CC–13 : Artificial Intelligence (Unit–3)
Knowledge representation: Humans are best at understanding, reasoning,
and interpreting knowledge. Human knows things, which is knowledge and as per
their knowledge they perform various actions in the real world. But how machines do
all these things comes under knowledge representation and reasoning.
Following are the various types of knowledge:
1. Declarative Knowledge – It includes concepts, facts, and objects.
2. Procedural Knowledge – It includes rules, strategies, procedures, agendas,
etc.
3. Meta-knowledge – Knowledge about the other types of knowledge is called
Meta-knowledge.
4. Heuristic knowledge – Heuristic knowledge are the experiences in a field or
subject which are good to work but not guaranteed.
5. Structural knowledge – It describes the relationship between concepts or
objects.
6. Knowledge-Base: A knowledge base is an organized collection of facts
about the system's domain.
Introduction to First Order Predicate Logic: Propositional logic (PL) is the
simplest form of logic where all the statements are made by propositions. It is a
technique of knowledge representation in logical and mathematical form. A
proposition is a declarative statement which is either true or false e.g.
a) It is Sunday.
b) The Sun rises from West (False proposition)
c) 3+3= 7(False proposition)
d) 5 is a prime number.
In propositional logic, we can only represent the facts, which are either true or false.
PL is not sufficient to represent the complex sentences or natural language
statements. So we required some more powerful logic, such as first-order logic.
First-order logic is also known as Predicate logic or First-order predicate logic. First-
order logic is a powerful language that develops information about the objects in a
more easy way and can also express the relationship between those objects. First-
order logic (like natural language) does not only assume that the world contains
facts like propositional logic but also assumes the following things in the world:
Objects: A, B, people, numbers, colours, wars, theories, squares, pits, ......
Relations: It can be unary relation such as: red, round, is adjacent, or n-any
relation such as: the sister of, brother of, has colour, comes between
Function: Father of, best friend, third inning of, end of, ......
Similar to natural language, first-order logic also has two main parts i.e. Syntax and
Semantics.
Syntax of First-Order logic: The syntax of FOL determines which collection of
symbols is a logical expression in first-order logic. The basic syntactic elements of
first-order logic are symbols. We write statements in short-hand notation in FOL.
Basic Elements of First-order logic: The basic elements of FOL are shown in the
table.
Manas Ku Mishra, Asst. Prof. of Comp. Sc., FM (A) College, BLS. Page 1 of 11
, Constant 1, 2, A, John, Mumbai, Cat, ....
Variables x, y, z, a, b,....
Predicates Brother, Father, >,....
Function sqrt, LeftLegOf, ....
Connectives ∧ , ∨ , ¬, ⇒ , ⇔
Equality ==
Quantifier ∀,∃
Atomic sentences:
Atomic sentences are the most basic sentences of first-order logic. These
sentences are formed from a predicate symbol followed by a parenthesis with
a sequence of terms.
We can represent atomic sentences as Predicate (term1, term2, ......, term n).
Example: Ravi and Ajay are brothers: Brothers (Ravi, Ajay).
Chinky is a cat: cat (Chinky).
Complex Sentences: Complex sentences are made by combining atomic
sentences using connectives.
First-order logic statements can be divided into two parts:
Subject: Subject is the main part of the statement.
Predicate: A predicate can be defined as a relation, which binds two atoms
together in a statement.
Consider the statement: "x is an integer.” it consists of two parts, the first part x is
the subject of the statement and second part "is an integer” is known as a
predicate.
Quantifiers in First-order logic:
A quantifier is a language element which generates quantification, and
quantification specifies the quantity of specimen in the universe of discourse.
These are the symbols that permit to determine or identify the range and
scope of the variable in the logical expression. There are two types of
quantifier:
a. Universal Quantifier, (for all, everyone, everything)
b. Existential quantifier, (for some, at least one).
Universal Quantifier: Universal quantifier is a symbol of logical representation,
which specifies that the statement within its range is true for everything or every
instance of a particular thing.
The Universal quantifier is represented by a symbol ∀ , which resembles an inverted
A.
Note: In universal quantifier we use implication "→".
If x is a variable, then ∀x is read as: For all x, For each x, For every x
Example: ∀ x man(x) → drink (x, coffee).
It will be read as: There are all x where x is a man who drink coffee.
