arXiv subjects
Publications and source records attributed to Nina Pardal.
We propose KG-ER, a conceptual schema language for knowledge graphs that describes the structure of knowledge graphs independently of their representation (relational databases, property graphs, RDF) while helping to capture the semantics of the information stored in a knowledge graph.
We investigate the notion of sufficient explanation, and a sufficiency-degree as attribution score for database tuples in relation to query answering. We also investigate and exploit connections with database repairs as used for dealing with inconsistent databases; and with causality-based necessary explanations, obtaining new computational results. We show how to use answer-set programs to specify sufficient explanations and compute sufficiency-degrees.
We consider database schemas consisting of a single binary relation, with key constraints and inclusion dependencies. Over this space of 20 schemas, we completely characterize when one schema is generically dominated by another schema. Generic dominance, a classical notion for measuring information capacity, expresses that every instance of a schema can be uniquely represented in the dominating schema, through application of a deterministic, generic data transformation. Our investigation is motivated both by current interest in schema design for graph databases, as well as by intrinsic scientific interest. We also consider the ternary case, but without inclusion dependencies, and discuss how the notions change in the presence of object identifiers.
A digraph consisting of a set of vertices $V$ and a set of arcs $E$ is called an interval digraph if there exists a family of closed intervals $\{I_u,J_u\}_{u \in V}$ such that $uv$ is an arc if and only if the intersection of $I_u$ and $J_v$ is non-empty. Interval digraphs naturally generalize interval graphs, by extending the classical interval intersection model to directed graphs. Several subclasses of interval digraphs have been studied in the literature-such as balanced, chronological and catch interval digraphs-each characterized by admitting interval representations that satisfy specific restrictions. Among these, interval nest digraphs are the ones that admit an interval representation in which $J_u$ is contained in $I_u$ for all vertices $u$ of $V$. In this work, we provide a complete characterization of interval nest digraphs in terms of vertex linear orderings with forbidden patterns, which we call nest orderings. This result completes the picture of vertex-ordering characterizations among the main subclasses of interval digraphs.
Local consistency arises in diverse areas, including Bayesian statistics, relational databases, and quantum foundations, and so does the notion of functional dependence. We adopt a general approach to study logical inference in a setting that enables both global inconsistency and local consistency. Our approach builds upon pairwise consistent families of K-relations, i.e, relations with tuples annotated with elements of some positive commutative monoid. The framework covers, e.g., families of probability distributions arising from quantum experiments and their possibilistic counterparts. As a first step, we investigate the entailment problem for functional dependencies (FDs) in this setting. Notably, the transitivity rule for FDs is no longer sound, but can be replaced by two novel axiom schemas. We provide a complete axiomatisation for, and establish NL-completeness of, the entailment problem of unary FDs, and demonstrate that even this restricted case exhibits context-dependent subtleties. In addition, we explore when contextual families over the Booleans have realisations as contextual families over various monoids.
Graph modification problems are computational tasks where the goal is to change an input graph $G$ using operations from a fixed set, in order to make the resulting graph satisfy a target property, which usually entails membership to a desired graph class $\mathcal{C}$. Some well-known examples of operations include vertex-deletion, edge-deletion, edge-addition and edge-contraction. In this paper we address an operation known as subgraph complement. Given a graph $G$ and a subset $S$ of its vertices, the subgraph complement $G \oplus S$ is the graph resulting of complementing the edge set of the subgraph induced by $S$ in $G$. We say that a graph $H$ is a subgraph complement of $G$ if there is an $S$ such that $H$ is isomorphic to $G \oplus S$. For a graph class $\mathcal{C}$, subgraph complementation to $\mathcal{C}$ is the problem of deciding, for a given graph $G$, whether $G$ has a subgraph complement in $\mathcal{C}$. This problem has been studied and its complexity has been settled for many classes $\mathcal{C}$ such as $\mathcal{H}$-free graphs, for various families $\mathcal{H}$, and for classes of bounded degeneracy. In this work, we focus on classes graphs of minimum/maximum degree upper/lower bounded by some value $k$. In particular, we answer an open question of Antony et al. [Information Processing Letters 188, 106530 (2025)], by showing that subgraph complementation to $\mathcal{C}$ is NP-complete when $\mathcal{C}$ is the class of graphs of minimum degree at least $k$, if $k$ is part of the input. We also show that subgraph complementation to $k$-regular parameterized by $k$ is fixed-parameter tractable.
