Malini Sen WESTERN LOGIC Presented by Assistant Professor

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Presentation transcript:

Malini Sen WESTERN LOGIC Presented by 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) Modus Ponens (M.P) 2) Modus Tollens (M.T) 3) Hypothetical Syllogism (H.S) 4) Disjunctive Syllogism (D.S) 5) Constructive Dilemma (C.D) 6) Absorption (Abs.) 7) Simplification (simp.) 8) Conjunction (Conj.) 9) Addition (Add.)

Modus Ponens (M.P) p q p q

Modus Tollens (M.T) p q q p

Hypothetical Syllogism (H.S) p q q r p r

Disjunctive Syllogism (D.S) p v q p q

Constructive Dilemma (C.D) (p q) (r s) p v r q v s

Absorption (Abs.) p q p (p q)

Simplification (simp.) p q p

Conjunction (Conj.) p q p q

Addition (Add.) p p v q

RULES OF REPLACEMENT 10) De Morgan’s theorem (De.M.) 11) Commutation (Com.) 12) Association (Assoc.) 13) Distribution (Dist.) 14) Double Negation (D.N) 15) Transposition (Trans.) 16) Material Implication (Impl.) 17) Material Equivalence (Equiv.) 18) Exportation (Exp.) 19) Tautology (Taut).

De Morgan’s Theorem (De.M.) (p q) ( p v q) (p v q) ( p q)

Commutation (Com.) (p v q) (q v p) (p q) (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 q) [(p q) (q p)] (p q) [(p q) v ( p q)]

Exportation (Exp.) (p q) r ] [p (q r)]

Tautology (Taut) p (p v p) p (p p)

THANK YOU