Combining explicit negation and negation by failure via Belnap's logic

Combining Explicit Negation and Negation by Failure via Belnap's Logic Combining Explicit Negation and Negation by Failure via Belnap's Logic

This paper deals with logic programs containing two kinds of negation: negation as failure and explicit negation, allowing two diierent forms of uncertainty reasoning in the presence of incomplete information. Such programs have been introduced by Gelfond and Lifschitz and called extended programs. We provide them with a logical semantics in the style of Kunen, based on Belnap's four-valued log...

Combining Explicit Negation and Negation by Failure Via Belnap's Logic

This paper deals with logic programs containing two kinds of negation: negation as failure and explicit negation. This allows two diierent forms of reasoning in the presence of incomplete information. Such programs have been introduced by Gelfond and Lifschitz and called extended programs. We provide them with a logical semantics in the style of Kunen, based on Belnap's four-valued logic, and a...

Implicit and Explicit Negation in Logic Programming

Negation Without Negation in Probabilistic Logic Programming

Probabilistic logic programs without negation can have cycles (with a preference for false), but cannot represent all conditional distributions. Probabilistic logic programs with negation can represent arbitrary conditional probabilities, but with cycles they create logical inconsistencies. We show how allowing negative noise probabilities allows us to represent arbitrary conditional probabilit...

Explicit Negation in Relational

Negative facts in relational databases have traditionally been inferred using the closed world assumption. There are situations where this is not appropriate. We need to resort to the open world assumption, where the negative facts are sometimes explicitly stated. We present a formalism which is capable of answering queries in the relational database context under the open world assumption. We ...