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A Compilation of Rules of Inference Keith Burgess-Jackson 28 November 2017 THESE RULES MAY BE APPLIED ONLY TO WHOLE LINES OF A PROOF (ONE-WAY RULES; INFER- ENCES) THESE RULES MAY BE APPLIED EI- THER TO WHOLE LINES OR TO PARTS OF LINES (TWO-WAY RULES; EQUIVALENCES) 1. Implication Rules • Modus Ponens (MP) • Modus Tollens (MT) • Hypothetical Syllogism (HS) • Disjunctive Syllogism (DS) • Constructive Dilemma (CD) • Simplification (Simp) • Conjunction (Conj) • Addition (Add) 2. Quantification Rules • Universal Instantiation (UI) • Universal Generalization (UG) • Existential Instantiation (EI) • Existential Generalization (EG) 3. Laws of Distribution • Universal Disjunction (UD) • Existential Conjunction (EC) 1. Replacement Rules • De Morgan’s Theorems (DM) • Commutation (Com) • Association (Assoc) • Distribution (Dist) • Double Negation (DN) • Transposition (Trans) • Material Implication (MI) • Material Equivalence (ME) • Exportation (Exp) • Tautology (Taut) 2. Change-of-Quantifier Rule (CQ) 3. Laws of Distribution • Universal Conjunction (UC) • Existential Disjunction (ED)

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A Compilation of Rules of Inference Keith Burgess-Jackson

28 November 2017

THESE RULES MAY BE APPLIED ONLY TO WHOLE LINES OF A PROOF (ONE-WAY RULES; INFER-ENCES)

THESE RULES MAY BE APPLIED EI-THER TO WHOLE LINES OR TO PARTS OF LINES (TWO-WAY RULES; EQUIVALENCES)

1. Implication Rules

• Modus Ponens (MP) • Modus Tollens (MT) • Hypothetical Syllogism (HS) • Disjunctive Syllogism (DS) • Constructive Dilemma (CD) • Simplification (Simp) • Conjunction (Conj) • Addition (Add)

2. Quantification Rules

• Universal Instantiation (UI) • Universal Generalization

(UG) • Existential Instantiation (EI) • Existential Generalization

(EG) 3. Laws of Distribution

• Universal Disjunction (UD) • Existential Conjunction

(EC)

1. Replacement Rules

• De Morgan’s Theorems (DM)

• Commutation (Com) • Association (Assoc) • Distribution (Dist) • Double Negation (DN) • Transposition (Trans) • Material Implication (MI) • Material Equivalence (ME) • Exportation (Exp) • Tautology (Taut)

2. Change-of-Quantifier Rule (CQ) 3. Laws of Distribution

• Universal Conjunction (UC) • Existential Disjunction (ED)

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