CSCE 235

Handout 7:  Rules of Inference for Quantified Statements

January 28, 2004 

 

1.                                                                                   Universal Instantiation

2.         for some specific element a                                 Existential Instantiation

3.         for an arbitrary element a                           Universal Generalization

4.         for some specific element a                                     Existential Generalization

 

Think about this:

 

For Universal Instantiation: If for all instances x, x has property P, then any element ‘a’ has property P.

 

For Existential Instantiation: If there exists at least one instance x that has property P, then there is some specific element ‘a’ that has property P.  Be very careful when using this rule.  To instantiate, the instances or elements must be specific.  Why?  Because not all instances or elements have property P; only some.

 

For Universal Generalization: If a has property P, for any a, then, yes, for all instances x, x has property P.  Be very careful when using this.  To generalize, the instances or elements must be arbitrary. Why? Because all must have the property; not just some.

 

For Existential Generalization: If there is an element a that has property P, then, yes, there exists one instance of x that has property P.

 

* Based on (Rosen 2003).