Logic in artificial intelligence
1.
What is
logic?
Logic
as per the definition of the Oxford dictionary, is "the reasoning conducted or
assessed according to strict principles and validity". In Artificial Intelligence also, it
carries somewhat the same meaning. Logic can be defined as the proof or validation
behind any reason provided. A logic must also define the semantics or meaning of
sentences. The semantics define the truth of each sentence with respect to each
possible world.
For example:The semantics for arithmetic specifies that the sentence “x + y = 4” is true
in a world where x is 2 and y is 2, but false in a world where x is 1 and y is 1. In standard
logics, every sentence must be either true or false in each possible world—there is no “in
between.”1
2.
X
Y
X+Y
2
2
TRUE
1
1
FALSE
What is
propositional calculus:propositional
A proposition has a specific truth value, either true or
calculus?
false.Propositional calculus is a branch of logic. It is also called propositional logic,
statement logic, or sometimes zeroth-order logic. It deals with propositions (which can be
true or false) and relations between propositions, including the construction of arguments
based on them.Compound propositions are formed by connecting propositions by logical
connectives. Propositions that contain no logical connectives are called atomic
propositions.
3.
Propositions
are
combined of
what?
There are five common connectives (conjunction, disjunction, negation, implication, and
equivalence), defined by the following truth table, where P and Q are (atomic or compound)
propositions:
P
Q
(P ∧ Q)
(P∨Q)
(¬P)
(P → Q)
(P ↔ Q)
T
T
T
T
F
T
T
T
F
F
T
F
F
F
F
T
F
T
T
T
F
F
F
F
F
T
T
T
∧
∨
¬
→
↔
AND
OR
NOT
IF THEN
IF AND ONLY IF
4.
Facts about
Propositional
Logic
 Since propositional logic works on 0 and 1 thus it is also known as ‘Boolean Logic’.
 Proposition logic can be either true or false it can never be both.
 In this type of logic, symbolic variables are used in order to represent the logic and
any logic can be used for representing the variable.
 t is comprised of objects, relations, functions, and logical connectives.
 Proposition formula which is always false is called ‘Contradiction’ whereas a
proposition formula which is always true is called ‘Tautology’.
5.
EXAMPLES
UNSOLVE QUESTIONS
SOLVE QUESTIONS
If statments not represent by alphabet
formula
Action word (who perform action + symbol+ on which action is perform)