Operational consistent query answering (CQA) is a recent framework for CQA, based on revised definitions of repairs and consistent answers, which opens up the possibility of efficient approximations with explicit error guarantees. The main idea is to iteratively apply operations (e.g., fact deletions), starting from an inconsistent database, until we reach a database that is consistent w.r.t. the given set of constraints. This gives us the flexibility of choosing the probability with which we apply an operation, which in turn allows us to calculate the probability of an operational repair, and thus, the probability with which a consistent answer is entailed. A natural way of assigning probabilities to operations is by targeting the uniform probability distribution over a reasonable space such as the set of operational repairs, the set of sequences of operations that lead to an operational repair, and the set of available operations at a certain step of the repairing process. This leads to what we generally call uniform operational CQA. The goal of this work is to perform a data complexity analysis of both exact and approximate uniform operational CQA, focusing on functional dependencies (and subclasses thereof) and conjunctive queries. The main outcome of our analysis, among other positive and negative results, is that uniform operational CQA pushes the efficiency boundaries further by ensuring the existence of efficient approximation schemes in scenarios that go beyond the simple case of primary keys, which seems to be the limit of the classical approach to CQA.

Datalog is a powerful rule-based language that allows us to express complex recursive queries and has found numerous applications over the years. Explaining why a result to a Datalog query is obtained is an essential task towards explainable and transparent data-intensive applications that rely on Datalog. A standard way of explaining a query result is the so-called why-provenance, which provides information about the witnesses to a query result in the form of subsets of the input database that as a whole can be used to derive that result. To our surprise, despite the fact that the notion of why-provenance for Datalog queries has been around for decades and intensively studied, its computational complexity remains unexplored. Our goal is to fill this gap in the why-provenance literature. Towards this end, we pinpoint the data complexity of why-provenance for Datalog queries and key subclasses thereof. The takeaway of our work is that why-provenance for recursive queries, even if the recursion is limited to be linear, is an intractable problem, whereas for non-recursive queries is highly tractable.

Operational consistent query answering (CQA) is a recent framework for CQA based on revised definitions of repairs, which are built by applying a sequence of operations (e.g., fact deletions) starting from an inconsistent database until we reach a database that is consistent w.r.t. the given set of constraints. It has been recently shown that there is an efficient approximation for computing the percentage of repairs that entail a given query when we focus on primary keys, conjunctive queries, and assuming the query is fixed (i.e., in data complexity). However, it has been left open whether such an approximation exists when the query is part of the input (i.e., in combined complexity). We show that this is the case when we focus on self-join-free conjunctive queries of bounded generelized hypertreewidth. We also show that it is unlikely that efficient approximation schemes exist once we give up one of the adopted syntactic restrictions, i.e., self-join-freeness or bounding the generelized hypertreewidth. Towards the desired approximation, we introduce a counting complexity class, called SpanTL, show that each problem in it admits an efficient approximation scheme by using a recent approximability result about tree automata, and then place the problem of interest in SpanTL.

Datalog is a well-established rule-based language that allows us to express complex recursive queries. As for every other query language, explaining why a result to a Datalog query is obtained is an essential task towards explainable and transparent query evaluation. A standard way of explaining a query result is the so-called why-provenance, which provides information about the witnesses to a query result in the form of subsets of the input database that as a whole can be used to derive that result. The data complexity of why-provenance for Datalog queries has been recently studied and it was shown to be intractable, namely NP-complete even if the recursion is linear. An interesting question that comes up is whether we can ensure tractable data complexity by considering a slightly less informative notion of provenance, in particular, whyminimal-provenance that keeps only subset-minimal witnesses to a query result. Another interesting question is whether we can adopt a more informative notion of provenance than why-provenance, in particular, whymultiplicity-provenance that also keeps track of how many times a certain fact occurs in a witness to a query result, without paying a price in data complexity. This work provides definitive answers to the above questions: (i) whyminimal-provenance ensures tractable data complexity, and (ii) whymultiplicity-provenance can be adopted without paying a price in complexity, apart from one surprising case where the data complexity becomes PSPACE-complete.

Operational consistent query answering (CQA) is a recent framework for CQA, based on revised definitions of repairs and consistent answers, which opens up the possibility of efficient approximations with explicit error guarantees. The main idea is to iteratively apply operations (e.g., fact deletions), starting from an inconsistent database, until we reach a database that is consistent w.r.t. the given set of constraints. This gives us the flexibility of choosing the probability with which we apply an operation, which in turn allows us to calculate the probability of an operational repair, and thus, the probability with which a consistent answer is entailed. A natural way of assigning probabilities to operations is by targeting the uniform probability distribution over a reasonable space such as the set of operational repairs, the set of sequences of operations that lead to an operational repair, and the set of available operations at a certain step of the repairing process. This leads to what we generally call uniform operational CQA. The goal of this work is to perform a data complexity analysis of both exact and approximate uniform operational CQA, focusing on functional dependencies (and subclasses thereof), and conjunctive queries. The main outcome of our analysis (among other positive and negative results), is that uniform operational CQA pushes the efficiency boundaries further by ensuring the existence of efficient approximation schemes in scenarios that go beyond the simple case of primary keys, which seems to be the limit of the classical approach to CQA.

A key task in the context of consistent query answering is to count the number of repairs that entail the query, with the ultimate goal being a precise data complexity classification. This has been achieved in the case of primary keys and self-join-free conjunctive queries (CQs) via an FP/#P-complete dichotomy. We lift this result to the more general case of functional dependencies (FDs). Another important task in this context is whenever the counting problem in question is intractable, to classify it as approximable, i.e., the target value can be efficiently approximated with error guarantees via a fully polynomial-time randomized approximation scheme (FPRAS), or as inapproximable. Although for primary keys and CQs (even with self-joins) the problem is always approximable, we prove that this is not the case for FDs. We show, however, that the class of FDs with a left-hand side chain forms an island of approximability. We see these results, apart from being interesting in their own right, as crucial steps towards a complete classification of approximate counting of repairs in the case of FDs and self-join-free CQs.