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Artificial Intelligence
Lecture 3
Logic
• Logic is a language used to represent
knowledge and facts
Knowledge Representation Techniques
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Using binary numbers
As a set of pixels
In graphical form
In prepositional logic
In predicate logic
Semantic net
Using conceptual dependency sturcture
Characteristics of Knowledge
Representation Techniques
• Should be adequate to express all the
necessary information
• Should provide natural scheme for expressing
the required knowledge
• Should support efficient execution for
inferencing purpose
Types of logic used in AI
• Propositional Calculus
• Predicate Calculus
Propositional Calculus
• PropositionStatements used in mathematics
• Value of proposition may be true or false
• For example
Dhaka is the capital of Bangladesh proposition
The square root of 9 is 3proposition
This statement is falseassertion
Types of Propositional Calculus
• Atomic Proposition  single proposition
• Molecular (Complex)Proposition  combines
two or more propositions
Symbols of Propositional Calculus
• Atomic symbol
• Logical connectives
Atomic symbols
• Any symbol that is proposition and can be true
or false is a atomic symbol
• Uppercase letters are used to denote atomic
symbols
• True and false are special proposition
Logical Connectives
• Used to join atomic symbols to form complex structure
• Valid connectives are as follows
i)Not or negation  Denoted by ̚  if P is true then ̚ P is false
ii)Conjunction Denoted by AND/˄ P˄Q will be true if both of
them is true
iii)Disjunction Denoted by OR/˅ P˅Q will be true if only one of
them is true
iv)Implication  Denoted by →  P→Q if P is true the Q is true
v) Biconditional  Denoted by ↔  P and Q are biconditional if
and only if both are same
vi)Equivalence Denoted by ≡
vii)() and [] are used for group symbols
Semantics of Propositional Calculus
• Defines meaning of sentence
• Assignment of truth value to a propositional
sentenceinterpretation
• Interpretation of negation̚ P is true(T) if P is false(F)
• Interpretation of conjunction is T only when both the
conjuncts have T values
• Interpretation of disjunctionis F only when both the
disjuncts have F value
• Interpretation of implication is T if the previous
statement has T value
• Interpretation of Biconditionalis T only when symbols on
the both sides are either T or F ,otherwise F
Truth Values of Connectives
Real world Example
Properties of Statements
• Valid  a sentence is valid if it is true for all values of
input
• Satisfiable  the statement has at least one
interpretation for which it is true
• Unsatisfiable complement of satisfiable
• Equivalence two statements are equivalent if for
every interpretation they have the same truth value
• Logical consequence two statements are logically
consequent to one another if one statement satisfies
all interpretation that are accepted by another
statement