Propositional Calculus - Basic and Derived Argument Forms

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:

    “... the basic experience of everyone is the experience of human limitation.”
    —Flannery O’Connor (1925–1964)

    “There is, it seems to us,
    At best, only a limited value
    In the knowledge derived from experience....”
    —T.S. (Thomas Stearns)

    “The difficult part in an argument is not to defend one’s opinion, but rather to know it.”
    —André Maurois (1885–1967)

    “We can imagine a society in which no one could survive as a social being because it does not correspond to biologically determined perceptions and human social needs. For historical reasons, existing societies might have such properties, leading to various forms of pathology.”
    —Noam Chomsky (b. 1928)