The proper thinness of a graph is an invariant that generalizes the concept of a proper interval graph. Every graph has a numerical value of proper thinness and the graphs with proper thinness~1 are exactly the proper interval graphs. A graph is proper $k$-thin if its vertices can be ordered in such a way that there is a partition of the vertices into $k$ classes satisfying that for each triple of vertices $r < s < t$, such that there is an edge between $r$ and $t$, it is true that if $r$ and $s$ belong to the same class, then there is an edge between $s$ and $t$, and if $s$ and $t$ belong to the same class, then there is an edge between $r$ and $s$. The proper thinness is the smallest value of $k$ such that the graph is proper $k$-thin. In this work we focus on the calculation of proper thinness for trees. We characterize trees of proper thinness~2, both structurally and by their minimal forbidden induced subgraphs. The characterizations obtained lead to a polynomial-time recognition algorithm. We furthermore show why the structural results obtained for trees of proper thinness~2 cannot be straightforwardly generalized to trees of proper thinness~3.
We embark on a study of the consistent answers of queries over databases annotated with values from a naturally ordered positive semiring. In this setting, the consistent answers of a query are defined as the minimum of the semiring values that the query takes over all repairs of an inconsistent database. The main focus is on self-join free conjunctive queries and key constraints, which is the most extensively studied case of consistent query answering over standard databases. We introduce a variant of first-order logic with a limited form of negation, define suitable semiring semantics, and then establish the main result of the paper: the consistent query answers of a self-join free conjunctive query under key constraints are rewritable in this logic if and only if the attack graph of the query contains no cycles. This result generalizes an analogous result of Koutris and Wijsen for ordinary databases, but also yields new results for a multitude of semirings, including the bag semiring, the tropical semiring, and the fuzzy semiring. Further, for the bag semiring, we show that computing the consistent answers of any self-join free conjunctive query whose attack graph has a strong cycle is not only NP-hard but also it is NP-hard to even approximate the consistent answers with a constant relative approximation guarantee.
We introduce a general abstract framework for database repairs, where the repair notions are defined using formal logic. We distinguish between integrity constraints and so-called query constraints. The former are used to model consistency and desirable properties of the data (such as functional dependencies and independencies), while the latter relate two database instances according to their answers to the query constraints. The framework allows for a distinction between hard and soft queries, allowing the answers to a core set of queries to be preserved, as well as defining a distance between instances based on query answers. We illustrate how different notions of repairs from the literature can be modelled within our unifying framework. The framework generalises both set-based and cardinality based repairs to semiring annotated databases. Furthermore, we initiate a complexity-theoretic analysis of consistent query answering and checking existence of a repair within the framework.
Attribution scores reflect how important the feature values in an input entity are for the output of a machine learning model. One of the most popular attribution scores is the SHAP score, which is an instantiation of the general Shapley value used in coalition game theory. The definition of this score relies on a probability distribution on the entity population. Since the exact distribution is generally unknown, it needs to be assigned subjectively or be estimated from data, which may lead to misleading feature scores. In this paper, we propose a principled framework for reasoning on SHAP scores under unknown entity population distributions. In our framework, we consider an uncertainty region that contains the potential distributions, and the SHAP score of a feature becomes a function defined over this region. We study the basic problems of finding maxima and minima of this function, which allows us to determine tight ranges for the SHAP scores of all features. In particular, we pinpoint the complexity of these problems, and other related ones, showing them to be NP-complete. Finally, we present experiments on a real-world dataset, showing that our framework may contribute to a more robust feature scoring.
Preferences are a pivotal component in practical reasoning, especially in tasks that involve decision-making over different options or courses of action that could be pursued. In this work, we focus on repairing and querying inconsistent knowledge bases in the form of graph databases, which involves finding a way to solve conflicts in the knowledge base and considering answers that are entailed from every possible repair, respectively. Without a priori domain knowledge, all possible repairs are equally preferred. Though that may be adequate for some settings, it seems reasonable to establish and exploit some form of preference order among the potential repairs. We study the problem of computing prioritized repairs over graph databases with data values, using a notion of consistency based on GXPath expressions as integrity constraints. We present several preference criteria based on the standard subset repair semantics, incorporating weights, multisets, and set-based priority levels. We show that it is possible to maintain the same computational complexity as in the case where no preference criterion is available for exploitation. Finally, we explore the complexity of consistent query answering in this setting and obtain tight lower and upper bounds for all the preference criteria introduced.
Given a property (graph class) $Π$, a graph $G$, and an integer $k$, the \emph{$Π$-completion} problem consists in deciding whether we can turn $G$ into a graph with the property $Π$ by adding at most $k$ edges to $G$. The $Π$-completion problem is known to be NP-hard for general graphs when $Π$ is the property of being a proper interval graph (PIG). In this work, we study the PIG-completion problem %when $Π$ is the class of proper interval graphs (PIG) within different subclasses of chordal graphs. We show that the problem remains NP-complete even when restricted to split graphs. We then turn our attention to positive results and present polynomial time algorithms to solve the PIG-completion problem when the input is restricted to caterpillar and threshold graphs. We also present an efficient algorithm for the minimum co-bipartite-completion for quasi-threshold graphs, which provides a lower bound for the PIG-completion problem within this graph class.
