The reasoning for this qualitative question is similar to the propositional question.

**Theorem ( c4):**

**Proof ! c4(c4):**
We begin with an instance of the first axiom for qualitative
questions

which, by definition of *c*3, can be written as

Instantiating the axiom for reply we have

and it follows from the two lines above that

which by definition of *c*4 we can write as

Due to the frame axioms, the conclusion established in the first question

also holds in context *c*4.

**Theorem (frame):**

**Proof !frame(frame):**
We first instantiate the second axiom for qualitative questions
to get

The two lines above imply

which, by definition of *c*3, can be written as

Now we apply the following instance of the reply axiom

to get

which, by definition of *c*4, can be written as

Sun Jul 12 14:45:30 PDT 1998