Rules for Quantative Logic

Linguistics 501Fall 05

Laws and Rules for Predicate Logic

(1) Laws of Quantifier DistributionLaw 1 (x)(x) (x)(x)Law 2 (x)((x) (x)) ((x)(x) (x)(x))Law 3 (x)((x) (x)) ((x)(x) (x)(x))Law 4 ((x)(x) (x)(x)) = (x)((x) (x))Law 5 (x)((x) (x)) = ((x)(x) (x)(x))

(2) Laws of Quantifier (In)DependenceLaw 6 (x)(y)(x, y) (y)(x)(x, y)Law 7 (x)(y)(x, y) (y)(x)(x, y)Law 8 (x)(y)(x, y) = (y)(x)(x, y)

(3) Laws of Quantifier MovementLaw 9 ( (x)(x)) (x)( (x))

Provided that x is not free in .Law 10 ( (x)(x)) (x)( (x))

Provided that x is not free in .Law 11 ((x)(x) ) (x)((x) )

Provided that x is not free in .Law 12 ((x)(x) ) (x)((x) )

Provided that x is not free in .

(4) Universal Instantiation (U.I.)(x)(x)

(c)

(5) Universal Generalization (U.G.)(v)

(x)(x)

(6) Existential Generalization (E.G.)(c)

(x)(x)

(7) Existential Instantiation (E.I.)(x)(x)

(w)where w is a new constant