Related papers: When Only Topology Matters
Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…
Software engineers typically interpret the domain description in natural language and translate it into a conceptual model. Three approaches are used in this domain modeling: textual languages, diagrammatic languages, and a mixed based of…
Topological quantum field theories (TQFTs) are symmetric monoidal functors out of cobordism categories. In dimension two, oriented TQFTs are famously classified by commutative Frobenius algebras. In the unoriented setting, the…
The complicated syntax structure of natural language is hard to be explicitly modeled by sequence-based models. Graph is a natural structure to describe the complicated relation between tokens. The recent advance in Graph Neural Networks…
Many formal languages have been proposed to express or represent Ontologies, including RDF, RDFS, DAML+OIL and OWL. Most of these languages are based on XML syntax, but with various terminologies and expressiveness. Therefore, choosing a…
It has recently been recognized by the author that the quantum contextuality paradigm may be formulated in terms of the properties of some subgroups of the two-letter free group $G$ and their corresponding point-line incidence geometry…
The theory uses methods and language of linear algebra to study nonlinear spaces. These techniques can be used particularly to describe analytic geometry of non-linear elliptic, hyperbolic, De Sitter and Anti de Sitter spaces. The main…
Topic modeling seems to be almost synonymous with generating lists of top words to represent topics within large text corpora. However, deducing a topic from such list of individual terms can require substantial expertise and experience,…
We study the problem of fitting ontologies and constraints to positive and negative examples that take the form of a finite relational structure. As ontology and constraint languages, we consider the description logics $\mathcal{E\mkern-2mu…
OWL (Web Ontology Language) ontologies which are able to formally represent complex knowledge and support semantic reasoning have been widely adopted across various domains such as healthcare and bioinformatics. Recently, ontology…
This paper introduces GraphOmni, a comprehensive benchmark designed to evaluate the reasoning capabilities of LLMs on graph-theoretic tasks articulated in natural language. GraphOmni encompasses diverse graph types, serialization formats,…
In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…
In this paper, we introduce the problem of rewriting finite formal languages using syntactic macros such that the rewriting is minimal in size. We present polynomial-time algorithms to solve variants of this problem and show their…
Formal/symbolic semantics can provide canonical, rigid controllability and interpretability to sentence representations due to their \textit{localisation} or \textit{composition} property. How can we deliver such property to the current…
Lettericity is a graph parameter responsible for many attractive structural properties. In particular, graphs of bounded lettericity have bounded linear clique-width and they are well-quasi-ordered by induced subgraphs. The latter property…
Topological gravity is the reduction of general relativity to flat space-times. A lattice model describing topological gravity is developed starting from a Hamiltonian lattice version of $B\w F$ theory. The extra symmetries not present in…
A new model of symbol grounding is presented, in which the structures of natural language, logical semantics, perception and action are represented categorically, and symbol grounding is modeled via the composition of morphisms between the…
We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bracket wires make the structure of the internal hom functor…
Matrix Graph Grammars (MGG) is a novel approach to the study of graph dynamics ([15]). In the present contribution we look at MGG as a formal grammar and as a model of computation, which is a necessary step in the more ambitious program of…
We show that the cyclic and epicyclic categories which play a key role in the encoding of cyclic homology and the lambda operations, are obtained from projective geometry in characteristic one over the infinite semifield F of "max-plus…