Negation as Instantiation

On Negation As Instantiation

Given a logic program P and a goal G, we introduce a notion which states when an SLD-tree for P fGg instantiates a set of variables V with respect to another one, W. We call this notion weak instantiation, as it is a generalisation of the instantiation property introduced by Di Pierro, Martelli and Palamidessi. A negation rule based on instanti-ation, the so-called Negation As Instantiation rul...

Negation as Instantiation

We propose a new negation rule for logic programming which derives existentially closed negative literals, and we de ne a version of completion for which this rule is sound and complete. The rule is called \Negation As Instantiation" (NAI). According to it, a negated atom succeeds whenever all the branches of the SLD-tree for the atom either fail or instantiate the atom. The set of the atoms wh...

Negation As Refutation

A refutation mechanism is introduced into logic programming, dual to the usual proof mechanism; then negation is treated via refutation. A four-valued logic is appropriate for the semantics: true, false, neither, both. Inconsistent programs are allowed, but inconsistencies remain localized. The four-valued logic is a well-known one, due to Belnap, and is the simplest example of Ginsberg’s bilat...

Neg{raising: Negation as Failure?

Order and Negation as Failure

We equip ordered logic programs with negation as failure, using a simple generalization of the preferred answer set semantics for ordered programs. This extension supports a convenient formulation of certain problems, which is illustrated by means of an intuitive simulation of logic programming with ordered disjunction. The simulation also supports a broader application of “ordered disjunction”...