scholarly journals CGs to FCA Including Peirce's Cuts

2013 ◽  
Vol 1 (1) ◽  
pp. 90-103
Author(s):  
Simon Polovina ◽  
Simon Andrews
Keyword(s):  
Formal Context ◽  
Formal Concept ◽  
Conceptual Graphs ◽  
Target Concept ◽  
Binary Relations ◽  
Financial Trading ◽  
Transaction Model ◽  
Conceptual Structures ◽  
Conceptual Graph

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.

scholarly journals Active Semantic Relations in Layered Enterprise Architecture Development

2021 ◽  
pp. 3-16
Author(s):  
Matt Baxter ◽  
Simon Polovina ◽  
Wim Laurier ◽  
Mark von Rosing
Keyword(s):  
Directed Graph ◽  
Enterprise Architecture ◽  
Directed Graphs ◽  
Building Blocks ◽  
Semantic Relations ◽  
Formal Concept ◽  
General Applicability ◽  
Conceptual Graph ◽  
Architecture Development

AbstractEnterprise Architecture (EA) metamodels align an organisation’s business, information and technology resources so that these assets best meet the organisation’s purpose. The Layered EA Development (LEAD) Ontology enhances EA practices by a metamodel with layered metaobjects as its building blocks interconnected by semantic relations. Each metaobject connects to another metaobject by two semantic relations in opposing directions, thus highlighting how each metaobject views other metaobjects from its perspective. While the resulting two directed graphs reveal all the multiple pathways in the metamodel, more desirable would be to have one directed graph that focusses on the dependencies in the pathways. Towards this aim, using CG-FCA (where CG refers to Conceptual Graph and FCA to Formal Concept Analysis) and a LEAD case study, we determine an algorithm that elicits the active as opposed to the passive semantic relations between the metaobjects resulting in one directed graph metamodel. We also identified the general applicability of our algorithm to any metamodel that consists of triples of objects with active and passive relations.

scholarly journals Three-Way Concept Analysis for Incomplete Formal Contexts

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Huilai Zhi ◽  
Hao Chao
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Binary Relations ◽  
Formal Concepts ◽  
Target Set ◽  
The Relationship ◽  
Negative Attributes

Recently, incomplete formal contexts have received more and more attention from the communities of formal concept analysis. Different from a complete context where the binary relations between all the objects and attribute are known, an incomplete formal context has at least a pair of object and attribute with a completely unknown binary relation. Partially known formal concepts use interval sets to indicate the incompleteness. Three-way formal concept analysis is capable of characterizing a target set by combining positive and negative attributes. However, how to describe target set, by pointing out what attributes it has with certainty and what attributes it has with possibility and what attributes it does not has with certainty and what attributes it does not has with possibility, is still an open problem. This paper combines the ideas of three-way formal concept analysis and partially known formal concepts and presents a framework of approximate three-way concept analysis. At first, approximate object-induced and attribute-induced three-way concept lattices are introduced, respectively. And then, the relationship between approximate three-way concept lattice and classical three-way concept lattice are investigated. Finally, examples are presented to demonstrate and verify the obtained results.

Capturing the Context of Concepts using the Transaction Graph through a Mobile NHS Case Study

2016 ◽  
Vol 4 (1) ◽  
pp. 35-47
Author(s):  
Ivan Launders
Keyword(s):  
Patient Record ◽  
Conceptual Graphs ◽  
Cost Of Treatment ◽  
Health Treatment ◽  
Business Context ◽  
Transaction Model ◽  
Economic Event ◽  
Medical Context ◽  
The Cost

This paper reports the use of Conceptual Graphs and Peirce Logic by enterprise architects, who need to capture conceptual context represented in business terms, which differ conceptually from the same terms used in the medical context. For example, in a UK Mobile NHS case study the medical context drug-drug refers to interactions in a health treatment regime of two or more drugs, where the effects of one drug on another can be increased or decreased, or can produce a new effect that neither produces alone. In a business context drug-drug refers to an economic event and resource impact alert in a patient record database that suggests a new or replacement drug that changes the cost of treatment. The paper explains how TrAM automation can capture typical (canonical) use, focused on economic events and associated resource impacts, and can provide exploration of the Resource, Events, and Agents of the Transaction Model through use of Transaction Graph ontology.

scholarly journals Modularising the Complex Meta-Models in Enterprise Systems Using Conceptual Structures

