Deduction Strategy Module    •    Simple Formal Logic    •    Arnold vander Nat    •    Routledge 2009

Rules of Traditional Logic


Pred-DN
... non-non-P
=   ... P

Q.N.
not (all S are P)
=   some S are non-P

Q.N.
not (some S are P)
=   all S are non-P

Q.N.
no S are P
=   all S are non-P

Q.N.
no S are P
=   not (some S are P)

Conv
some S are P
=   some P are S

Conv
no S are P
=   no P are S

Contrap
all S are P
=   all non-P are non-S



Univ Syll
all S are M,     all M are P   ⁄∴   all S are P

Part Syll
some S are M, all M are P   ⁄∴   some S are P

Sup Univ Syll
all S are M,     all M are N, all N are P  ⁄∴  all S are P

Sup Part Syll
some S are M, all M are N, all N are P ⁄∴ some S are P

Sing Univ Syll
all S are P,   n is S   ⁄∴   n is P

Sing Part Syll
n is S,   n is P   ⁄∴   some S are P

Name-Neg
not (n is P)   =   n is non-P