Quantitative deduction and its fixpoint theory
Journal of Logic Programming
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Bilattices and the semantics of logic programming
Journal of Logic Programming
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Theory of generalized annotated logic programming and its applications
Journal of Logic Programming
The Semantics of Predicate Logic as a Programming Language
Journal of the ACM (JACM)
Fuzzy Sets and Systems
Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning
Logic-based artificial intelligence
Hybrid Probabilistic Logic Programs as Residuated Logic Programs
JELIA '00 Proceedings of the European Workshop on Logics in Artificial Intelligence
Algebraic Properties of The Space of Multivalued and Paraconsistent Logic Programs
Proceedings of the Ninth Conference on Foundations of Software Technology and Theoretical Computer Science
Soundness and Completeness of Non-classical SLD-Resolution
ELP '96 Proceedings of the 5th International Workshop on Extensions of Logic Programming
Multi-adjoint Logic Programming with Continuous Semantics
LPNMR '01 Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Monotonic and Residuated Logic Programs
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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
Towards a Fuzzy Answer Set Semantics for Residuated Logic Programs
WI-IAT '08 Proceedings of the 2008 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology - Volume 03
General Fuzzy Answer Set Programs
WILF '09 Proceedings of the 8th International Workshop on Fuzzy Logic and Applications
Answer Sets in a Fuzzy Equilibrium Logic
RR '09 Proceedings of the 3rd International Conference on Web Reasoning and Rule Systems
Parametrized logic programming
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
Query answering in normal logic programs under uncertainty
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Aggregated Fuzzy Answer Set Programming
Annals of Mathematics and Artificial Intelligence
A core language for fuzzy answer set programming
International Journal of Approximate Reasoning
Fuzzy Equilibrium Logic: Declarative Problem Solving in Continuous Domains
ACM Transactions on Computational Logic (TOCL)
Fuzzy Description Logic Programs under the Answer Set Semantics for the Semantic Web
Fundamenta Informaticae
International Journal of Approximate Reasoning
Fuzzy autoepistemic logic and its relation to fuzzy answer set programming
Fuzzy Sets and Systems
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In a previous work we have defined Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truth-values with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs and Fuzzy Logic Programming [3,4]. However, none of these semantics define a form of non-monotonic negation, which is fundamental for several knowledge representation applications. In the spirit of our previous work, we generalise our framework of Monotonic Logic Programs to allow for rules with arbitrary antitonic bodies over general complete lattices, of which normal programs are a special case. We then show that all the standard logic programming theoretical results carry over to Antitonic Logic Programs, defining Stable Model and Well-founded Model alike semantics. We also apply and illustrate our theory to logic programs with costs, extending the original presentation of [17] with a class of negations.