if a universal sentence φ of L has a model it has one which differs from a
Herbrand model only by having equality assigned to a congruence relation on
U
L
. Let us call this a Herbrand /quotient model. And if φ does not contain the
equality symbol this congruence relation can be taken to be identity, i.e., the
model can be a Herbrand model. This is the typical situation in Wysiwym logic
programming. There the program Ρ is a conjunction of a finite set of clauses
which are implicitly universally quantified, the query Q is an existential sen-
tence and neither Ρ nor Q contains the equality symbol. So th
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