Related papers: Formalizing Mathematical Knowledge as a Biform The…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
Graph transformation formalisms have proven to be suitable tools for the modelling of chemical reactions. They are well established in theoretical studies and increasingly also in practical applications in chemistry. The latter is made…
Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
A graph $G$ is defined encapsulating the number theoretic notion of the Fundamental Theorem of Arithmetic. We then provide a graph theoretic approach to the fundamental results on the coprimality of two natural numbers, through the use of…
The objective of knowledge graph embedding is to encode both entities and relations of knowledge graphs into continuous low-dimensional vector spaces. Previously, most works focused on symbolic representation of knowledge graph with…
Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this…
In this work, we present two results: The first result is the formalization of Tutte's theorem in Lean, a key theorem concerning matchings in graph theory. As this formalization is ready to be integrated in Lean's mathlib, it provides a…
Hypercomputational formal theories will, clearly, be both structurally and foundationally different from the formal theories underpinning computational theories. However, many of the maps that might guide us into this strange realm have…
The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…
Widespread use of the Internet and social networks invokes the generation of big data, which is proving to be useful in a number of applications. To deal with explosively growing amounts of data, data analytics has emerged as a critical…
We present a novel method that can learn a graph representation from multivariate data. In our representation, each node represents a cluster of data points and each edge represents the subset-superset relationship between clusters, which…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
Graphs have become the best way we know of representing knowledge. The computing community has investigated and developed the support for managing graphs by means of digital technology. Graph databases and knowledge graphs surface as the…
We report on implementing graph grammars for intelligence analysis in OCaml. Graph grammars are represented as elements of an algebraic data type in OCaml. In addition to algebraic data types, we use other concepts from functional…
Conceptual Graphs (CG) are a graph-based knowledge representation and reasoning formalism; fuzzy Conceptual Graphs (fCG) constitute an extension that enriches their expressiveness, exploiting the fuzzy set theory so as to relax their…
This paper describes a new technique, called "knowledge patterns", for helping construct axiom-rich, formal ontologies, based on identifying and explicitly representing recurring patterns of knowledge (theory schemata) in the ontology, and…
Human knowledge is made up of the conceptual structures of many communities of interest. In order to establish coherence in human knowledge representation, it is important to enable communication between the conceptual structures of…