Inference Rules Flashcards
1
Q
Modus Ponens
A
p
p → q
. . . . . . . . .
q
2
Q
Modus Tollens
A
¬q
p → q
. . . . . . . . .
¬p
3
Q
Hypothetical Syllogism
A
p → q
q → r
. . . . . . . . .
p → r
4
Q
Disjunctive Syllogism
A
p ∨ q
¬p
. . . . . . . . .
q
5
Q
Addition
A
p
. . . . . . . . .
p ∨ q
6
Q
Simplification
A
p ∧ q
. . . . . . . . .
p
7
Q
Conjunction
A
p
q
. . . . . . . . .
p ∧ q
8
Q
Resolution
A
p ∨ q
¬p ∨ r
. . . . . . . . .
q ∨ r
9
Q
Universal Instantiation
A
∀ x P(x)
. . . . . . . . .
P(c)
10
Q
Universal Generalization
A
P(c) for an arbitrary, c
. . . . . . . . .
∀ x P(x)
11
Q
Existential Instantiation
A
∃ x P(x)
. . . . . . . . .
P(c) for some element, c
12
Q
Existential Generalization
A
P(c) for some element, c
. . . . . . . . .
∃ x P(x)
