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We address the issue of incorporating a particular yet expressive form of integrity constraints (namely, denial constraints) into probabilistic databases. To this aim, we move away from the common way of giving semantics to probabilistic databases, which relies on considering a unique interpretation of the data, and address two fundamental problems: consistency checking and query evaluation. The former consists in verifying whether there is an interpretation which conforms to both the marginal probabilities of the tuples and the integrity constraints. The latter is the problem of answering queries under a "cautious" paradigm, taking into account all interpretations of the data in accordance with the constraints. In this setting, we investigate the complexity of the above-mentioned problems, and identify several tractable cases of practical relevance.

We discuss quantum non-locality and contextuality, emphasising logical and structural aspects. We also show how the same mathematical structures arise in various areas of classical computation.

In view of the paradigm shift that makes science ever more data-driven, in this paper we consider deterministic scientific hypotheses as uncertain data. In the form of mathematical equations, hypotheses symmetrically relate aspects of the studied phenomena. For computing predictions, however, deterministic hypotheses are used asymmetrically as functions. We refer to Simon's notion of structural equations in order to extract the (so-called) causal ordering embedded in a hypothesis. Then we encode it into a set of functional dependencies (fd's) that is basic input to a design-theoretic method for the synthesis of U-relational databases (DB's). The causal ordering captured from a formally-specified system of mathematical equations into fd's determines not only the constraints (structure), but also the correlations (uncertainty chaining) hidden in the hypothesis predictive data. We show how to process it effectively through original algorithms for encoding and reasoning on the given hypotheses as constraints and correlations into U-relational DB's. The method is applicable to both quantitative and qualitative hypotheses and has underwent initial tests in a realistic use case from computational science.

In view of the paradigm shift that makes science ever more data-driven, in this paper we consider deterministic scientific hypotheses as uncertain data. In the form of mathematical equations, hypotheses symmetrically relate aspects of the studied phenomena. For computing predictions, however, deterministic hypotheses are used asymmetrically as functions. We refer to Simon's notion of structural equations in order to extract the (so-called) causal ordering embedded in a hypothesis. Then we encode it into a set of functional dependencies (fd's) that is basic input to a design-theoretic method for the synthesis of U-relational databases (DB's). The causal ordering captured from a formally-specified system of mathematical equations into fd's determines not only the constraints (structure), but also the correlations (uncertainty chaining) hidden in the hypothesis predictive data. We show how to process it effectively through original algorithms for encoding and reasoning on the given hypotheses as constraints and correlations into U-relational DB's. The method is applicable to both quantitative and qualitative hypotheses and has underwent initial tests in a realistic use case from computational science.

Causality has been recently introduced in databases, to model, characterize and possibly compute causes for query results (answers). Connections between queryanswer causality, consistency-based diagnosis, database repairs (wrt. integrity constraint violations), abductive diagnosis and the view-update problem have been established. In this work we further investigate connections between query-answer causality and abductive diagnosis and the view-update problem. In this context, we also define and investigate the notion of query-answer causality in the presence of integrity constraints.