As schema languages for RDF data become more mature, we are seeing efforts to extend them with recursive semantics, applying diverse ideas from logic programming and description logics. While ShEx has an official recursive semantics based on greatest fixpoints (GFP), the discussion for SHACL is ongoing and seems to be converging towards least fixpoints (LFP). A practical study we perform shows that, indeed, ShEx validators implement GFP, whereas SHACL validators are more heterogeneous. This situation creates tension between ShEx and SHACL, as their semantic commitments appear to diverge, potentially undermining interoperability and predictability. We aim to clarify this design space by comparing the main semantic options in a principled yet accessible way, hoping to engage both theoreticians and practicioners, especially those involved in developing tools and standards. We present a unifying formal semantics that treats LFP, GFP, and supported model semantics (SMS), clarifying their relationships and highlighting a duality between LFP and GFP on stratified fragments. Next, we investigate to which extent the directions taken by SHACL and ShEx are compatible. We show that, although ShEx and SHACL seem to be going in different directions, they include large fragments with identical expressive power. Moreover, there is a strong correspondence between these fragments through the aforementioned principle of duality. Finally, we present a complete picture of the data and combined complexity of ShEx and SHACL validation under LFP, GFP, and SMS, showing that SMS comes at a higher computational cost under standard complexity-theoretic assumptions.

Graphs have emerged as a foundation for a variety of applications, including capturing factual knowledge, semantic data integration, social networks, and informing machine learning algorithms. Formalising properties of the data and ensuring data quality requires describing schemas of such graphs. Driven by diverse applications, the Semantic Web and database communities developed not only different graph data models-RDF and property graphs-but also different graph schema languages-SHACL, ShEx, and PG-Schema. Each language has its unique approach to defining constraints and validating graph data, leaving potential users in the dark about their commonalities and differences. In this paper, we provide concise formal definitions of the core components of these languages, employ a uniform framework to facilitate a comprehensive comparison between them, and identify a common set of functionalities, shedding light on both overlapping and distinctive features.

The Shapes Constraint Language (SHACL) was standardized by the World Wide Web as a constraint language to describe and validate RDF data graphs. SHACL uses the notion of shapes graph to describe a set of shape constraints paired with targets, that specify which nodes of the RDF graph should satisfy which shapes. An important question in practice is how to handle data graphs that do not validate the shapes graph. A solution is to tolerate the non-validation and find ways to obtain meaningful and correct answers to queries despite the non-validation. This is known as consistent query answering (CQA) and there is extensive literature on CQA in both the database and the KR setting. We study CQA in the context of SHACL for a fundamental fragment of the Semantic Web query language SPARQL. The goal of our work is a detailed complexity analysis of CQA for various semantics and possible restrictions on the acceptable repairs. It turns out that all considered variants of the problem are intractable, with complexities ranging between the first and third level of the polynomial hierarchy.

OWL and SHACL are two prominent W3C standards for managing RDF graphs, the data model of the Web. They are used for different purposes and make different assumptions about the completeness of data: SHACL is used for expressing integrity constraints on complete data, while OWL allows inferring implicit facts from incomplete data; SHACL reasoners perform validation, while OWL reasoners do logical inference. Integrating these two tasks into one uniform approach is a relevant but challenging problem. The SHACL standard envisions graph validation in combination with OWL entailment, but it does not provide technical guidance on how to realize this. To address this problem, we propose a new intuitive semantics for validating SHACL constraints with OWL 2 QL ontologies based on a suitable notion of the chase. We propose an algorithm that rewrites a set of recursive SHACL constraints (with stratified negation) and an OWL 2 QL ontology into a stand-alone set of SHACL constraints that preserves validation for every input graph, which can in turn be evaluated using an off-the-shelf SHACL validator. We show that validation in this setting is EXPTIME-complete in combined complexity, but only PTIME-complete in data complexity, i.e., if the constraints and the ontology are fixed.

A key prerequisite for the successful adoption of the Shapes Constraint Language (SHACL)---the W3C standardized constraint language for RDF graphs---is the availability of automated tools that efficiently validate targeted constraints (known as shapes graphs ) over possibly very large RDF graphs. There are already significant efforts to produce optimized engines for SHACL validation, but they focus on restricted fragments of SHACL. For unrestricted SHACL, that is SHACL with unrestricted recursion and negation, there is no validator beyond a proof-of-concept prototype, and existing techniques are inherently incompatible with the goal-driven approaches being pursued by existing validators. Instead they require a global computation on the entire data graph that is not only computationally very costly, but also brittle, and can easily result in validation failures due to conflicts that are irrelevant to the validation targets. To address these challenges, we present a 'magic' transformation---based on Magic Sets as known from Logic Programming---that transforms a SHACL shapes graph S into a new shapes graph S' whose validation considers only the relevant neighbourhood of the targeted nodes. The new S' is equivalent to S whenever there are no conflicts between the constraints and the data, and in case the validation of S fails due to conflicts that are irrelevant to the target, S' may still admit a lazy, target-oriented validation. We implement the algorithm and run preliminary experiments, showing our approach can be a stepping stone towards validators for full SHACL, and that it can significantly improve the performance of the only prototype validator that currently supports full recursion and negation.

