Knowledge Representation & Reasoning
Discrete Structures

Representing English Sentences in FOL

Last Update: 27 February 2005

Note: NEW or UPDATED material is highlighted

This document uses "pretend-it's-English" semantics, for convenience only :-)

Mark Twain is wiseWise(mt)
Mark Twain is Samuel Clemensmt = sc
All dogs are animals Ax[Dog(x) > Animal(x)]
Some dogs are pets.Ex[Dog(x) ^ Pet(x)]
No dogs are fish.¬Ex[Dog(x) ^ Fish(x)]
All dogs are not fish.Ax[Dog(x) > ¬Fish(x)]
Some dogs are not pets.Ex[Dog(x) ^ ¬Pet(x)]
No dogs are not mammals.¬Ex[Dog(x) ^ ¬Mammal(x)]
Not all dogs are pets.¬Ax[Dog(x) > Pet(x)]
All that glitters is not gold.¬Ax[Glitters(x) > Gold(x)] (!)
Every boy loves a girl.Ax[Boy(x) > Ey[Girl(y) ^ Loves(x,y)]]
(There is) A girl (who) is loved by every boy.Ey[Girl(y) ^ Ax[Boy(x) > Loves(x,y)]]
Everyone loves someone.AxEy.Loves(x,y)
Someone is loved by everyone.EyAx.Loves(x,y)
There is exactly one P.Ex[P(x) ^ Ay[P(y) > y=x]]
There are exactly two P's.ANSWER
The present King of France is bald. Ex[is_a_present_king_of_France(x) ^ Ay[is_a_present_king_of_France(y) > y=x] ^ Bald(x)]
The present King of France is not bald.Ex[is_a_present_king_of_France(x) ^ Ay[is_a_present_king_of_France(y) > y=x] ^ ¬Bald(x)]
The present King of France is not bald.¬Ex[is_a_present_king_of_France(x) ^ Ay[is_a_present_king_of_France(y) > y=x] ^ Bald(x)]
John goes to school.Goes(john, school) (?)
John goes to school.Goes(john-3, school-173) (?)
John goes to school. Ex[Named(x, "John") ^ Ey[School(y) ^ Goes(x,y)]]
ExEy[Named(x, "John") ^ School(y) ^ Goes(x,y)]

Need an ontology of names!

John goes to school.above, conjoined with:
Person(x) ^ Male(x) ^ Az[School(z) >...]
John sold a book to Mary. ExEyEz[Named(x, "John") ^ Named(y, "Mary") ^ Book(z) ^ Sold(x,y,z)]
John sold a book to Mary. ExEyEzEt[Time(t) ^ Named(x, "John") ^ Named(y, "Mary") ^ Book(z) ^ Sell(x,y,z,t) ^ Before(t,n) ^ Now(n)] (?)

Need an ontology of time!

Mary bought a book from John.As above
AxAyAz[Sold(x,y,z) <u>=</u> Buy(y,x,z)]
A cube is a block.ANSWER
A label of a cube is a label of a block.ANSWER
(any passage from the CVA website)?????

Copyright © 2005 by William J. Rapaport (
file: 563S05/fol-translation-2005-02-27.html