| 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
Famous quotes containing the words basic, derived, argument and/or forms:
“Justice begins with the recognition of the necessity of sharing. The oldest law is that which regulates it, and this is still the most important law today and, as such, has remained the basic concern of all movements which have at heart the community of human activities and of human existence in general.”
—Elias Canetti (b. 1905)
“The sceptics assert, though absurdly, that the origin of all religious worship was derived from the utility of inanimate objects, as the sun and moon, to the support and well-being of mankind.”
—David Hume (1711–1776)
“Any authentic work of art must start an argument between the artist and his audience.”
—Rebecca West (1892–1983)
“The failure of women to produce genius of the first rank in most of the supreme forms of human effort has been used to block the way of all women of talent and ambition for intellectual achievement.”
—Anna Garlin Spencer (1851–1931)