Expressivity and Complexity of MongoDB Queries

In this paper, we consider MongoDB, a widely adopted but not formally understood database system managing JSON documents and equipped with a powerful query mechanism, called the aggregation framework. We provide a clean formal abstraction of this query language, which we call MQuery. We study the expressivity of MQuery, showing the equivalence of its well-typed fragment with nested relational algebra. We further investigate the computational complexity of significant fragments of it, obtaining several (tight) bounds in combined complexity, which range from LogSpace to alternating exponential-time with a polynomial number of alternations

Formal verification of neural agents in non-deterministic environments

We introduce a model for agent-environment systems where the agents are implemented via feed-forward ReLU neural networks and the environment is non-deterministic. We study the verification problem of such systems against CTL properties. We show that verifying these systems against reachability properties is undecidable. We introduce a bounded fragment of CTL, show its usefulness in identifying shallow bugs in the system, and prove that the verification problem against specifications in bounded CTL is in coNEXPTIME and PSPACE-hard. We introduce sequential and parallel algorithms for MILP-based verification of agent-environment systems, present an implementation, and report the experimental results obtained against a variant of the VerticalCAS use-case and the frozen lake scenario

Representability in DL-Lite_R Knowledge Base Exchange

Knowledge base exchange can be considered as a generalization of data exchange in which the aim is to exchange between a source and a target connected through mappings, not only explicit knowledge, i.e., data, but also implicit knowledge in the form of axioms. Such problem has been investigated recently using Description Logics (DLs) as representation formalism, thus assuming that the source and target KBs are given as a DL TBox+ABox, while the mappings have the form of DL TBox assertions. In this paper we are interested in the problem of representing a given source TBox by means of a target TBox that captures at best the intensional information in the source. In previous work, results on representability have been obtained for DL-LiteRDFS , a DL corresponding to the FOL fragment of RDFS. We extend these results to the positive fragment of DLLiteR, in which, differently from DL-LiteRDFS , the assertions in the TBox and the mappings may introduce existentially implied individuals. For this we need to overcome the challenge that the chase, a key notion in data and knowledge base exchange, is not guaranteed anymore to be finite

Knowledge base exchange: the case of OWL 2 QL

In this article, we define and study the problem of exchanging knowledge between a source and a target knowledge base (KB), connected through mappings. Differently from the traditional database exchange setting, which considers only the exchange of data, we are interested in exchanging implicit knowledge. As representation formalism we use Description Logics (DLs), thus assuming that the source and target KBs are given as a DL TBox+ABox, while the mappings have the form of DL TBox assertions. We define a general framework of KB exchange, and study the problem of translating the knowledge in the source KB according to the mappings expressed in OWL 2 QL, the profile of the standard Web Ontology Language OWL 2 based on the description logic DL-LiteR. We develop novel game- and automata-theoretic techniques, and we provide complexity results that range from NLogSpace to ExpTim

Games for query inseparability of description logic knowledge bases

We consider conjunctive query inseparability of description logic knowledge bases with respect to a given signature---a fundamental problem in knowledge base versioning, module extraction, forgetting and knowledge exchange. We give a uniform game-theoretic characterisation of knowledge base conjunctive query inseparability and develop worst-case optimal decision algorithms for fragments of Horn-ALCHI, including the description logics underpinning OWL 2 QL and OWL 2 EL. We also determine the data and combined complexity of deciding query inseparability. While query inseparability for all of these logics is P-complete for data complexity, the combined complexity ranges from P- to ExpTime- to 2ExpTime-completeness. We use these results to resolve two major open problems for OWL 2 QL by showing that TBox query inseparability and the membership problem for universal conjunctive query solutions in knowledge exchange are both ExpTime-complete for combined complexity. Finally, we introduce a more flexible notion of inseparability which compares answers to conjunctive queries in a given signature over a given set of individuals. In this case, checking query inseparability becomes NP-complete for data complexity, but the ExpTime- and 2ExpTime-completeness combined complexity results are preserved