretationmakes S true
24CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
11/66
Example 2
Blocks WorldGoal: to create a set of expressions that isto represent a static snapshot of the blocks
world.Assumption: predicates evaluated top-
down, and left-right.
on(b,a)ontable(a)ontable(d)
on(c,d)clear(b)clear(c)hand_empty
b
da
c
The blocks worldin this figure is amodelfor thisinterpretation
25CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
12/66
Example 2
Blocks WorldWhen is a block clear?
A block in our world is clear if there are no other blocks on top of it
X ((Y on(Y,X)) clear(X))How can we clear a block clear?
X ((Y on(Y,X)) clear(X))
conditions action
How can we stack a block on top of another?
XY (hand_empty clear(X) clear(Y) pick_up(X) put_down(X,Y) stack(X,Y))
b
da
c
26CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
13/66
Using FOL to Represent a Domain Domain: A part of the world of which we would like to express some
knowledge. Components:
assertions axioms (basic sentences that do not need to be proven)
facts about the domainon(a, b) properties of objects or predicates (possibly partial)
XY(on(Y,X) ontable(Y)) definitions
X (((Y on(Y,X)) clear(X)) (clear(X)(Y on(Y,X)))
theorems (entailed by axioms )X ((Y on(Y,X)) clear(X)) (assuming the definition is used in KB)
queries/goals clear(a) => repsonse should be F X clear(X) => response: {X/b, X/c} Substitution list
27CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
14/66
Knowledge Endgineering
The general process of knowledge base construction
(Russell and Norvig, 2003)
28CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
15/66
Knowledge Endgineering Process1. Identify the task
2. Assemble the relevant information
3. Decide on a vocabulary of predicates, functions, andconstants.
4. Encode general knowledge about the domain
5. Encode a description of the specific problem instance
6. Pose queries to the inference procedure and get answers.7. Debug the knowledge base
29CP468, Dr. Reem K. Al-Halimi
E l 3
7/28/2019 Knowledge Representation-Part 2
16/66
Example 3
A Logic-Based Financial Advisor
Goal: to help the user decide whether to invest in a savings account, thestock market only, or a combination of the two.
Recommendations will be based on the investors current savings andtheir income according to the criteria:
1. Individuals with an inadequate savings account should make
increasing their savings a first priority.2. Individuals with an adequate savings account and an adequate
income should consider investing in the stock market.
3. Individuals with an adequate savings account and a lower incomeshould consider splitting their surplus income between savings
and stocks. the adequacy of their savings account is determined by the number
of dependents: s/he has to have at least $5000/dependent.
An adequate income must be steady, at least $15,000/year plus anadditional $4,000 per dependent.
30CP468, Dr. Reem K. Al-Halimi
E l 3
7/28/2019 Knowledge Representation-Part 2
17/66
Example 3
A Logic-Based Financial Advisor
1. Identify the task
Goal: to help the user decide whether to invest in a savingsaccount, the stock market only, or a combination of the
two.
31CP468, Dr. Reem K. Al-Halimi
E l 3
7/28/2019 Knowledge Representation-Part 2
18/66
Example 3
A Logic-Based Financial Advisor
2. Assemble the relevant information
Recommendations will be based on the investors current savings and theirincome according to the criteria:
1. Individuals with an inadequate savings account should makeincreasing their savings a first priority.
2. Individuals with an adequate savings account and an adequate incomeshould consider investing in the stock market.
3. Individuals with an adequate savings account and a lower income
should consider splitting their surplus income between savings andstocks.
the adequacy of their savings account is determined by the number ofdependents: s/he has to have at least $5000/dependent.
An adequate income must be steady, at least $15,000/year plus an
additional $4,000 per dependent. 32CP468, Dr. Reem K. Al-Halimi
E l 3
7/28/2019 Knowledge Representation-Part 2
19/66
Example 3
A Logic-Based Financial Advisor
3. Decide on a vocabulary of predicates, functions, andconstants.
Recommendations will be based on the investors current savings andtheir income according to the criteria:
1. Individuals with an inadequate savings account should make
increasing their savings a first priority.
2. Individuals with an adequate savings account and an adequateincome should consider investing in the stock market.
3. Individuals with an adequate savings account and a lower incomeshould consider splitting their surplus income between savingsand stocks.
the adequacy of their savings account is determined by the numberof dependents: s/he has to have at least $5000/dependent.
