Jens Kötters

TU Dresden | TUD · Institut für Algebra

p>Conceptual scaling is a method, developed in the framework of Formal Concept Analysis (FCA), that transforms a many-valued context (a collection of objects, described by attributes with values, such as name, size or color) into a formal context (a binary schema from which formal concepts are derived). Relational scaling extends conceptual scaling...

p>Conceptual scaling is a method, developed in the framework of Formal Concept Analysis (FCA), that transforms a many-valued context (a collection of objects, described by attributes with values, such as name, size or color) into a formal context (a binary schema from which formal concepts are derived). Relational scaling extends conceptual scaling...

These are presentation slides. The article can be found at https://link.springer.com/book/10.1007/978-3-031-16663-1

The paper introduces orbital concept lattices, which enhance concept lattices of relational structures with a semigroup action that encodes projection, renaming and duplication operations on concept extents, and fuses them with their counterparts on concept intents (formalized by tableau queries). This strengthens the existing connections between t...

Orbital semilattices are introduced as bounded semilattices that are, in addition, equipped with an outer multiplication (a semigroup action) and diagonals (a concept borrowed from cylindric algebra), where each semilattice element has a certain domain. An example of an orbital semilattice is a table algebra, where the domain is the schema, the dia...

Previous work on concept graphs combining Formal Concept Analysis with Conceptual Graphs is revisited in this paper in the context of conjunctive database queries. The paper presents the conjunctive database query model as a special case of Ganter and Kuznetsov’s pattern structures, where patterns are considered as conjunctive queries. It further p...

FCA4AI presentation at IJCAI 2018 in Stockholm

In Formal Concept Analysis, a many-valued context is a collection of objects described by attributes that take on more than binary values, such as age (as integers or ranges of integer values) or color (a list or even a hierarchy of color combinations). Conceptual scaling is the process by which such a many-valued context is transformed into a form...

The concept lattice of an RDF graph is defined. The intents are described by graph patterns rather than sets of attributes, a view that is supported by the fact that RDF data is essentially a graph. A simple formalization by triple graphs defines pattern closures as connected components of graph products. The patterns correspond to conjunctive quer...

Conceptual patterns can be described by graphs, entailment by graph homomorphism. The mapping of a pattern to its set of instantiations, represented as a table, constitutes one half of a Galois connection. The join operation is the infimum in a complete lattice of tables, and a most descriptive pattern can be assigned to each table by means of a ca...

A Galois connection is stated between a knowledge base and queries over this knowledge. Queries are stated as conjunctions. Both the knowledge and queries are represented by certain graphs. This Galois connection gives rise to lattices of pattern concepts implicitly contained in the theory (all derivable facts) over the knowledge base. The formal f...

Conventional means of querying a database for relevant information require some degree of knowledge about the nature and the structural representation of such information. The paper addresses the case where sufficient knowledge is not readily available a priori. A method for data exploration based on the refinement of graphs, which represent summar...

The article introduces a representation of a formal context by an undirected graph called a context graph with the formal objects being the nodes of the graph. We use as a defining property for this graph that it contains every concept extent as a connected subgraph. The graph is not uniquely defined by this property — we focus on those graphs that...

A graph is called asymmetric if it has the identity mapping as its only automorphism. In [P. Erdõs, A. Rényi, Asymmetric Graphs, Acta Math. Acad. Sci. Hungar. 14 (1963) 295–315], P. Erdõs and A. Rényi have proven that almost all graphs are asymmetric. A graph is called rigid if it has the identity mapping as its only endomorphism, which is a strong...

A context graph of a one-valued context is a graph which has formal objects as its vertices, and whose edges connect the objects in such a way that concept extents form connected subgraphs of this graph. This allows to retrieve objects similar to a given object by a recursive traversal of that objects neighborhood. The approach has been introduced...