The alternating fixpoint of logic programs with negation
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Extended stable semantics for normal and disjunctive programs
Logic programming
Well-founded semantics coincides with three-valued stable semantics
Fundamenta Informaticae
Bilattices and the semantics of logic programming
Journal of Logic Programming
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Artificial Intelligence
Unfounded sets and well-founded semantics for general logic programs
Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Hypothesis-Founded Semantics for Datalog Programs with Negation
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Hypothesis Support for Information Integration in Four-Valued Logics
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
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The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the assumption that every such atom is false, while the Kripke-Kleene semantics corresponds to the assumption that every such atom is unknown. In this paper, we propose to unify and extend this assumption-based approach by introducing parameterized semantics for logic programs. The parameter holds the value that one assumes for all atoms whose logical values cannot be inferred from the rules. We work within Belnap's four-valued logic, and we consider the class of logic programs defined by Fitting. Following Fitting's approach, we define a simple operator that allows us to compute the parameterized semantics, and to compare and combine semantics obtained for different values of the parameter. The semantics proposed by Fitting corresponds to the value false. We also show that our approach captures and extends the usual semantics of conventional logic programs thereby unifying their computation.