An adequate income must be steady, at least $15,000/year plus an
additional $4,000 per dependent. 33CP468, Dr. Reem K. Al-Halimi
E l 3
7/28/2019 Knowledge Representation-Part 2
20/66
Example 3
A Logic-Based Financial Advisor
3. Decide on a vocabulary of predicates, functions, andconstants.
Concepts
the investors current savings
adequate/inadequate
the investors income
adequate/inadequate
steady/unsteady
investment
savings stock
combination (savings and stock)
the number of dependents
An adequate income must be steady
34CP468, Dr. Reem K. Al-Halimi
E l 3
7/28/2019 Knowledge Representation-Part 2
21/66
Example 3
A Logic-Based Financial Advisor
3. Decide on a vocabulary of predicates, functions, andconstants.
Symbol Type Concept Name
Function Symbols the investors current savings amount_saved
the investors income earningsConstants adequate adequate
inadequate inadequate
savings savings
stock stock
combination combination
steady steady
unsteady unsteady
Predicate Symbols invest invest
dependents dependents 35CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
22/66
Example 3
A Logic-Based Financial Advisor4. Encode general knowledge about the domain
Decisions are based on savings_account(adequate)
savings_account(inadequate)
income(adequate)
income(inadequate)
decisions: invest(savings)
invest(stocks)
invest(combination)
36CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
23/66
Example 3
A Logic-Based Financial Advisor4. Encode general knowledge about the domain
Decision criteria:1. savings_account(inadequate) invest(savings)
2. savings_account(adequate) income(adequate) invest(stocks)
3. savings_account(adequate) income(inadequate) invest(combination)
37CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
24/66
Example 3
A Logic-Based Financial Advisor4. Encode general knowledge about the domain
adequate savings? the adequacy of their savings account is determined by the
number of dependents: s/he has to have at least
$5000/dependent.
How many dependents? Y such that dependents(Y) is true
What is the minimum savings required?
minsavings(Y) = 5000*Y What are the actual savings?
amount_saved(X) Are the actual savings greater than the minimum?
greaterThan(X, minsavings(Y))
38CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
25/66
Example 3:A Logic-Based Financial Advisor
3. Decide on a vocabulary of predicates, functions, and constants.
Symbol Type Concept NameFunction Symbols the investors current savings amount_saved
the investors income earnings
minimum adequate savings minsavings
Constants adequate adequate
inadequate inadequate
savings savings
stock stock
combination combination
steady steadyunsteady unsteady
Predicate Symbols invest invest
dependents dependents
test if one number is greater than another greaterThan 39CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
26/66
Example 3
A Logic-Based Financial Advisor4. Encode general knowledge about the domain
adequate savings? Are the savings adequate (check all amounts saved)?
X amount_saved(X) Y (dependents(Y) greaterThan(X,minsavings(Y)) savings_account(adequate)
X amount_saved(X) Y (dependents(Y) greaterThan(X,minsavings(Y)) savings_account(inadequate)
40CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
27/66
Example 3
A Logic-Based Financial Advisor4. Encode general knowledge about the domain
adequate income? An adequate income must be steady, at least $15,000/year
plus an additional $4,000 per dependent
What is the minimum savings required? minincome(Y) = 15000 + 4000*Y
What are the actual savings? earnings(X, Z)
Are the actual earnings greater than the minimum? greaterThan(X, minincome(Y))
41CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
28/66
Example 3:A Logic-Based Financial Advisor
3. Decide on a vocabulary of predicates, functions, and constants.
Symbol Type Concept NameFunction Symbols the investors current savings amount_saved
the investors income earnings
minimum adequate savings minsavings
minimum adequate income minincome
Constants adequate adequate
inadequate inadequate
savings savings
stock stock
combination combinationsteady steady
unsteady unsteady
Predicate Symbols invest invest
dependents dependents
test if one number is greater than another greaterThan 42CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
29/66
Example 3
A Logic-Based Financial Advisor4. Encode general knowledge about the domain
adequate income? An adequate income must be steady, at least $15,000/year
plus an additional $4,000 per dependent
Are the savings adequate (check all amounts saved)? X earnings(X, steady) Y (dependents(Y) greaterThan(X,
minincome(Y)) income(adequate) X earnings(X, steady) Y (dependents(Y) greaterThan(X,
minincome(Y)) income(inadequate)
X earnings(X, unsteady) income(inadequate)
43CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
30/66
Example 3
A Logic-Based Financial Advisor5. Encode a description of the specific problem
instance
Given a particular investor, we add his/her informationto the knowledge base:
e.g. an investor with three children, $22,000 in savings,and $25,000 in steady income:
earnings(25000, steady)
amount_saved(22000)
dependents(3)
44CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
31/66
Example 3
A Logic-Based Financial Advisor6. Pose queries to the inference procedure and get
answers.
What type of investment should the customer make?
X invest(X)
How can the system find out the answer?
45CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
32/66
Components of First-Order Logic
Proof System In propositional logic we could test an assumption
using a truth table.
