Stable Model Semantics - Relation To Nonmonotonic Logic

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.