WESTERN LOGIC Presented by Malini Sen Assistant Professor
WESTERN LOGIC Presented by Malini Sen Assistant Professor Department of Philosophy Maheshtala College B. B. T. Road. Kolkata - 700141
FORMAL PROOF OF VALIDITY 1) RULES OF INFERENCE 2) RULES OF REPLACEMENT
RULES OF INFERENCE 1) 2) 3) 4) 5) 6) 7) 8) 9) Modus Ponens (M. P) Modus Tollens (M. T) Hypothetical Syllogism (H. S) Disjunctive Syllogism (D. S) Constructive Dilemma (C. D) Absorption (Abs. ) Simplification (simp. ) Conjunction (Conj. ) Addition (Add. )
Modus Ponens (M. P) p p q q
Modus Tollens (M. T) p q q p
Hypothetical Syllogism (H. S) p q r r
Disjunctive Syllogism (D. S) p v q p q
Constructive Dilemma (C. D) (p q) (r s) pvr qvs
Absorption (Abs. ) p q p (p q)
Simplification (simp. ) p q p
Conjunction (Conj. ) p q
Addition (Add. ) p pvq
RULES OF REPLACEMENT 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) De Morgan’s theorem (De. M. ) Commutation (Com. ) Association (Assoc. ) Distribution (Dist. ) Double Negation (D. N) Transposition (Trans. ) Material Implication (Impl. ) Material Equivalence (Equiv. ) Exportation (Exp. ) Tautology (Taut).
De Morgan’s Theorem (De. M. ) (p q) ( p v q) ( p q)
Commutation (Com. ) (p v q) (p q) (q v p) (q p)
Association (Assoc. ) [p v (p v q)] [(p v q) v r] [p (p q)] [(p q) r]
Distribution (Dist. ) [p (q v r)] [(p q) v (p r) [p v (p r)] [(p v q) (p v r)]
Double Negation (D. N) p p
Transposition (Trans. ) (p q) ( q p)
Material Implication (Impl. ) (p q) ( p v q)
Material Equivalence (Equiv. ) (p (p q) q) [(p q) (q p)] [(p q) v ( p q)]
Exportation (Exp. ) (p q) r ] [p (q r)]
Tautology (Taut) p p (p v p) (p p)
THANK YOU
- Slides: 24