PREDICATE LOGIC: RULES
Simple non-relational statements
Ms (Socrates is mortal)
Compound non-relational statements (contain &, v, →, ~)
Ac & Jb (Claire is an acrobat and Bob is a juggler)
Simple two-place relational predicates (predicate-subject-object)
Lbc (Bob loves Claire)
Simple three-place relational predicates
Gcfb (Claire gave Fido to Bob)
Compound two-place relational predicates (contain &, v, →, ~)
Rbj → Rjb (if Bob respects Joe then Joe will respect Bob)
Compound three-place relational predicates (contain &, v, →, ~)
Gdbc & Gcfb (Donna gossiped about Bob to Claire and Claire gave Fido to Bob)
Symmetrical relationship
Mbc → Mcb (if Bob is married to Claire, then Claire is married to Bob)
Asymmetrical relationship
Fej → ~Fje (if Ed is the father of Joe, then Joe is not the father of Ed)
Nonsymmetrical relationship
Abc → (Acb v ~Acb) (if Bob admires Claire, then Claire may or may not admire Bob)
Transitive relationship
(Tje & Tea) → Tja (if Jill is taller than Ella, and Ella is tall than Agnus, then Jill is taller than Agnus)
Intransitive relationship
(Fej & Fja)→ ~Fea (if Ed is the father of Joe, and Joe is the father of Al, then Ed is not the father of Al)
Nontransitive relationship
(Abs & Asj)→(Abj v ~Abj) (If Bob admires Sue and Sue admires Joe, then Bob will/won’t admire Joe)
A: all S is P (all students are people)
∀x(Sx → Px)
E: no S is P (no student is a pelican)
∀x(Sx → ~Px)
I: some S is P (some students are pilots)
Ǝx(Sx & Px)
O: some S is not P (some students are not partiers)
Ǝx(Sx & ~Px)
Identity predicate
t=c (Mark Twain is Samuel Clemens)
The only
Gj & ∀x(Gx → x=j) (Joe is the only guitarist in town)
Only
Sj & ∀x(Sx → x=j) (Only Joe survived)
No . . . except
Pj & Sj & ∀x[(Px & Sx) → x=j] (No pilots survived except Joe)
All . . . except
Pj & ~Sj & ∀x[(Px & ~x=j) → Sx] (All pilots survived except Joe)
Superlatives
Tj & ∀x[(Tx & ~x=j) → Gjx] (Joe is the greatest trombonist)
At most
∀x ∀y(x=y) (At most one thing exists)
At least
Ǝx Ǝy(~x=y) (At least two things exist)
Exactly
Ǝx ∀y(x=y) (Exactly one thing exists)
Definite Description
Ǝx[Axi & ∀y(Ayi → y=x) & x=h] (Homer is the author of the Iliad)