martes, 13 de octubre de 2009

Reglas de inferencia 1

Enrique Arias Valencia


MODUS PONENS

p → q
p
∴q

MODUS TOLLENS

p → q
¬ q
∴¬p

SILOGISMO HIPOTÉTICO

p → q
q → r
∴p → r

SILOGISMO DISYUNTIVO

p ∨ q
¬p
∴ q

DILEMA CONSTRUCTIVO

(p → q) ∧ (r → s)

p ∨ r
∴ q ∨ s

DILEMA DESTRUCTIVO

(p → q) ∧ (r → s)
¬q ∨ ¬s
∴¬p ∨ ¬r

SIMPLIFICACIÓN

p ∧ q
∴p

CONJUNCIÓN

p
q
∴p ∧ q

ADICIÓN

p
q
∴ p ∨ q

CONMUTACIÓN

p ∨ q
∴ q ∨ p

LEY DE ABSORCIÓN

p → q
∴ p → (p ∧ q)

LEYES DE De MORGAN

¬ (p ∨ q) (¬ p ∧¬ q)
¬ (p ∧q) ≡ (¬p ∨ ¬ q)

EQUIVALENCIAS

¬ (p ∧q) ≡ p → ¬ q
¬ (p → q) ≡ p ∧¬q

DOBLE NEGACIÓN

p 𠪪p

LEY DEL BICONDICIONAL

p ↔ q ≡ (p → q) ∧ (q → p)

LEY DE EXPORTACIÓN

p → (q → r) ≡ (p ∧q) → r

TRANSPOSICIÓN

p → q ≡ ¬ q → ¬p

ASOCIACIÓN

[p ∨ (q ∨ r)] ≡ [(p ∨ q) ∨ r]
[p ∧(q ∧r)] ≡ [(p ∧q) ∧r]

DISTRIBUCIÓN

[p ∧(q ∨r)] ≡ [[(p ∧q) ∨(p ∧r)]
[p ∨(q ∧r)] ≡ [[(p ∨q) ∧(P ∨r)]

IMPLICACIÓN MATERIAL

p → q ≡ ¬ p ∨q

EQUIVALENCIA MATERIAL

p ≡ q ≡ (p → q) ∧ (q → p)
p ≡ q ≡ (p ∧ q) ∨ (¬ p ∧¬ q)

TAUTOLOGÍA

p ≡ p ∨p

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