Quasi-Realizations
We remind you of what we said in the introduction to this chapter. Substitution can be complicated, and while it cannot be avoided in proving realization, its complexities can be localized.
Quasi-realizers are like realizers but with a more complicated structure, and showing their existence avoids substitution. Quasi- realizers convert into realizers, and this is where substitution comes in.The following is exactly like Definition 7.4 except for one case, that of F ?. We are still assuming v1, v2,... is a fixed enumeration of all justification variables with no variable repeated.
Definition 7.7 (Potential Quasi-Realizers) The mapping (■) is defined recursively, as follows.
We use terminology with this mapping similar to that for potential realizers, except that of course now we talk about potential quasi-realizers. Thus members
Example 7.8 In Example 7.5 we computed the set of potential realizers for the signed formula
Now we compute the set of
7.5