We can use the same approach for sentences notcontaining variables
46CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
33/66
Components of First-Order Logic
Proof System Let us take an example:
if it is sunny, the weather will be warm
S W (1) if it is warm, the school will be open
W O (2)
It is sunny
S (3)
Will the school be open?
i.e. is true that in every world in which all of the abovesentences are true that O is true as well? Does Ologically follow from sentences 1, 2, and 3 above?
47CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
34/66
Components of First-Order Logic
Proof SystemS W O SW WO
T T F T F
T T T T T
T F T F T
T F F F T
F T T T T
F T F T F
F F T T T
F F F T T
48CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
35/66
Components of First-Order Logic
Proof SystemS W O SW WO
T T F T F
T T T T T
T F T F T
T F F F T
F T T T T
F T F T FF F T T T
F F F T T
49CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
36/66
Components of First-Order Logic
Proof SystemS W O SW WO
T T F T F
T T T T T
T F T F T
T F F F T
F T T T T
F T F T FF F T T T
F F F T T
Yes! The School will be open!
50CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
37/66
Components of First-Order Logic
Proof System In propositional logic we could test an assumption
using a truth table.
this cannot necessarily be done in first-order logic.Why not?
Solution? Use rules to create new conclusions fromgiven predicates
51CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
38/66
Components of First-Order Logic
Proof System Logical inference is the ability to infer new correct
expressions from a set of true assertions.
Aproof procedure is a combination of an inference ruleand an algorithm for applying that rule on a set oflogical expressions to generate new sentences
52CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
39/66
Knowledge-Based System(from previous lectures) Consists of
world knowledge (knowledge base) and a way to reason about this knowledge.
KnowledgeBase
InferenceEngine
53CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
40/66
Knowledge-Based SystemWorld knowledge is expressed in a language using the
languages syntax and semantics rules.
KnowledgeBase
InferenceEngine
Chirpy is a birdBirds have wings
54CP468, Dr. Reem K. Al-Halimi
World knowledge is expressed as a set of trueassertions about a problem domain.
7/28/2019 Knowledge Representation-Part 2
41/66
Knowledge-Based System Inference rules are used to reason about the world inorder to determine when a predicate expressionlogically follows from a knowledge base.
KnowledgeBase
InferenceEngine
Chirpy is a birdBirds have wingsChirpy has wings
55CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
42/66
Using Inference RulesA sentence (predicate expression) P is said to logically
followfroma set of assertions S if and only if everyinterpretation and variable assignment that makes S
true, also makes P true.
S PS entails P
S is true
interpretations
S is true
56CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
43/66
Using Inference Rules In our financial advisor problem our question is:
given the knowledge base KB, does it logically followfrom the facts in KB that
X invest(X)
57CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
44/66
Using Inference RulesAn inference rule is soundif every predicate calculus
expression produced by the rule from a set S ofpredicate calculus expressions logically follows from S.
An inference rule is complete if, given a set S ofpredicate calculus expressions, the rule can infer every
expression that logically follows from S.
58CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
45/66
Using Inference Rules
Examples Modus Ponens
PQ
P
Q
Modus ponens is a sound inference rule.
Example:
lawyer(john)
rich(john)lawyer(john)
We can conclude:
rich(john)
59CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
46/66
Using Inference Rules
Examples Modus Tollens
PQ
Q
P
Modus tollens is a sound inference rule.
Example:
lawyer(john)
rich(john)rich(john)
We can conclude:
lawyer(john)
60CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
47/66
Using Inference Rules
Examples Elimination
P Q P Q
Q P Elimination is a sound inference rule.
Example:
cat(snowball) white(snowball)
We can conclude:
cat(snowball )
white(snowball)
61CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
48/66
Using Inference Rules
ExamplesAnd Introduction
P
Q
P Q
And introduction is a sound inference rule.
Example:
cat(snowball )white(snowball)
We can conclude:
cat(snowball) white(snowball)
62CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
49/66
Using Inference Rules
Examples Universal Instantionation
X P(X)
P(a) Universal instantiation is a sound inference rule.
Example:
X mortal(X)
if russell is in the domain of X, we can conclude:
mortal(russell)
63CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
50/66
Using Inference Rules
ExamplesX (man(X)mortal(X))
man(socrates)
Prove that Socrates is mortal?
X (man(X)mortal(X))
man(socrates)mortal(socrates) using Universal Instantiation
mortal(socrates) by applying modus ponens
64CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
51/66
Using Inference Rules
Unification Unification is an algorithm for determining the
substitutions needed to make two or more predicateexpressions match.
To use the unification algorithm all variables in alogical database must be universally quantified.
65CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
52/66
Using Inference Rules
Unification unify:
1. mortal(X) and mortal(socrates)
{socrates/X}
2. knows(john, X) and knows(john, jane){jane/X}
3. knows(john, X) and knows(Y, bill)
{bill/X, john/Y}
4. knows(john, X) and knows(Y, mother(Y))
{john/Y, mother(john)/X}
5. knows(john, X) and knows(X, bill)fail
Substitution list
66CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
53/66
Using Inference Rules
Unification substitution list {X/Y} means: X replaces Y in the
original expression
67CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
54/66
Using Inference Rules
Unification Rules1. constants cannot be replaced2. a variable cannot be unified with a term containing
it.
e.g. X cannot be replaced by f(X)
Why?
3. Once a variable has been bound, future unifications
must take the value of this binding into account.
68CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
55/66
Using Inference Rules
Unification Algorithm Basic idea:
1. sentences are represented as lists
2. equal constants return an empty substitution list
3. individual variables are bound to whatever occurs inthe other sentence.
4. if either expression is empty, unification fails
5. sentences are bound by
1. recursively unifying the first elements in each,2. then applying the substitution list to the rest of each list
3. recursively unifying the remainder of the two lists.
4. creating a single substitution list bycomposition of the listsfrom steps 5.1 and 5.3 above.
69CP468, Dr. Reem K. Al-Halimi
Using In erence Ru es
7/28/2019 Knowledge Representation-Part 2
56/66
Using In erence Ru esUnification Algorithm
Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 70CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
57/66
Using Inference Rules
Unification Algorithm: Composition Composition the process of creating a single
substitution list from two or more lists by applying oneto the other:
{X/Y, W/Z} and {V/X} and {a/V, f(b)/W}
1. composing {V/X} and {a/V, f(b)/W}:
{a/X, a/V, f(b)/W}
2. composing {X/Y, W/Z} and {a/X, a/V, f(b)/W}{a/Y, a/X, a/V, f(b)/Z, f(b)/W}
71CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
58/66
Using Inference Rules
Unification Algorithm: Composition Composition is associative
composition(sub1, composition(sub2, sub3)) =composition(composition(sub1, sub2), sub3)
but not commutative
composition(sub1, sub2) composition(sub1, sub2)
72CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
59/66
Using Inference Rules
Unification Algorithm: Most General Unifier Unify:
knows(john, X)knows(Y,Z)
Possible substitutions:G = {john/Y, Z/X}S = {john/Y, john/X, john/Z}
G is the substitution list with the least restrictions on thevariable values => G is called the most general unifier The unification algorithm described earlier calculates the
most general unifier for any given set of expressions .
73CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
60/66
Using Inference Rules
Unification Algorithm Unify:
knows(john, X)
knows(Y,Z)
74CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
61/66
Using Inference Rules
Unification Algorithmunify((knows john X), (knows Y Z))
unify(knows, knows )
return {}
unify(( john X), (Y Z))
unify(john, Y)
return {john/Y}
unify((X), (Z))
unify(X, Z)
return {Z/X}
unify((), ())
return {}
return {Z/X}
return {john/Y, Z/X}
1 2 3
4 5 6
7 89
11
12
10
75CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
62/66
Using Inference Rules
Financial Advisor Example continued How can we choose which investment is best for the
investor?
One approach: Goal-directed, depth-first search
Goal: X invest(X)
76CP468, Dr. Reem K. Al-Halimi
Using In erence Ru es
7/28/2019 Knowledge Representation-Part 2
63/66
Using In erence Ru esFinancial Advisor Example continued
Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009
77CP468, Dr. Reem K. Al-Halimi
s ng n erence u es
7/28/2019 Knowledge Representation-Part 2
64/66
s ng n erence u esFinancial Advisor Example continued
Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009From Fig 3.26 And/or graph searched by the financial advisor.
1. savings_account(inadequate) invest(savings)
78CP468, Dr. Reem K. Al-Halimi
Using In erence Ru es
7/28/2019 Knowledge Representation-Part 2
65/66
Using In erence Ru esFinancial Advisor Example continued
Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009From Fig 3.26 And/or graph searched by the financial advisor.
X amount_saved(X) Y (dependents(Y) greaterThan(X,
minsavings(Y)) savings_account(inadequate)
Unificationresult
{20000/X}
Unificationresult {2/Y}
79CP468, Dr. Reem K. Al-Halimi
7/28/2019 Knowledge Representation-Part 2
66/66
Summary Presented First Order Logic (FOL) as a powerful knowledge
representation language. Discussed the component of FOL: alphabet, syntax, semantics,
and proof systems.
Defined models and interpretations.
Looked at the components of a knowledge base and the
procedure involved in creating a knowledge-based system. Discussed inference rules and their properties: valid, satisfiable,
and unsatisfiable.
Looked at the use of sound inference rules in generating newfacts from a given set of assertions.
Presented important sound inference rules: modus ponens,modus tollens, and elimination, and universal instantiation.
Looked at the use of inference rules and search in a simple expertsystem through the financial advisor example.
Top Related