First Order Logic

Explain the role of first order logic
(FoL) in AI.
PRESENTED BY MUHAMMAD MUBEEN YASEEN
REG NO: 17-NTU-1228
PRESENTED TO : DR.REHAN

Content:
Pros and cons Propositional logic.
Limitation of propositional logic.
Predicate logic.
What is FOL?
Syntax of FOL, Basic elements.
Atomic Sentence.
Complex Sentence.
Universal quantifier.
Existential quantifier.

Pros and cons Propositional logic.
• Propositional Logic is a declarative.
• Propositional Logic allow partial/disjunctive/negated Information.
• Propositional logic is a compositional.
• Meaning of B1,1 ^ P1,2 is derived from meaning of B1,1 and P1,2.
• Meaning in propositional Logic is context independent.
• Propositional Logic has very limited expressive power.

Limitation of propositional logic.
• Suppose you want to say “All Human are mortal”
• In Propositional Logic you need ~6.7 billion statement
• Suppose you want to say “some people cam run a marathon”
• You would need a disjunction of ~6.7 billion statement

Predicate logic.
• Whereas the propositional logic assume the world contain facts.
• First Order logic assume the world contain:
• Objects: People, houses, numbers, color, baseball, games
• Relations: Red, round, brother of, bigger than
• Function Relations: father of, best friend, one more than, plus

What is FOL?
• First-order logic is another way of knowledge representation in artificial intelligence. It is an
extension to propositional logic.
• FOL is sufficiently expressive to represent the natural language statements in a concise
way.
• 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 an easy
way and can also express the relationship between those objects.

Syntax of FOL, Basic elements.
Constant 1, 2, A, John, Mumbai, cat,....
Variables x, y, z, a, b,....
Predicates Brother, Father, >,....
Function sqrt, LeftLegOf, ....
Connectives ∧, ∨, ¬, ⇒, ⇔
Equality ==
Quantifier ∀, ∃
Following are the basic elements of FOL syntax:

Atomic Sentence.
• 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).

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.
X is an integer
Subject Predicate
Is an integerX

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 thing.
• The Universal quantifier is represented by a symbol ∀, which resembles an inverted A.
• If x is a variable, then ∀x is read as:
• For all x
• For each x
• For every x.

Example of Universal quantifier:
• All man drink coffee.
• ∀x man(x) → drink (x, coffee).
• It will be read as: There are all x where x is a man who drink coffee.

Existential quantifier:
• Existential quantifiers are the type of quantifiers, which express that the statement within its
scope is true for at least one instance of something.
• It is denoted by the logical operator ∃, which resembles as inverted E. When it is used with a
predicate variable then it is called as an existential quantifier.
• If x is a variable, then existential quantifier will be ∃x or ∃(x). And it will be read as:
• There exists a 'x.'
• For some 'x.'
• For at least one 'x.'

Example of Existential quantifier:
• Some boys are intelligent.
• ∃x: boys(x) ∧ intelligent(x)
• It will be read as: There are some x where x is a boy who is intelligent.

First Order Logic

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First Order Logic