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The use of symbolic knowledge representation and reasoning as a way to resolve the lack of transparency of machine learning classifiers is a research area that lately attracts many researchers. In this work, we use knowledge graphs as the…
In this paper, we present a generalization of Grothendieck pretopologies -- suited for semicartesian categories with equalizers $C$ -- leading to a closed monoidal category of sheaves, instead of closed cartesian category. This is proved…
Recent years have witnessed the successful application of low-dimensional vector space representations of knowledge graphs to predict missing facts or find erroneous ones. However, it is not yet well-understood to what extent ontological…
Despite growing interest, accurately and reliably representing unstructured data, such as court decisions, in a structured form, remains a challenge. Recent advancements in generative AI applied to language modeling enabled the…
The task of completing knowledge triplets has broad downstream applications. Both structural and semantic information plays an important role in knowledge graph completion. Unlike previous approaches that rely on either the structures or…
In this work we consider the topological analysis of symbolic formal systems in the framework of network theory. In particular we analyse the network extracted by Principia Mathematica of B. Russell and A.N. Whitehead, where the vertices…
Graph Neural Networks (GNNs) have gained considerable traction for their capability to effectively process topological data, yet their interpretability remains a critical concern. Current interpretation methods are dominated by post-hoc…
Contextual information is widely considered for NLP and knowledge discovery in life sciences since it highly influences the exact meaning of natural language. The scientific challenge is not only to extract such context data, but also to…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…
Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…
We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of sheaves on a given site $({\mathcal{C}}, J)$ and that of…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
Understanding a visual scene goes beyond recognizing individual objects in isolation. Relationships between objects also constitute rich semantic information about the scene. In this work, we explicitly model the objects and their…
Knowledge graphs represent the meaning of properties of real-world entities and relationships among them in a natural way. Exploiting semantics encoded in knowledge graphs enables the implementation of knowledge-driven tasks such as…
In this paper a Set Theoretic approach has been reported for analyzing inter-relationship between any numbers of RDF Graphs. An RDF Graph represents triples in Resource Description Format of semantic web. So the identification and…
We show that an interesting class of feed-forward neural networks can be understood as quantitative argumentation frameworks. This connection creates a bridge between research in Formal Argumentation and Machine Learning. We generalize the…
This paper introduces a novel approach to learn visually grounded meaning representations of words as low-dimensional node embeddings on an underlying graph hierarchy. The lower level of the hierarchy models modality-specific word…
In recent years, there has been a resurgence in methods that use distributed (neural) representations to represent and reason about semantic knowledge for robotics applications. However, while robots often observe previously unknown…
Understanding the road genome is essential to realize autonomous driving. This highly intelligent problem contains two aspects - the connection relationship of lanes, and the assignment relationship between lanes and traffic elements, where…