Manas Ku Mishra, Asst. Prof. of Comp. Sc., FM (A) College, BLS. Page 2 of 11
Knowledge representation: Humans are best at understanding, reasoning,
and interpreting knowledge. Human knows things, which is knowledge and as per
their knowledge they perform various actions in the real world. But how machines do
all these things comes under knowledge representation and reasoning.
Following are the various types of knowledge:
1. Declarative Knowledge – It includes concepts, facts, and objects.
2. Procedural Knowledge – It includes rules, strategies, procedures, agendas,
etc.
3. Meta-knowledge – Knowledge about the other types of knowledge is called
Meta-knowledge.
4. Heuristic knowledge – Heuristic knowledge are the experiences in a field or
subject which are good to work but not guaranteed.
5. Structural knowledge – It describes the relationship between concepts or
objects.
6. Knowledge-Base: A knowledge base is an organized collection of facts
about the system's domain.
Introduction to First Order Predicate Logic: Propositional logic (PL) is the
simplest form of logic where all the statements are made by propositions. It is a
technique of knowledge representation in logical and mathematical form. A
proposition is a declarative statement which is either true or false e.g.
a) It is Sunday.
b) The Sun rises from West (False proposition)
c) 3+3= 7(False proposition)
d) 5 is a prime number.
In propositional logic, we can only represent the facts, which are either true or false.
PL is not sufficient to represent the complex sentences or natural language
statements. So we required some more powerful logic, such as first-order logic.
First-order logic is also known as Predicate logic or First-order predicate logic. First-
order logic is a powerful language that develops information about the objects in a
more easy way and can also express the relationship between those objects. First-
order logic (like natural language) does not only assume that the world contains
facts like propositional logic but also assumes the following things in the world:
Objects: A, B, people, numbers, colours, wars, theories, squares, pits, ......
Relations: It can be unary relation such as: red, round, is adjacent, or n-any
relation such as: the sister of, brother of, has colour, comes between
Function: Father of, best friend, third inning of, end of, ......
Similar to natural language, first-order logic also has two main parts i.e. Syntax and
Semantics.
Syntax of First-Order logic: The syntax of FOL determines which collection of
symbols is a logical expression in first-order logic. The basic syntactic elements of
first-order logic are symbols. We write statements in short-hand notation in FOL.
Basic Elements of First-order logic: The basic elements of FOL are shown in the
table.
Manas Ku Mishra, Asst. Prof. of Comp. Sc., FM (A) College, BLS. Page 1 of 11
, Constant 1, 2, A, John, Mumbai, Cat, ....
Variables x, y, z, a, b,....
Predicates Brother, Father, >,....
Function sqrt, LeftLegOf, ....
Connectives ∧ , ∨ , ¬, ⇒ , ⇔
Equality ==
Quantifier ∀,∃
Atomic sentences:
Atomic sentences are the most basic sentences of first-order logic. These
sentences are formed from a predicate symbol followed by a parenthesis with
a sequence of terms.
We can represent atomic sentences as Predicate (term1, term2, ......, term n).
Example: Ravi and Ajay are brothers: Brothers (Ravi, Ajay).
Chinky is a cat: cat (Chinky).
Complex Sentences: Complex sentences are made by combining atomic
sentences using connectives.
First-order logic statements can be divided into two parts:
Subject: Subject is the main part of the statement.
Predicate: A predicate can be defined as a relation, which binds two atoms
together in a statement.
Consider the statement: "x is an integer.” it consists of two parts, the first part x is
the subject of the statement and second part "is an integer” is known as a
predicate.
Quantifiers in First-order logic:
A quantifier is a language element which generates quantification, and
quantification specifies the quantity of specimen in the universe of discourse.
These are the symbols that permit to determine or identify the range and
scope of the variable in the logical expression. There are two types of
quantifier:
a. Universal Quantifier, (for all, everyone, everything)
b. Existential quantifier, (for some, at least one).
Universal Quantifier: Universal quantifier is a symbol of logical representation,
which specifies that the statement within its range is true for everything or every
instance of a particular thing.
The Universal quantifier is represented by a symbol ∀ , which resembles an inverted
A.
Note: In universal quantifier we use implication "→".
If x is a variable, then ∀x is read as: For all x, For each x, For every x
Example: ∀ x man(x) → drink (x, coffee).
It will be read as: There are all x where x is a man who drink coffee.
Manas Ku Mishra, Asst. Prof. of Comp. Sc., FM (A) College, BLS. Page 2 of 11