For a fixed property (graph class) $Π$, given a graph G and an integer k, the $Π$-deletion problem consists in deciding if we can turn $G$ into a graph with the property $Π$ by deleting at most $k$ edges. The $Π$-deletion problem is known to be NP-hard for most of the well-studied graph classes, such as chordal, interval, bipartite, planar, comparability and permutation graphs, among others; even deletion to cacti is known to be NP-hard for general graphs. However, there is a notable exception: the deletion problem to trees is polynomial. Motivated by this fact, we study the deletion problem for some classes similar to trees, addressing in this way a knowledge gap in the literature. We prove that deletion to cacti is hard even when the input is a bipartite graph. On the positive side, we show that the problem becomes tractable when the input is chordal, and for the special case of quasi-threshold graphs we give a simpler and faster algorithm. In addition, we present sufficient structural conditions on the graph class $Π$ that imply the NP-hardness of the $Π$-deletion problem, and show that deletion from general graphs to some well-known subclasses of forests is NP-hard.
Repairing inconsistent knowledge bases is a task that has been assessed, with great advances over several decades, from within the knowledge representation and reasoning and the database theory communities. As information becomes more complex and interconnected, new types of repositories, representation languages and semantics are developed in order to be able to query and reason about it. Graph databases provide an effective way to represent relationships among data, and allow processing and querying these connections efficiently. In this work, we focus on the problem of computing preferred (subset and superset) repairs for graph databases with data values, using a notion of consistency based on a set of Reg-GXPath expressions as integrity constraints. Specifically, we study the problem of computing preferred repairs based on two different preference criteria, one based on weights and the other based on multisets, showing that in most cases it is possible to retain the same computational complexity as in the case where no preference criterion is available for exploitation.
Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse contexts such as databases, quantum mechanics, and statistics by extending first-order logic with atoms that describe dependencies between variables. Combining these two, we propose a unifying approach for analysing the concepts of dependence and independence via a novel semiring team semantics, which subsumes all the previously considered variants for first-order team semantics. In particular, we study the preservation of satisfaction of dependencies and formulae between different semirings. In addition we create links to reasoning tasks such as provenance, counting, and repairs.
Graph databases are becoming widely successful as data models that allow to effectively represent and process complex relationships among various types of data. As with any other type of data repository, graph databases may suffer from errors and discrepancies with respect to the real-world data they intend to represent. In this work we explore the notion of probabilistic unclean graph databases, previously proposed for relational databases, in order to capture the idea that the observed (unclean) graph database is actually the noisy version of a clean one that correctly models the world but that we know partially. As the factors that may be involved in the observation can be many, e.g, all different types of clerical errors or unintended transformations of the data, we assume a probabilistic model that describes the distribution over all possible ways in which the clean (uncertain) database could have been polluted. Based on this model we define two computational problems: data cleaning and probabilistic query answering and study for both of them their corresponding complexity when considering that the transformation of the database can be caused by either removing (subset) or adding (superset) nodes and edges.
In the deeply interconnected world we live in, pieces of information link domains all around us. As graph databases embrace effectively relationships among data and allow processing and querying these connections efficiently, they are rapidly becoming a popular platform for storage that supports a wide range of domains and applications. As in the relational case, it is expected that data preserves a set of integrity constraints that define the semantic structure of the world it represents. When a database does not satisfy its integrity constraints, a possible approach is to search for a 'similar' database that does satisfy the constraints, also known as a repair. In this work, we study the problem of computing subset and superset repairs for graph databases with data values using a notion of consistency based on a set of Reg-GXPath expressions as integrity constraints. We show that for positive fragments of Reg-GXPath these problems admit a polynomial-time algorithm, while the full expressive power of the language renders them intractable.
A $(0,1)$-matrix has the consecutive-ones property (C1P) if its columns can be permuted to make the $1$'s in each row appear consecutively. This property was characterised in terms of forbidden submatrices by Tucker in 1972. Several graph classes were characterised by means of this property, including interval graphs and strongly chordal digraphs. In this work, we define and characterise 2-nested matrices, which are $(0,1)$-matrices with a variant of the C1P and for which there is also certain assignment of one of two colors to each block of consecutive $1$'s in each row. The characterization of 2-nested matrices in the present work is of key importance to characterise split graphs that are also circle by minimal forbidden induced subgraphs.