CGs to FCA Including Peirce's Cuts

Previous work has demonstrated a straightforward mapping from Conceptual Graphs (CGs) to Formal Concept Analysis (FCA), and the combined benefits these types of Conceptual Structures bring in capturing and reasoning about the semantics in system design. As in that work, a CGs Transaction Model (or `Transaction Graph') exemplar is used, but in the form of a richer Financial Trading (FT) case study that has its business rules visualised in Peirce's cuts. The FT case study highlights that cuts can meaningfully be included in the CGs to FCA mapping. Accordingly, the case study's CGs Transaction Graph with its cuts is translated into a form suitable for the CGtoFCA algorithm described in that previous work. The process is tested through the CG-FCA software that implements the CGtoFCA algorithm. The algorithm describes how a Conceptual Graph (CG), represented by triples of the form source-concept, relation, target-concept can be transformed into a set of binary relations of the form target-concept, source-conceptnrelation thus creating a formal context in FCA. Cuts though can now be included in the same formal, rigorous, reproducible and general way. The mapping develops the Transaction Graph into a Transaction Concept, capturing and unifying the features of Conceptual Structures that CGs and FCA collectively embody

Evaluating the transaction graph through a financial trading case study

The Transaction Graph is argued as leading to a better understanding of the concepts and relations in enterprise transactions and their semantics with business rules. This design process begins with an analysis of case study narrative through the Transactional Use-Case, using a Financial Trading case study in this evaluation. The lexicon or dictionary of words and their underlying concepts are explored in order to model transactions. Peirce logic (i.e. Peirce’s visual Extential Graphs as extended by Sowa and Heaton) is then applied to the business rules to visualise the inferences in Conceptual Graphs and therefore any further possible Transaction Graph refinements. Model automation provides validation checking removing errors in semantics and syntactics. The paper demonstrates the reuse and refinement of a generic Transaction Model highlighting inference and logical operations with business rules. Additionally the paper demonstrates the reuse of the automated Transaction Model’s ontology coupled with its conceptual catalogue