CGs to FCA Including Peirce's Cuts

CGs to FCA Including Peirce's Cuts

Simon Polovina (Conceptual Structures Research Group, Sheffield Hallam University, Sheffield, UK) and Simon Andrews (Conceptual Structures Research Group, Sheffield Hallam University, Sheffield, UK)
DOI: 10.4018/ijcssa.2013010105
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Abstract

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.
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A Financial Trading Example

The case study is about a Financial Trading (FT) enterprise called TechRules Advisors (TRA Inc.), a fictitious asset management firm (© Said Tabet and Gerd Wagner). The firm buys and sells numbers of shares of securities and manages its clients' assets. Portfolio managers create and manage accounts. As in the previous work, a CGs Transaction Model (or 'Transaction Graph') illustration is used (Andrews & Polovina, 2011; Launders, 2011a; Polovina & Andrews, 2011). However unlike its simple case study scenario (namely a university's community objectives), the FT case study includes business rules visualised through Peirce's cuts. The detail of the case study is described as follows.

Description of the Case Study

The company (TRA Inc.) buys and sells shares of securities and manages its clients' assets. Portfolio managers create and manage accounts. A portfolio is owned by a legal entity. The portfolio is managed by a portfolio manager who works for an investment firm. A portfolio is described by a creation date and a value. It has a number of positions. Each position holds an asset and is described by a quantity and an acquisition date. The value of a portfolio is the total value of all the securities held in the portfolio.

There are three different categories of assets: real estate, cash, and securities. Real estate and cash are described by a name. Securities are described by: a security ID, a name and a price. There are three categories of securities: options, bonds, and stocks. Securities are issued by a legal entity that is called an issuer. The issuer can be: a company, a municipality, an agency, or a government.

There are many reasons that motivate issuers to issue securities. For example, the issuer might need to repay debts or raise capital (get some money to invest). Issuers and the securities they have issued can be positively or negatively affected by market events. Market events could be upgrades or downgrades by credit rating agencies. Some issuers are classified as `restricted' by portfolio owners and investment firms. Orders (for buying or selling assets) are placed in the interest of a portfolio. An order is placed by a trader or by a portfolio manager.

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