Basic and Derived Argument Forms | ||
---|---|---|
Name | Sequent | Description |
Modus Ponens | If then ; ; therefore | |
Modus Tollens | If then ; not ; therefore not | |
Hypothetical Syllogism | If then ; if then ; therefore, if then | |
Disjunctive Syllogism | Either or, or both; not ; therefore, | |
Constructive Dilemma | If then ; and if then ; but or ; therefore or | |
Destructive Dilemma | If then ; and if then ; but not or not ; therefore not or not | |
Bidirectional Dilemma | If then ; and if then ; but or not ; therefore or not | |
Simplification | and are true; therefore is true | |
Conjunction | and are true separately; therefore they are true conjointly | |
Addition | is true; therefore the disjunction ( or ) is true | |
Composition | If then ; and if then ; therefore if is true then and are true | |
De Morgan's Theorem (1) | The negation of ( and ) is equiv. to (not or not ) | |
De Morgan's Theorem (2) | The negation of ( or ) is equiv. to (not and not ) | |
Commutation (1) | ( or ) is equiv. to ( or ) | |
Commutation (2) | ( and ) is equiv. to ( and ) | |
Commutation (3) | ( is equiv. to ) is equiv. to ( is equiv. to ) | |
Association (1) | or ( or ) is equiv. to ( or ) or | |
Association (2) | and ( and ) is equiv. to ( and ) and | |
Distribution (1) | and ( or ) is equiv. to ( and ) or ( and ) | |
Distribution (2) | or ( and ) is equiv. to ( or ) and ( or ) | |
Double Negation | is equivalent to the negation of not | |
Transposition | If then is equiv. to if not then not | |
Material Implication | If then is equiv. to not or | |
Material Equivalence (1) | ( is equiv. to ) means (if is true then is true) and (if is true then is true) | |
Material Equivalence (2) | ( is equiv. to ) means either ( and are true) or (both and are false) | |
Material Equivalence (3) | ( is equiv. to ) means, both ( or not is true) and (not or is true) | |
Exportation | from (if and are true then is true) we can prove (if is true then is true, if is true) | |
Importation | If then (if then ) is equivalent to if and then | |
Tautology (1) | is true is equiv. to is true or is true | |
Tautology (2) | is true is equiv. to is true and is true | |
Tertium non datur (Law of Excluded Middle) | or not is true | |
Law of Non-Contradiction | and not is false, is a true statement |
Read more about this topic: Propositional Calculus
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