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We study quadrangular properties of binary relations on a set $X$~--i.e., properties defined on configurations of four elements--~within an agonistic interpretation, where $xRy$ is interpreted as $x$ ``attacks''~$y$. Such relations induce a…
We prove two completeness results for Kleene algebra with tests and a top element, with respect to guarded string languages and binary relations. While the equational theories of those two classes of models coincide over the signature of…
Processes with indefinite causal order can arise when quantum theory is locally valid and they allow accomplishing new informational tasks. Despite recent progress, the correlations allowed in such processes have not been clearly…
The connection between inconsistent databases and Dung's abstract argumentation framework has recently drawn growing interest. Specifically, an inconsistent database, involving certain types of integrity constraints such as functional and…
Incomputability results in Formal Logic and the Theory of Computation (i.e., incompleteness and undecidability) have deep implications for the foundations of mathematics and computer science. Likewise, Social Choice Theory, a branch of…
Many real world systems need to operate on heterogeneous information networks that consist of numerous interacting components of different types. Examples include systems that perform data analysis on biological information networks; social…
Temporal knowledge bases associate relational (s,r,o) triples with a set of times (or a single time instant) when the relation is valid. While time-agnostic KB completion (KBC) has witnessed significant research, temporal KB completion…
Modelling across engineering, systems science, and formal methods remains limited by binary relations, implicit semantics, and diagram-centred notations that obscure multilevel structure and hinder mechanisation. Hypernetwork Theory (HT)…
Detecting structural similarity between queries is essential for selecting examples in in-context learning models. However, assessing structural similarity based solely on the natural language expressions of queries, without considering SQL…
Graph data is becoming increasingly prevalent due to the growing demand for relational insights in AI across various domains. Organizations regularly use graph data to solve complex problems involving relationships and connections. Causal…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…
Motivated by the incompleteness of modern knowledge graphs, a new setup for query answering has emerged, where the goal is to predict answers that do not necessarily appear in the knowledge graph, but are present in its completion. In this…
We consider equivalence relations and preorders complete for various levels of the arithmetical hierarchy under computable, component-wise reducibility. We show that implication in first order logic is a complete preorder for $\SI 1$, the…
We investigate a class of first-order temporal-epistemic logics for reasoning about multi-agent systems. We encode typical properties of systems including perfect recall, synchronicity, no learning, and having a unique initial state in…
Effectively using full syntactic parsing information in Neural Networks (NNs) to solve relational tasks, e.g., question similarity, is still an open problem. In this paper, we propose to inject structural representations in NNs by (i)…
Integrating deep learning and causal discovery has encouraged us to spot that learning causal structures and representations in dialogue and video is full of challenges. We defined These data forms as "Indefinite Data", characterized by…
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the…
Heterogeneous graph neural networks have become popular in various domains. However, their generalizability and interpretability are limited due to the discrepancy between their inherent inference flows and human reasoning logic or…
Knowledge Graphs are pivotal for semantic data integration. The real-world data they model is often inherently uncertain. Within knowledge graphs, uncertainty manifests in three distinct levels: imprecise attribute values, probabilistic…