KEY CONCEPTS FOR SECOND EXAM

 

PROPOSITIONAL LOGIC (Nolt, chapter 3)

Definitions: formal logic, valid deductive argument, propositional logic

Three deductively valid arguments: disjunctive syllogism, modus ponens, modus tollents

Logical operators: negation, conjunction, disjunction, conditional, biconditional

Terms: well-formed formula (wff), truth value, principle of bivalence

Truth tables: for each logical operator, for each complex wff, for argument forms

 

PROPOSITIONAL CALCULUS (use online material, not Nolt)

Basic Rules of Inference (non-hypothetical):

Negation Elimination (~E – version of double negation DN)

Conditional Elimination (→E – modus ponens MP)

Conjunction Introduction (&I – conjunction CONJ)

Conjunction Elimination (&E – simplification SIMP)

Disjunction Introduction (vI – addition ADD)

Disjunction Elimination (vE – version of constructive dilemma CD)

Biconditional Introduction (↔I – version of material equivalence ME)

Biconditional Elimination (↔E – version of material equivalence ME)

Derived Rules

Modus Tollens (MT)

Hypothetical Syllogism (HS)

Disjunctive Syllogism (DS)

Absorption (ABS)

Constructive Dilemma (CD)

Repeat (RE)

Contradiction (CON)

Theorem Introduction (TI)

Equivalences (also called rules of replacement)

De Morgan’s Law (DM)

Commutation (COM)

Association (ASSOC)

Distribution (DIST)

Double Negation (DN)

Transposition (TRANS)

Material implication (MI)

Material Equivalence (ME)

Exportation (EXP)

Tautology (TAUT)

Hypothetical Rules (rules using assumptions)

Negation Introduction (~I – indirect proof IP)

Conditional Introduction (→I – conditional proof CP)