Properties of The Stable Model Semantics
In this section, as in the definition of a stable model above, by a logic program we mean a set of rules of the form
where are ground atoms.
Head atoms: If an atom belongs to a stable model of a logic program then is the head of one of the rules of .
Minimality: Any stable model of a logic program is minimal among the models of relative to set inclusion.
The antichain property: If and are stable models of the same logic program then is not a proper subset of . In other words, the set of stable models of a program is an antichain.
NP-completeness: Testing whether a finite ground logic program has a stable model is NP-complete.
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“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
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