Answer Set Programming (ASP) is a prominent problem-modeling and solving framework, whose solutions are called answer sets. Epistemic logic programs (ELP) extend ASP to reason about all or some answer sets. Solutions to an ELP can be seen as consequences over multiple collections of answer sets, known as world views. While the complexity of propositional programs is well studied, the non-ground case remains open. This paper establishes the complexity of non-ground ELPs. We provide a comprehensive picture for well-known program fragments, which turns out to be complete for the class NEXPTIME with access to oracles up to \Sigma^P_2. In the quantitative setting, we establish complexity results for counting complexity beyond #EXP. To mitigate high complexity, we establish results in case of bounded predicate arity, reaching up to the fourth level of the polynomial hierarchy. Finally, we provide ETH-tight runtime results for the parameter treewidth, which has applications in quantitative reasoning, where we reason on (marginal) probabilities of epistemic literals.

Structural decomposition methods, such as generalized hypertree decompositions, have been successfully used for solving constraint satisfaction problems (CSPs). As decompositions can be reused to solve CSPs with the same constraint scopes, investing resources in computing good decompositions is beneficial, even though the computation itself is hard. Unfortunately, current methods need to compute a completely new decomposition even if the scopes change only slightly. In this paper, we make the first steps toward solving the problem of updating the decomposition of a CSP $P$ so that it becomes a valid decomposition of a new CSP $P'$ produced by some modification of $P$. Even though the problem is hard in theory, we propose and implement a framework for effectively updating GHDs. The experimental evaluation of our algorithm strongly suggests practical applicability.

Datalog /- is a conceptually very simple formalism that extends plain Datalog with features such as existential quantifiers, equalities, and the falsum in rule heads and, at the same time, restricts the rule syntax so as to achieve decidability and, when required, tractability. Datalog /- provides a uniform framework for query answering and reasoning with incomplete data.

We consider the scenario of ontology-based data access where a conjunctive query is evaluated against a database enriched with intensional knowledge via an ontology. It is generally accepted that true scalability of query answering in this setting can only be achieved by using standard relational database management systems (RDBMSs). An approach to query answering that enables the use of RDBMSs is the so-called polynomial combined approach. We investigate this approach for the main guarded- and sticky-based classes of existential rules, and we highlight the assumptions on the underlying schema which are sufficient for the polynomial combined first-order rewritability of those classes. To the best of our knowledge, this is the first work which explicitly studies the polynomial combined approach for existential rules.

We tackle a long-standing open research problem and prove the decidability of query answering under the stable model semantics for guarded existential rules, where rule bodies may contain negated atoms, and provide complexity results. The results extend to guarded Datalog /- with negation, and thus provide a natural and decidable stable model semantics to description logics such as ELHI and DL-LiteR.

SPARQL is the de facto language for querying RDF data, since its standardization in 2008. A new version, called SPARQL 1.1, was released in 2013, with the aim of enriching the 2008 language with reasoning capabilities to deal with RDFS and OWL vocabularies, and a mechanism to express navigation patterns through regular expressions. However, SPARQL 1.1 is not powerful enough for expressing some relevant navigation patterns, and it misses a general form of recursion. In this work, we focus on OWL 2 QL and we propose TriQ-Lite 1.0, a tractable rule-based formalism that supports the above functionalities, and thus it can be used for querying RDF data. Unlike existing composite approaches, our formalism has simple syntax and semantics in the same spirit as good old Datalog.

We consider the scenario of ontology-based query answering. It is generally accepted that true scalability in this setting can only be achieved via query rewriting, which in turn allows for the exploitation of standard RDBMSs. In this work, we close two open fundamental questions related to query rewriting. We establish that linear existential rules are polynomially combined rewritable, while full linear rules are polynomially (purely) rewritable; in both cases, the target query language consists of first-order or non-recursive Datalog queries. An immediate consequence of our results is that DLR-Lite_R, the extension of DL-Lite_R with n-ary roles, is polynomially combined rewritable.

We investigate the computational complexity of mining guarded clauses from clausal datasets through the framework of inductive logic programming (ILP). We show that learning guarded clauses is NP-complete and thus one step below the $\sigma^P_2$-complete task of learning Horn clauses on the polynomial hierarchy. Motivated by practical applications on large datasets we identify a natural tractable fragment of the problem. Finally, we also generalise all of our results to $k$-guarded clauses for constant $k$.

Constraint Satisfaction Problems (CSPs) play a central role in many applications in Artificial Intelligence and Operations Research. In general, solving CSPs is NP-complete. The structure of CSPs is best described by hypergraphs. Therefore, various forms of hypergraph decompositions have been proposed in the literature to identify tractable fragments of CSPs. However, also the computation of a concrete hypergraph decomposition is a challenging task in itself. In this paper, we report on recent progress in the study of hypergraph decompositions and we outline several directions for future research.

Reasoning over OWL 2 is a very expensive task in general, and therefore the W3C identified tractable profiles exhibiting good computational properties. Ontological reasoning for many fragments of OWL 2 can be reduced to the evaluation of Datalog queries.