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A dichotomy theorem for maximum generalized satisfiability problems
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Efficient query evaluation on probabilistic databases
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
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Read-once functions and query evaluation in probabilistic databases
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Tractability in probabilistic databases
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Knowledge compilation meets database theory: compiling queries to decision diagrams
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Faster query answering in probabilistic databases using read-once functions
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A dichotomy in the complexity of deletion propagation with functional dependencies
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Local structure and determinism in probabilistic databases
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
On the tractability of query compilation and bounded treewidth
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Probabilistic databases with MarkoViews
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The dichotomy of probabilistic inference for unions of conjunctive queries
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Ontology-based access to probabilistic data with OWL QL
ISWC'12 Proceedings of the 11th international conference on The Semantic Web - Volume Part I
Provenance-based dictionary refinement in information extraction
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Oblivious bounds on the probability of boolean functions
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Multi-tuple deletion propagation: approximations and complexity
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Anytime approximation in probabilistic databases
The VLDB Journal — The International Journal on Very Large Data Bases
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We describe an algorithm that evaluates queries over probabilistic databases using Mobius' inversion formula in incidence algebras. The queries we consider are unions of conjunctive queries (equivalently: existential, positive First Order sentences), and the probabilistic databases are tuple-independent structures. Our algorithm runs in PTIME on a subset of queries called "safe" queries, and is complete, in the sense that every unsafe query is hard for the class FP#P. The algorithm is very simple and easy to implement in practice, yet it is non-obvious. Mobius' inversion formula, which is in essence inclusion-exclusion, plays a key role for completeness, by allowing the algorithm to compute the probability of some safe queries even when they have some subqueries that are unsafe. We also apply the same lattice-theoretic techniques to analyze an algorithm based on lifted conditioning, and prove that it is incomplete.