Evidential support logic programming
Fuzzy Sets and Systems
On the representation and querying of sets of possible worlds
Selected papers of the workshop on Deductive database theory
Non-commutativity and Expressive Deductive Logic Databases
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Fuzzy logic programming via multilattices
Fuzzy Sets and Systems
Representing Uncertainty in RuleML
Fundamenta Informaticae
On the Relationship between Hybrid Probabilistic Logic Programs and Stochastic Satisfiability
SUM '08 Proceedings of the 2nd international conference on Scalable Uncertainty Management
A Logical Approach to Qualitative and Quantitative Reasoning
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Sound and Complete SLD-Resolution for Bilattice-Based Annotated Logic Programs
Electronic Notes in Theoretical Computer Science (ENTCS)
Annals of Mathematics and Artificial Intelligence
Towards the computation of stable probabilistic model semantics
KI'06 Proceedings of the 29th annual German conference on Artificial intelligence
On reachability of minimal models of multilattice-based logic programs
MICAI'07 Proceedings of the artificial intelligence 6th Mexican international conference on Advances in artificial intelligence
Transactions on large-scale data- and knowledge-centered systems III
Interval-Valued neural multi-adjoint logic programs
IWINAC'05 Proceedings of the First international conference on Mechanisms, Symbols, and Models Underlying Cognition: interplay between natural and artificial computation - Volume Part I
Hybrid probabilistic logic programs with non-monotonic negation
ICLP'05 Proceedings of the 21st international conference on Logic Programming
Incomplete knowledge in hybrid probabilistic logic programs
JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
Multi-lattices as a basis for generalized fuzzy logic programming
WILF'05 Proceedings of the 6th international conference on Fuzzy Logic and Applications
A top-k query answering procedure for fuzzy logic programming
Fuzzy Sets and Systems
Representing Uncertainty in RuleML
Fundamenta Informaticae
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We propose a framework for modeling uncertainty where both belief and doubt can be given independent, first-class status. We adopt probability theory as the mathematical formalism for manipulating uncertainty. An agent can express the uncertainty in her knowledge about a piece of information in the form of a confidence level, consisting of a pair of intervals of probability, one for each of her belief and doubt. The space of confidence levels naturally leads to the notion of a trilattice, similar in spirit to Fitting's bilattices. Intuitively, the points in such a trilattice can be ordered according to truth, information, or precision. We develop a framework for probabilistic deductive databases by associating confidence levels with the facts and rules of a classical deductive database. While the trilattice structure offers a variety of choices for defining the semantics of probabilistic deductive databases, our choice of semantics is based on the truth-ordering, which we find to be closest to the classical framework for deductive databases. In addition to proposing a declarative semantics based on valuations and an equivalent semantics based on fixpoint theory, we also propose a proof procedure and prove it sound and complete. We show that while classical Datalog query programs have a polynomial time data complexity, certain query programs in the probabilistic deductive database framework do not even terminate on some input databases. We identify a large natural class of query programs of practical interest in our framework, and show that programs in this class possess polynomial time data complexity, i.e. not only do they terminate on every input database, they are guaranteed to do so in a number of steps polynomial in the input database size.