In this paper, we explore the issue of inconsistency handling in DatalogMTL, an extension of Datalog with metric temporal operators. Since facts are associated with time intervals, there are different manners to restore consistency when they contradict the rules, such as removing facts or modifying their time intervals. Our first contribution is the definition of relevant notions of conflicts (minimal explanations for inconsistency) and repairs (possible ways of restoring consistency) for this setting and the study of the properties of these notions and the associated inconsistency-tolerant semantics. Our second contribution is a data complexity analysis of the tasks of generating a single conflict / repair and query entailment under repair-based semantics.

Biomedical ontologies contain numerous concept or role names involving negative knowledge such as lacks_part, absence_of. Such a representation with labels rather than logical constructors would not allow a reasoner to interpret lacks_part as a kind of negation of has_part. It is known that adding negation to the tractable Description Logic (DL) EL allowing for conjunction, existential restriction and concept inclusion makes it intractable since the obtained logic includes implicitly disjunction and universal restriction which interact with other constructors. In this paper, we propose a new extension of EL with a weakened negation allowing to represent negative knowledge while retaining tractability. To this end, we introduce categorical semantics of all logical constructors of the DL SH including EL with disjunction, negation, universal restriction, role inclusion and transitive roles. The categorical semantics of a logical constructor is usually described as a set of categorical properties referring to several objects without using set membership. To restore tractability, we have to weaken semantics of disjunction and universal restriction by identifying \emph{independent} categorical properties that are responsible for intractability, and dropping them from the set of categorical properties. We show that the logic resulting from weakening semantics is more expressive than EL with the bottom concept, transitive roles and role inclusion.

Recent advances in open-vocabulary object detection models will enable Automatic Target Recognition systems to be sustainable and repurposed by non-technical end-users for a variety of applications or missions. New, and potentially nuanced, classes can be defined with natural language text descriptions in the field, immediately before runtime, without needing to retrain the model. We present an approach for improving non-technical users' natural language text descriptions of their desired targets of interest, using a combination of analysis techniques on the text embeddings, and proper combinations of embeddings for contrastive examples. We quantify the improvement that our feedback mechanism provides by demonstrating performance with multiple publicly-available open-vocabulary object detection models.

We present machine-learning-based approaches for determining the \emph{degree} of inconsistency -- which is a numerical value -- for propositional logic knowledge bases. Specifically, we present regression- and neural-based models that learn to predict the values that the inconsistency measures $\incmi$ and $\incat$ would assign to propositional logic knowledge bases. Our main motivation is that computing these values conventionally can be hard complexity-wise. As an important addition, we use specific postulates, that is, properties, of the underlying inconsistency measures to infer symbolic rules, which we combine with the learning-based models in the form of constraints. We perform various experiments and show that a) predicting the degree values is feasible in many situations, and b) including the symbolic constraints deduced from the rationality postulates increases the prediction quality.

We investigate the power soltera2 is a positive example for C, and of labeled examples for describing description-logic px10 and teslaY are negative examples for C concepts. Specifically, we systematically study the In fact, as it turns out, C is the only EL-concept (up to equivalence) existence and efficient computability of finite characterisations, that fits these three labeled examples. In other words, i.e., finite sets of labeled examples these three labeled examples "uniquely characterize" C within that uniquely characterize a single concept, for a the class of all EL-concepts. This shows that the above three wide variety of description logics between EL and labeled examples are a good choice of examples. Adding any ALCQI,both without an ontology and in the presence additional examples would be redundant. Note, however, that of a DL-Lite ontology. Finite characterisations this depends on the choice of description logic. For instance, are relevant for debugging purposes, and their existence the richer concept language ALC allows for other concept is a necessary condition for exact learnability expressions such as Bicycle Contains.Basket that also fit.

Recent works have explored the use of counting queries coupled with Description Logic ontologies. The answer to such a query in a model of a knowledge base is either an integer or $\infty$, and its spectrum is the set of its answers over all models. While it is unclear how to compute and manipulate such a set in general, we identify a class of counting queries whose spectra can be effectively represented. Focusing on atomic counting queries, we pinpoint the possible shapes of a spectrum over $\mathcal{ALCIF}$ ontologies: they are essentially the subsets of $\mathbb{N} \cup \{ \infty \}$ closed under addition. For most sublogics of $\mathcal{ALCIF}$, we show that possible spectra enjoy simpler shapes, being $[ m, \infty ]$ or variations thereof. To obtain our results, we refine constructions used for finite model reasoning and notably rely on a cycle-reversion technique for the Horn fragment of $\mathcal{ALCIF}$. We also study the data complexity of computing the proposed effective representation and establish the $\mathsf{FP}^{\mathsf{NP}[\log]}$-completeness of this task under several settings.

