This rule employs a variable instead of a ground term.
2.
L & sigma;, is the set of all ground terms of L & sigma;.
3.
The conclusion is then that both denotations exhibit equivalent behavior on ground terms, hence are equivalent.
4.
That is, the Herbrand universe consists of all ground terms : terms that have no variables in them.
5.
The main problem of tableau without unification is how to choose a ground term t for the universal quantifier rule.
6.
A set of ground terms is "'recognizable "'if there exists a tree automaton that accepts it.
7.
Indeed, every possible ground term can be used, but clearly most of them might be useless for closing the tableau.
8.
A first-order formula \ forall x . \ gamma ( x ) implies all formulae \ gamma ( t ) where t is a ground term.
9.
The energy of the ground state is taken to be zero for all field strengths, and the energies of all other terms and their components are plotted with respect to the ground term.
10.
An atomic formula or "'atom "'is commonly defined as a predicate applied to a tuple of terms; a ground atom is then a predicate in which only ground terms appear.
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