We develop a flexible, open-source framework for query answering on relational databases by adopting methods and techniques from the Semantic Web community and the data exchange community, and we apply this framework to a medical use case. We first deploy module-extraction techniques to derive a concise and relevant sub-ontology from an external reference ontology. We then use the chase procedure from the data exchange community to materialize a universal solution that can be subsequently used to answer queries on an enterprise medical database. Along the way, we identify a new class of well-behaved acyclic EL-ontologies extended with role hierarchies, suitably restricted functional roles, and domain/range restrictions, which cover our use case. We show that such ontologies are C-stratified, which implies that the chase procedure terminates in polynomial time. We provide a detailed overview of our real-life application in the medical domain and demonstrate the benefits of this approach, such as discovering additional answers and formulating new queries.

The Shapes Constraint Language (SHACL) is a recently standardized language for describing and validating constraints over RDF graphs. The SHACL specification describes the so-called validation reports, which are meant to explain to the users the outcome of validating an RDF graph against a collection of constraints. Specifically, explaining the reasons why the input graph does not satisfy the constraints is challenging. In fact, the current SHACL standard leaves it open on how such explanations can be provided to the users. In this paper, inspired by works on logic-based abduction and database repairs, we study the problem of explaining non-validation of SHACL constraints. In particular, in our framework non-validation is explained using the notion of a repair, i.e., a collection of additions and deletions whose application on an input graph results in a repaired graph that does satisfy the given SHACL constraints. We define a collection of decision problems for reasoning about explanations, possibly restricting to explanations that are minimal with respect to cardinality or set inclusion. We provide a detailed characterization of the computational complexity of those reasoning tasks, including the combined and the data complexity.

The goal of this paper is to understand the relative expressiveness of the query language in which queries are specified by a set of guarded (disjunctive) tuple-generating dependencies (TGDs) and an output (or 'answer') predicate. Our main result is to show that every such query can be translated into a polynomially-sized (disjunctive) Datalog program if the maximal number of variables in the (disjunctive) TGDs is bounded by a constant. To overcome the challenge that Datalog has no direct means to express the existential quantification present in TGDs, we define a two-player game that characterizes the satisfaction of the dependencies, and design a Datalog query that can decide the existence of a winning strategy for the game. For guarded disjunctive TGDs, we can obtain Datalog rules with disjunction in the heads. However, the use of disjunction is limited, and the resulting rules fall into a fragment that can be evaluated in deterministic single exponential time. We proceed quite differently for the case when the TGDs are not disjunctive and we show that we can obtain a plain Datalog query. Notably, unlike previous translations for related fragments, our translation requires only polynomial time if the maximal number of variables in the (disjunctive) TGDs is bounded by a constant.

In this article, we consider the setting of graph-structured data that evolves as a result of operations carried out by users or applications. We study different reasoning problems, which range from deciding whether a given sequence of actions preserves the satisfaction of a given set of integrity constraints, for every possible initial data instance, to deciding the (non)existence of a sequence of actions that would take the data to an (un)desirable state, starting either from a specific data instance or from an incomplete description of it. For describing states of the data instances and expressing integrity constraints on them, we use description logics (DLs) closely related to the two-variable fragment of first-order logic with counting quantifiers. The updates are defined as actions in a simple yet flexible language, as finite sequences of conditional insertions and deletions, which allow one to use complex DL formulas to select the (pairs of) nodes for which (node or arc) labels are added or deleted. We formalize the preceding data management problems as a static verification problem and several planning problems and show that, due to the adequate choice of formalisms for describing actions and states of the data, most of these data management problems can be effectively reduced to the (un)satisfiability of suitable formulas in decidable logical formalisms. Leveraging this, we provide algorithms and tight complexity bounds for the formalized problems, both for expressive DLs and for a variant of the popular DL-Lite, advocated for data management in recent years.

SPARQL entailment regimes are strongly influenced by the big body of works on ontology-based query answering, notably in the area of Description Logics (DLs). However, the semantics of query answering under SPARQL entailment regimes is defined in a more naive and much less expressive way than the certain answer semantics usually adopted in DLs. The goal of this work is to introduce an intuitive certain answer semantics also for SPARQL and to show the feasibility of this approach. For OWL 2 QL entailment, we present algorithms for the evaluation of an interesting fragment of SPARQL (the so-called well-designed SPARQL). Moreover, we show that the complexity of the most fundamental query analysis tasks (such as query containment and equivalence testing) is not negatively affected by the presence of OWL 2 QL entailment under the proposed semantics.

In this paper we consider the setting of graph-structured data that evolves as a result of operations carried out by users or applications. We study different reasoning problems, which range from ensuring the satisfaction of a given set of integrity constraints after a given sequence of updates, to deciding the (non-)existence of a sequence of actions that would take the data to an (un)desirable state, starting either from a specific data instance or from an incomplete description of it. We consider a simple action language in which actions are finite sequences of insertions and deletions of nodes and labels, and use Description Logics for describing integrity constraints and (partial) states of the data. We then formalize the data management problems mentioned above as a static verification problem and several planning problems. We provide algorithms and tight complexity bounds for the formalized problems, both for an expressive DL and for a variant of DL-Lite.