We present High-Throughput Hypothesis Evaluation in Description Logic (HT-HEDL). HT-HEDL is a high-performance hypothesis evaluation engine that accelerates hypothesis evaluation computations for inductive logic programming (ILP) learners using description logic (DL) for their knowledge representation; in particular, HT-HEDL targets accelerating computations for the $\mathcal{ALCQI}^{\mathcal{(D)}}$ DL language. HT-HEDL aggregates the computing power of multi-core CPUs with multi-GPUs to improve hypothesis computations at two levels: 1) the evaluation of a single hypothesis and 2) the evaluation of multiple hypotheses (i.e., batch of hypotheses). In the first level, HT-HEDL uses a single GPU or a vectorized multi-threaded CPU to evaluate a single hypothesis. In vectorized multi-threaded CPU evaluation, classical (scalar) CPU multi-threading is combined with CPU's extended vector instructions set to extract more CPU-based performance. The experimental results revealed that HT-HEDL increased performance using CPU-based evaluation (on a single hypothesis): from 20.4 folds using classical multi-threading to $\sim85$ folds using vectorized multi-threading. In the GPU-based evaluation, HT-HEDL achieved speedups of up to $\sim38$ folds for single hypothesis evaluation using a single GPU. To accelerate the evaluation of multiple hypotheses, HT-HEDL combines, in parallel, GPUs with multi-core CPUs to increase evaluation throughput (number of evaluated hypotheses per second). The experimental results revealed that HT-HEDL increased evaluation throughput by up to 29.3 folds using two GPUs and up to $\sim44$ folds using two GPUs combined with a CPU's vectorized multi-threaded evaluation.

The quality of Machine Learning (ML) models strongly depends on the input data, as such generating high-quality features is often required to improve the predictive accuracy. This process is referred to as Feature Engineering (FE). However, since manual feature engineering is time-consuming and requires case-by-case domain knowledge, Automated Feature Engineering (AutoFE) is crucial. A major challenge that remains is to generate interpretable features. To tackle this problem, we introduce SMART, a hybrid approach that uses semantic technologies to guide the generation of interpretable features through a two-step process: Exploitation and Exploration. The former uses Description Logics (DL) to reason on the semantics embedded in Knowledge Graphs (KG) to infer domain-specific features, while the latter exploits the knowledge graph to conduct a guided exploration of the search space through Deep Reinforcement Learning (DRL). Our experiments on public datasets demonstrate that SMART significantly improves prediction accuracy while ensuring a high level of interpretability.

Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex and symbolic. We propose geometric relational embeddings, a paradigm of relational embeddings that respect the underlying symbolic structures. Specifically, this dissertation introduces various geometric relational embedding models capable of capturing: 1) complex structured patterns like hierarchies and cycles in networks and knowledge graphs; 2) logical structures in ontologies and logical constraints applicable for constraining machine learning model outputs; and 3) high-order structures between entities and relations. Our results obtained from benchmark and real-world datasets demonstrate the efficacy of geometric relational embeddings in adeptly capturing these discrete, symbolic, and structured properties inherent in relational data.

We present a novel approach to querying classical inconsistent description logic (DL) knowledge bases by adopting a~paraconsistent semantics with the four Belnapian values: exactly true ($\mathbf{T}$), exactly false ($\mathbf{F}$), both ($\mathbf{B}$), and neither ($\mathbf{N}$). In contrast to prior studies on paraconsistent DLs, we allow truth value operators in the query language, which can be used to differentiate between answers having contradictory evidence and those having only positive evidence. We present a reduction to classical DL query answering that allows us to pinpoint the precise combined and data complexity of answering queries with values in paraconsistent $\mathcal{ALCHI}$ and its sublogics. Notably, we show that tractable data complexity is retained for Horn DLs. We present a comparison with repair-based inconsistency-tolerant semantics, showing that the two approaches are incomparable.