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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)