Quantitative deduction and its fixpoint theory
Journal of Logic Programming
Logic programs with classical negation
Logic programming
Logic programs with exceptions
Logic programming
A database needs two kinds of negation
MFDBS 91 Proceedings of the 3rd symposium on Mathematical fundamentals of database and knowledge base systems
Bilattices and the semantics of logic programming
Journal of Logic Programming
Theory of generalized annotated logic programming and its applications
Journal of Logic Programming
Well founded semantics for logic programs with explicit negation
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
Probabilistic logic programming
Information and Computation
The Semantics of Predicate Logic as a Programming Language
Journal of the ACM (JACM)
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
A Parametric Approach to Deductive Databases with Uncertainty
IEEE Transactions on Knowledge and Data Engineering
LPNMR '01 Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning
Monotonic and Residuated Logic Programs
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Soundness and Completeness of Non-classical SLD-Resolution
ELP '96 Proceedings of the 5th International Workshop on Extensions of Logic Programming
On a theory of probabilistic deductive databases
Theory and Practice of Logic Programming
Logic programs with uncertainties: a tool for implementing rule-based systems
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 1
Any-world assumptions in logic programming
Theoretical Computer Science
Epistemic foundation of stable model semantics
Theory and Practice of Logic Programming
Foundations of Paraconsistent Resolution
Fundamenta Informaticae
A Top-Down Query Answering Procedure for Normal Logic Programs Under the Any-World Assumption
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Quasi-Classical Model Semantics for Logic Programs --- A Paraconsistent Approach
ISMIS '09 Proceedings of the 18th International Symposium on Foundations of Intelligent Systems
Foundations of Paraconsistent Resolution
Fundamenta Informaticae
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We propose a framework which extends Antitonic Logic Programs [2] to an arbitrary complete bilattice of truth-values, where belief and doubt are explicitly represented. Based on Fitting's ideas, this framework allows a precise definition of important operators found in logic programming such as explicit negation and the default negation. In particular, it leads to a natural integration of explicit negation with the default negation through the coherence principle [19]. According to this principle, the explicit negation entails the default negation. We then define Coherent Answer Sets, and the Paraconsistent Well-founded Model semantics, generalizing paraconsistent semantics for logic programs (for instance, WFSXp [4]). Our framework is an extension of important classes of Antitonic Logic Programs, and is general enough to capture Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs, and Fuzzy Logic Programming. Thus, we have a powerful mathematical formalism for dealing with default reasoning, paraconsistency, and uncertainty.