Stable Models
The definition of a stable model below, reproduced from, uses two conventions. First, a truth assignment is identified with the set of atoms that get the value T. For instance, the truth assignment
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is identified with the set . This convention allows us to use the set inclusion relation to compare truth assignments with each other. The smallest of all truth assignments is the one that makes every atom false; the largest truth assignment makes every atom true.
Second, a logic program with variables is viewed as shorthand for the set of all ground instances of its rules, that is, for the result of substituting variable-free terms for variables in the rules of the program in all possible ways. For instance, the logic programming definition of even numbers
is understood as the result of replacing in this program by the ground terms
in all possible ways. The result is the infinite ground program
Read more about this topic: Stable Model Semantics
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