Stable Models of A Set of Propositional Formulas
Rules, and even disjunctive rules, have a rather special syntactic form, in comparison with arbitrary propositional formulas. Each disjunctive rule is essentially an implication such that its antecedent (the body of the rule) is a conjunction of literals, and its consequent (head) is a disjunction of atoms. David Pearce and Paolo Ferraris showed how to extend the definition of a stable model to sets of arbitrary propositional formulas. This generalization has applications to answer set programming.
Pearce's formulation looks very different from the original definition of a stable model. Instead of reducts, it refers to equilibrium logic -- a system of nonmonotonic logic based on Kripke models. Ferraris's formulation, on the other hand, is based on reducts, although the process of constructing the reduct that it uses differs from the one described above. The two approaches to defining stable models for sets of propositional formulas are equivalent to each other.
Read more about this topic: Stable Model Semantics
Famous quotes containing the words stable, models, set and/or formulas:
“And neigh like Boanerges—
Then—punctual as a Star
Stop—docile and omnipotent
At its own stable door—”
—Emily Dickinson (1830–1886)
“Friends broaden our horizons. They serve as new models with whom we can identify. They allow us to be ourselves—and accept us that way. They enhance our self-esteem because they think we’re okay, because we matter to them. And because they matter to us—for various reasons, at various levels of intensity—they enrich the quality of our emotional life.”
—Judith Viorst (20th century)
“This happy breed of men, this little world,
This precious stone set in the silver sea,
Which serves it in the office of a wall,
Or as a moat defensive to a house,
Against the envy of less happier lands,
This blessed plot, this earth, this realm, this England.”
—William Shakespeare (1564–1616)
“That’s the great danger of sectarian opinions, they always accept the formulas of past events as useful for the measurement of future events and they never are, if you have high standards of accuracy.”
—John Dos Passos (1896–1970)