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Logic Rules
Implicational and Eqivalence Rules
18
Philosophy
Undergraduate 1
03/10/2009
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Term
Modus Ponens (MP)
 Definition
p -> q

p

∴ q
Term
Modus Tollens (MT)
 Definition
p -> q

~q

∴ ~p
Term
Hypothetical Syllogism (HS)
 Definition
p -> q

q -> r

∴ p -> r
Term
Disjunctive Syllogism (DS)
 Definition

p v q       p v q

~p    or   ~q

∴ q         ∴ p
Term
Constructive Dilemma (CD)
 Definition

p v q

p -> r

q -> s

∴ r v s
Term
Simplification (Simp)
 Definition

p.q    p.q

∴p  or  ∴q
Term
Conjunction (Conj)
 Definition

p

q

∴ p.q
Term
Addition (Add)
 Definition

p               q

∴ p v q   or     ∴q v p
Term
Double-negation (DN)
 Definition
p::~~p
Term
Commutation (Com)
 Definition

(p v q)::(q v p)

(p.q)::(q.p)
Term
Association (As)
 Definition

(p v(q v r)::((p v q)v r)

(p.(q.r))::((p.q).r)
Term
De Morgan's Law (DeM)
 Definition

~(p.q)::(~p v ~q)

~(p v q):: (~p.~q)
Term
Contraposition (Cont)
 Definition
(p -> q)::(~q -> ~p)
Term
Distribution (Dist)
 Definition

(p.(q v r))::((p.q) v (p.r))

(p v(q.r))::((p v q).(p v r))
Term
Exportation (Ex)
 Definition
((p.q) -> r)::(p ->(q -> r))
Term
Redundancy (Re)
 Definition

p::(p.p)

p::(p v p)
Term
Material Equivalence (ME)
 Definition

(p <-> q)::((p -> q).(q->p))

(p <-> q)::((p.q) v (~p.~q)
Term
Material Implication (MI)
 Definition
(p -> q)::(~p v q)
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