Knowledge graph (KG) reasoning is becoming increasingly popular in both academia and industry. Conventional KG reasoning based on symbolic logic is deterministic, with reasoning results being explainable, while modern embedding-based reasoning can deal with uncertainty and predict plausible knowledge, often with high efficiency via vector computation. A promising direction is to integrate both logic-based and embedding-based methods, with the vision to have advantages of both. It has attracted wide research attention with more and more works published in recent years. In this paper, we comprehensively survey these works, focusing on how logics and embeddings are integrated. We first briefly introduce preliminaries, then systematically categorize and discuss works of logic and embedding-aware KG reasoning from different perspectives, and finally conclude and discuss the challenges and further directions.

The Semantic Web has garnered a reputation for complexity among both Javascript and Python developers, primarily because, well, it's not JSON, and JSON has become the data language of the web. Why learn some obscure language when JSON is perfectly capable of describing everything, right? The problem that JSON faces, is actually a pretty subtle one, and has to do with the distinction between something occurring by value rather than by reference. Let's say that you have an education setting involving three courses and two teachers, where the two teachers co-teach one of the classes. The description is straightforward until you get to the very last teacher entry.

Ontological knowledge modelling of epics, though being an established research arena backed by concrete multilingual and multicultural works, still suffer from two key shortcomings. Firstly, all epic ontological models developed till date have been designed following ad-hoc methodologies, most often, combining existing general purpose ontology development methodologies. Secondly, none of the ad-hoc methodologies consider the potential reuse of existing epic ontological models for enrichment, if available. The paper presents, as a unified solution to the above shortcomings, the design and development of GENOME - the first dedicated methodology for iterative ontological modelling of epics, potentially extensible to works in different research arenas of digital humanities in general. GENOME is grounded in transdisciplinary foundations of canonical norms for epics, knowledge modelling best practices, application satisfiability norms and cognitive generative questions. It is also the first methodology (in epic modelling but also in general) to be flexible enough to integrate, in practice, the options of knowledge modelling via reuse or from scratch. The feasibility of GENOME is validated via a first brief implementation of ontological modelling of the Indian epic - Mahabharata by reusing an existing ontology. The preliminary results are promising, with the GENOME-produced model being both ontologically thorough and performance-wise competent

The use of Semantic Technologies - in particular the Semantic Web - has revealed to be a great tool for describing the cultural heritage domain and artistic practices. However, the panorama of ontologies for musicological applications seems to be limited and restricted to specific applications. In this research, we propose HaMSE, an ontology capable of describing musical features that can assist musicological research. More specifically, HaMSE proposes to address issues that have been affecting musicological research for decades: the representation of music and the relationship between quantitative and qualitative data. To do this, HaMSE allows the alignment between different music representation systems and describes a set of musicological features that can allow the music analysis at different granularity levels.

We study the problem to decide, given sets T1,T2 of tuple-generating dependencies (TGDs), also called existential rules, whether T2 is a conservative extension of T1. We consider two natural notions of conservative extension, one pertaining to answers to conjunctive queries over databases and one to homomorphisms between chased databases. Our main results are that these problems are undecidable for linear TGDs, undecidable for guarded TGDs even when T1 is empty, and decidable for frontier-one TGDs.

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We define generalized ontology-based production systems (GOPSs), which formalize a very general and powerful combination of ontologies and production systems. We show that GOPSs capture and generalize many existing formal notions of production systems. We introduce a powerful verification query language for GOPSs, which is able to express the most relevant formal properties of production systems previously considered in the literature. We establish a general sufficient condition for the decidability of answering verification queries over GOPSs. Then, we define Lite-GOPS, a particular class of GOPSs based on the use of a light-weight ontology language (DL-Llite_A), a light-weight ontology query language (EQL-Lite(UCQ)), and a tractable semantics for updates over Description Logic ontologies. We show decidability of all the above verification tasks over Lite-GOPSs, and prove tractability of some of such tasks.

In ontology-based data access (OBDA), ontologies are used as an interface for querying instance data. Since in typical applications the size of the data is much larger than the size of the ontology and query, data complexity is the most important complexity measure. In this paper, we propose a new method for investigating data complexity in OBDA: instead of classifying whole logics according to their complexity, we aim at classifying each individual ontology within a given master language. Our results include a P/coNP-dichotomy theorem for ontologies of depth one in the description logic ALCFI, the equivalence of a P/coNP-dichotomy theorem for ALC/ALCI-ontologies of unrestricted depth to the famous dichotomy conjecture for CSPs by Feder and Vardi, and a non-P/coNP-dichotomy theorem for ALCF-ontologies.

We present a novel rewriting technique for conjunctive query answering over OWL 2 QL ontologies. In general, the obtained rewritings are not necessarily correct and can be of exponential size in the length of the query. We argue, however, that in most, if not all, practical cases the rewritings are correct and of polynomial size. Moreover, we prove some sufficient conditions, imposed on queries and ontologies, that guarantee correctness and succinctness. We also support our claim by experimental results.

Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a key problem in knowledge representation and databases. This problem can be solved using the chase (aka materialisation) algorithm; however, CQ answering is undecidable for general existential rules, so the chase is not guaranteed to terminate. Several acyclicity conditions provide sufficient conditions for chase termination. In this paper, we present two novel such conditions--model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA)--that generalise many of the acyclicity conditions known so far in the literature. Materialisation provides the basis for several widely-used OWL 2 DL reasoners.