Knowledge representation through graphs

Due to the increasing amount of data, knowledge aggregation, representation and reasoning are highly important for companies. In this paper, knowledge aggregation is presented as the first step. In the sequel, successful knowledge representation, for instance through graphs, enables knowledge-based reasoning. There exist various forms of knowledge representation through graphs; some of which allow to handle uncertainty and imprecision by invoking the technology of fuzzy sets. The paper provides an overview of different types of graphs stressing their relationships and their essential features

GRAPH ISOMORPHISMS AND MATRIX SIMILARITY: SWITCHING BETWEEN REPRESENTATIONS

A proof whether two graphs (possibly oriented graphs or multigraphs, etc.) are isomorphic or not can be derived by various methods. Some of them are reasonable for small numbers of vertices and/or edges, but not for larger numbers. Switching from iconic representation to a matrix representation transforms the problem of Graph Theory into a problem in Linear Algebra. The support provided by a Computer Algebra System is analyzed, in particular with regard to the building of new mathematical knowledge through a transition from graphical to algebraic representation. Moreover two important issues are discussed: a. the need for more than one representation; b. the direction of the switch between representations, which is non standard, from graphical to algebraic

ProGS: Property Graph Shapes Language (Extended Version)

Property graphs constitute data models for representing knowledge graphs. They allow for the convenient representation of facts, including facts about facts, represented by triples in subject or object position of other triples. Knowledge graphs such as Wikidata are created by a diversity of contributors and a range of sources leaving them prone to two types of errors. The first type of error, falsity of facts, is addressed by property graphs through the representation of provenance and validity, making triples occur as first-order objects in subject position of metadata triples. The second type of error, violation of domain constraints, has not been addressed with regard to property graphs so far. In RDF representations, this error can be addressed by shape languages such as SHACL or ShEx, which allow for checking whether graphs are valid with respect to a set of domain constraints. Borrowing ideas from the syntax and semantics definitions of SHACL, we design a shape language for property graphs, ProGS, which allows for formulating shape constraints on property graphs including their specific constructs, such as edges with identities and key-value annotations to both nodes and edges. We define a formal semantics of ProGS, investigate the resulting complexity of validating property graphs against sets of ProGS shapes, compare with corresponding results for SHACL, and implement a prototypical validator that utilizes answer set programming