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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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