Relation To Nonmonotonic Logic
The meaning of negation in logic programs is closely related to two theories of nonmonotonic reasoning -- autoepistemic logic and default logic. The discovery of these relationships was a key step towards the invention of the stable model semantics.
The syntax of autoepistemic logic uses a modal operator that allows us to distinguish between what is true and what is believed. Michael Gelfond proposed to read in the body of a rule as " is not believed", and to understand a rule with negation as the corresponding formula of autoepistemic logic. The stable model semantics, in its basic form, can be viewed as a reformulation of this idea that avoids explicit references to autoepistemic logic.
In default logic, a default is similar to an inference rule, except that it includes, besides its premises and conclusion, a list of formulas called justifications. A default can be used to derive its conclusion under the assumption that its justifications are consistent with what is currently believed. Nicole Bidoit and Christine Froidevaux proposed to treat negated atoms in the bodies of rules as justifications. For instance, the rule
can be understood as the default that allows us to derive from assuming that is consistent. The stable model semantics uses the same idea, but it does not explicitly refer to default logic.
Read more about this topic: Stable Model Semantics
Famous quotes containing the words relation to, relation and/or logic:
“Any relation to the land, the habit of tilling it, or mining it, or even hunting on it, generates the feeling of patriotism. He who keeps shop on it, or he who merely uses it as a support to his desk and ledger, or to his manufactory, values it less.”
—Ralph Waldo Emerson (1803–1882)
“When needs and means become abstract in quality, abstraction is also a character of the reciprocal relation of individuals to one another. This abstract character, universality, is the character of being recognized and is the moment which makes concrete, i.e. social, the isolated and abstract needs and their ways and means of satisfaction.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“The American Constitution, one of the few modern political documents drawn up by men who were forced by the sternest circumstances to think out what they really had to face instead of chopping logic in a university classroom.”
—George Bernard Shaw (1856–1950)