A generalization of ACP using 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...

A knowledge representation based on the Belnap's four-valued logic

Cut - free Display Calculi for Nominal Tense

We deene cut-free display calculi for nominal tense logics extending the minimal nominal tense logic (MNTL) by addition of primitive axioms. To do so, we use a translation of MNTL into the minimal tense logic of inequality (MTL6 =) which is known to be properly displayable by application of Kracht's results. The rules of the display calculus MNTL for MNTL mimic those of the display calculus MTL...

Belnap's Epistemic States and Negation-as-Failure

Generalizing Belnap's system of epistemic states [Bel77] we obtain the system of disjunctive factbases which is the paradigm for all other kinds of disjunctive knowledge bases. Disjunctive factbases capture the nonmonotonic reasoning based on paraminimal models. In the schema of a disjunctive factbase, certain predicates of the resp. domain are declared to be exact, i.e. two-valued, and in turn...