Formal concept analysis over graphs and hypergraphs (original) (raw)

Conceptual graphs and formal concept analysis

Conceptual structures: Fulfilling Peirce's dream, 1997

Analysis may be combined to obtain a formalization of Elementary Logic which is useful for knowledge representation and processing. For this, a translation of conceptual graphs to formal contexts and concept lattices is described through an example. Using a suitable mathematization of conceptual graphs, basics of a uni ed mathematical theory for Elementary Logic are proposed.

Formal Concept Analysis – Overview and Applications

Procedia Engineering, 2014

In this article we give a brief overview of the theory behind the formal concept analysis, a novel method for data representation and analysis. From given tabular input data this method finds all formal concepts and computes a concept lattice, a directed, acyclic graph, in which all formal concepts are hierarchically ordered. We describe the link between this method and formal logic, as well as graph theory. Finally we present one example of an application of this method in the field of computer aided learning.

1 2 O ct 2 01 8 Formal Concept Analysis with Many-sorted Attributes

This paper unites two problem-solving traditions in computer science: (1) constraint-based reasoning; and (2) formal concept analysis. For basic definitions and properties of networks of constraints, we follow the foundational approach of Montanari and Rossi [3]. This paper advocates distributed relations as a more semantic version of networks of constraints. The theory developed here uses the theory of formal concept analysis, pioneered by Rudolf Wille and his colleagues [5], as a key for unlocking the hidden semantic structure within distributed relations. Conversely, this paper offers distributed relations as a seamless manysorted extension to the formal contexts of formal concept analysis. Some of the intuitions underlying our approach were discussed in a preliminary fashion by Freuder and Wallace [1].

On the connection of hypergraph theory with formal concept analysis and rough set theory

Information Sciences, 2015

We present a unique framework for connecting different topics: hypergraphs from one side and Formal Concept Analysis and Rough Set Theory from the other. This is done through the formal equivalence among Boolean information tables, formal contexts and hypergraphs. Links with generic (i.e., not Boolean) information tables are established, through so-called nominal scaling. The particular case of k-uniform complete hypergraphs will then be studied. In this framework, we are able to solve typical problems of Rough Set Theory and Formal Concept Analysis using combinatorial techniques. More in detail, we will give a formula to compute the degree of dependency and the partial implication between two sets of attributes, compute the set of reducts and define the structure of the partitions generated by all the definable indiscernibility relations.

Towards a theory of formal classification

2005

Classifications have been used for centuries with the goal of cataloguing and searching large sets of objects. In the early days it was mainly books; lately it has become Web pages, pictures and any kind of electronic information items. Classifications describe their contents using natural language labels, an approach which has proved very effective in manual classification. However natural language labels show their limitations when one tries to automate the process, as they make it almost impossible to reason about classifications and their contents. In this paper we introduce the novel notion of Formal Classification, as a graph structure where labels are written in a logical concept language. The main property of Formal Classifications is that each node can be associated a normal form formula which univocally describes its contents. This in turn allows us to reduce document classification and query answering to fully automatic propositional reasoning.

Acquisition And Structuring Of An Ontology Within Conceptual Graphs

1994

The elicitation of the ontology i.e. the objects of a domain is a key issue of conceptual modelling and therefore of knowledge acquisition. The Conceptual Graph Theory provides a knowledge representation formalism to be used in knowledgebased systems with an explicit type lattice" to account for the ontology. Since knowledge is in most AI applications non formal, it has to be normalized to ensure that the formal exploitation of its representation conforms to its meaning in the domain. Noting the intensional nature of types, which re ect the essences of the objects they denote, this normalization relies on a commitment o n t ype de nitions by necessary and su cient conditions at the knowledge level. Our claim is that the taxonomic structure that accounts for the intensional nature of the ontology can be nothing but a tree, precluding tangled taxonomies. From this starting point, we derive methodological principles to constrain the acquisition of the type tree", thus helping in the design of a domain ontology. These principles are currently applied to acquire the ontology and related knowledge in the context of the knowledgebased part of Menelas, a natural language understanding project in the medical domain, which uses Conceptual Graphs as its core formalism.

A Parallel between Extended Formal Concept Analysis and Bipartite Graphs Analysis

Lecture Notes in Computer Science, 2010

The paper offers a parallel between two approaches to conceptual clustering, namely formal concept analysis (augmented with the introduction of new operators) and bipartite graph analysis. It is shown that a formal concept (as defined in formal concept analysis) corresponds to the idea of a maximal bi-clique, while a "conceptual world" (defined through a Galois connection associated of the new operators) is a disconnected sub-graph in a bipartite graph. The parallel between formal concept analysis and bipartite graph analysis is further exploited by considering "approximation" methods on both sides. It leads to suggests new ideas for providing simplified views of datasets.

Formal concept analysis with many-sorted attributes

Proceedings of ICCI'93: 5th International Conference on Computing and Information, 1993

This paper unites two problem-solving traditions in computer science: (1) constraint-based reasoning; and (2) formal concept analysis. For basic definitions and properties of networks of constraints, we follow the foundational approach of Montanari and Rossi [3]. This paper advocates distributed relations as a more semantic version of networks of constraints. The theory developed here uses the theory of formal concept analysis, pioneered by Rudolf Wille and his colleagues [5], as a key for unlocking the hidden semantic structure within distributed relations. Conversely, this paper offers distributed relations as a seamless manysorted extension to the formal contexts of formal concept analysis. Some of the intuitions underlying our approach were discussed in a preliminary fashion by Freuder and Wallace [1].

Symbolic Objects in Formal Concept Analysis

. Symbolic objects are the basic elements for knowledge representation in symbolic data analysis. This paper aims to integrate symbolic objects into formal concept analysis in order to compare and tie together both approaches. 1 Introduction Symbolic objects are the basic elements of a formal language which has been developed since 1987 in symbolic data analysis. The general aim was to extend the field of application, methods and algorithms of classic data analysis to more complex data. Meanwhile, the formalism of symbolic objects is not only used in a broad field of data analysis, but also in knowledge representation and knowledge processing. From the point of view of formal concept analysis, the most interesting parts of symbolic data analysis are those which are concerned with knowledge processing and conceptual classifications. These parts of symbolic data analysis and formal concept analysis both emphasize the intensional view. Hence, there are various points of common interest...