Section 1.8
Predicate Logic with multiple variables
Activity #1 (Review)
How would you write these in English? Assume that the
domain for x is all humans.
( x) [ GoesToUNI(x)  Smart(x) ]
( x) [ GoesToUNI(x)  Smart(x) ]
( x) [ GoesToIowa(x)  Smart(x) ]
( x) [ GoesToIowa(x)  Smart(x) ]
Multiple variables
• What do you do when you need to use more
than one variable?
• For example, Monday in one of the sections
of this class someone introduced the
predicate:
– Everyone likes cheese
Multiple variables
• Everyone likes cheese
• One way to say this is:
 x LikesCheese(x)
• Another way is to say:
 x Likes(x,CHEESE)
Multiple variables
 x Likes(x,CHEESE)
• The advantage of this last statement is that
it allows us to easily make related
statements about people who like
CHOCOLATE or COFFEE or anything.
Multiple variables
• And once you have that you can start to talk
about generic things that generic people
like:
( x)(  y) Likes(x,y)
Multiple variables
• If a predicate has more than one variable,
each variable must be bound by a separate
quantifier
Order matters.
• These two statements actually mean very
different things:
• ( x)(  y) Likes(x,y)
• ( y)( x) Likes(x,y)
Activity #2
• How would you write these in English? Assume
that the domain for x and y is humans.
–
–
–
–
–
–
( x)( y) Likes(x,y)
( x)(  y) Likes(x,y)
( x)(  y) Likes(x,y)
( x)( y) Likes(x,y)
( y)( x) Likes(x,y)
( y)(  x) Likes(x,y)