Quantitative deduction and its fixpoint theory
Journal of Logic Programming
On the semantics of rule-based expert systems with uncertainty
Lecture notes in computer science on ICDT '88
The alternating fixpoint of logic programs with negation
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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
Probabilistic logic programming
Information and Computation
Probabilistic deductive databases
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Probabilistic Datalog: implementing logical information retrieval for advanced applications
Journal of the American Society for Information Science
Annotated fuzzy logic programs
Fuzzy Sets and Systems
A Parametric Approach to Deductive Databases with Uncertainty
IEEE Transactions on Knowledge and Data Engineering
Stable Model Semantics for Probabilistic Deductive Databases
ISMIS '91 Proceedings of the 6th International Symposium on Methodologies for Intelligent Systems
Integration of Information in Four-Valued Logics under Non-Uniform Assumptions
ISMVL '00 Proceedings of the 30th IEEE International Symposium on Multiple-Valued Logic
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
Annals of Mathematics and Artificial Intelligence
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Different many-valued logic programming frameworks have been proposed to manage uncertain information in deductive databases and logic programming. A feature of these frameworks is that they rely on a predefined assumption or hypothesis, i.e. an interpretation that assigns the same default truth value to all the atoms of a program, e.g. in the open world assumption, by default all atoms have unknown truth value. In this paper we extend these frameworks along three directions: (i) we will introduce non-monotonic modes of negation; (ii) the default truth values of atoms need not necessarily to be all equal each other; and (iii) a hypothesis can be a partial interpretation. We will show that our approach extends the usual ones: if we restrict our attention to classical logic programs and consider total uniform hypotheses, then our semantics reduces to the usual semantics of logic programs. In particular, under the everything false assumption, our semantics captures and extends the well-founded semantics to these frameworks.