2018 ◽  
pp. 261-283 ◽  
Author(s):  
Simon Polovina ◽  
Hans-Jurgen Scheruhn ◽  
Mark von Rosing
Keyword(s):  
Information Processing ◽  
Formal Concept Analysis ◽  
Enterprise Architecture ◽  
Enterprise Systems ◽  
Concept Analysis ◽  
Formal Concept ◽  
Conceptual Graphs ◽  
Enterprise Information ◽  
Meta Model ◽  
Conceptual Structures

The development of meta-models in Enterprise Modelling, Enterprise Engineering, and Enterprise Architecture enables an enterprise to add value and meet its obligations to its stakeholders. This value is however undermined by the complexity in the meta-models which have become difficult to visualise thus deterring the human-driven process. These experiences have driven the development of layers and levels in the modular meta-model. Conceptual Structures (CS), described as “Information Processing in Mind and Machine”, align the way computers work with how humans think. Using the Enterprise Information Meta-model Architecture (EIMA) as an exemplar, two forms of CS known as Conceptual Graphs (CGs) and Formal Concept Analysis (FCA) are brought together through the CGtoFCA algorithm, thereby mathematically evaluating the effectiveness of the layers and levels in these meta-models. The work reveals the useful contribution that this approach brings in actualising the modularising of complex meta-models in enterprise systems using conceptual structures.

A FORMALISM FOR REPRESENTING AND REASONING WITH LINGUISTIC INFORMATION

2002 ◽  
Vol 10 (03) ◽  
pp. 281-307 ◽  
Author(s):  
TRU H. CAO
Keyword(s):  
Artificial Intelligence ◽  
Fuzzy Logic ◽  
Natural Language ◽  
Functional Relation ◽  
Computing With Words ◽  
Conceptual Graphs ◽  
Graph Language ◽  
Conceptual Graph ◽  
Knowledge Representation Language ◽  
Representation Language

Conceptual graphs and fuzzy logic are two logical formalisms that emphasize the target of natural language, where conceptual graphs provide a structure of formulas close to that of natural language sentences while fuzzy logic provides a methodology for computing with words. This paper proposes fuzzy conceptual graphs as a knowledge representation language that combines the advantages of both the two formalisms for artificial intelligence approaching human expression and reasoning. Firstly, the conceptual graph language is extended with functional relation types for representing functional dependency, and conjunctive types for joining concepts and relations. Then fuzzy conceptual graphs are formulated as a generalization of conceptual graphs where fuzzy types and fuzzy attribute-values are used in place of crisp types and crisp attribute-values. Projection and join as basic operations for reasoning on fuzzy conceptual graphs are defined, taking into account the semantics of fuzzy set-based values.

scholarly journals Continuous Domains in Formal Concept Analysis*

2021 ◽  
Vol 179 (3) ◽  
pp. 295-319
Author(s):  
Longchun Wang ◽  
Lankun Guo ◽  
Qingguo Li
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Continuous Functions ◽  
Formal Context ◽  
Formal Concept ◽  
Contractive Mappings ◽  
Continuous Domains ◽  
Algebraic Domains ◽  
Scott Continuous ◽  
Continuous Domain

Formal Concept Analysis (FCA) has been proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notion of contractive mappings over formal contexts is proposed, which can be viewed as a generalization of interior operators on sets into the framework of FCA. Then, by considering subset-selections consistent with contractive mappings, the notions of attribute continuous formal contexts and continuous concepts are introduced. It is shown that the set of continuous concepts of an attribute continuous formal context forms a continuous domain, and every continuous domain can be restructured in this way. Moreover, the notion of F-morphisms is identified to produce a category equivalent to that of continuous domains with Scott continuous functions. The paper also investigates the representations of various subclasses of continuous domains including algebraic domains and stably continuous semilattices.

scholarly journals A Web Page Clustering Method Based on Formal Concept Analysis

Information ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 228 ◽  
Author(s):  
Zuping Zhang ◽  
Jing Zhao ◽  
Xiping Yan
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Web Pages ◽  
Web Page ◽  
Data Links ◽  
Web Page Clustering ◽  
The Web

Web page clustering is an important technology for sorting network resources. By extraction and clustering based on the similarity of the Web page, a large amount of information on a Web page can be organized effectively. In this paper, after describing the extraction of Web feature words, calculation methods for the weighting of feature words are studied deeply. Taking Web pages as objects and Web feature words as attributes, a formal context is constructed for using formal concept analysis. An algorithm for constructing a concept lattice based on cross data links was proposed and was successfully applied. This method can be used to cluster the Web pages using the concept lattice hierarchy. Experimental results indicate that the proposed algorithm is better than previous competitors with regard to time consumption and the clustering effect.

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