Exploring, Reasoning with and Validating Directed Graphs by Applying Formal Concept Analysis to Conceptual Graphs

Abstract

Although tools exist to aid practitioners in the construction of directed graphs typified by Conceptual Graphs (CGs), it is still quite possible for them to draw the wrong model, mistakenly or otherwise. In larger or more complex CGs it is furthermore often difficult-without close inspection-to see clearly the key features of the model. This paper thereby presents a formal method, based on the exploitation of CGs as directed graphs and the application of Formal Concept Analysis (FCA). FCA elucidates key features of CGs such as pathways and dependencies, inputs and outputs, cycles, and joins. The practitioner is consequently empowered in exploring, reasoning with and validating their real-world models. Exploring, Reasoning with and Validating Directed Graphs by Applying Formal Concept Analysis to Conceptual Graphs

Enhancing Layered Enterprise Architecture Development Through Conceptual Structures

“…3 Analysing the Meta-Model with CG-FCA CG-FCA brings to the meta-models the mathematical rigour of FCA [3,12]. A formal concept in FCA is the result of when certain conditions are met in a formal context:…”

“…The motivation for this approach will be elaborated as part of the related research discussion in subsection 5.2 of section 5 below. Whereas CG-FCA formerly converted Conceptual Graphs (CGs) only, it can now read 3-column CSV files thereby (primitively) allowing any form of ternary relations to benefit from CG-FCA [3].…”

“…Meta-Object, semantic relation, Meta-Object) and indirect (i.e. Meta-Object, semantic relation, ... 3 , semantic relation, Meta-Object). These pathways allow us to define a meta-object's view, which is the set of all metaobjects that can be associated with the meta-object defining the view through direct and indirect associations in a single direction (i.e.…”

Using Conceptual Structures in Enterprise Architecture to Develop a New Way of Thinking and Working for Organisations

“…A second form of conceptual structure known as Formal Concept Analysis (FCA) which is used in information science [5]. FCA provides an objective mathematical interpretation of CGs' logical but subjective human interpretations and is brought to bear through the CGtoFCA algorithm [1]. A Formal Concept in FCA is the result of when certain conditions are met in a formal context:…”

“…Manual inspection of the CG makes identifying these much harder, especially for the much more comprehensive meta-models encountered in practice than the simple illustration given in Table 1. And we haven't accounted for discovering and rectifying errors in drawing the CGs, such as the arrows in the CGs pointing in the wrong direction or mistyped concepts as simple examples from other work have demonstrated [1,4].…”