Baris Sertkaya

Frankfurt University of Applied Sciences · Faculty of Computer Science and Engineering

We propose an approach based on Formal Concept Analysis (FCA) for computing stable extensions of Abstract Argumentation Frameworks (AFs). To this purpose, we represent an AF as a formal context in which stable extensions of the AF are closed sets called concept intents. We make use of algorithms developed in FCA for computing concept intents in ord...

In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large....

In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large....

In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large....

Lightweight description logics are knowledge representation formalisms characterised by the low complexity of their standard reasoning tasks. They have been successfully employed for constructing large ontologies that model domain knowledge in several different practical applications. In order to maintain these ontologies, it is often necessary to...

Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive Description Logics (DLs) whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to re-use concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend...

In this chapter we give a thorough overview over ontology learning approaches based on Formal Concept Analysis. By using information provided by a domain expert, our approaches learn the relationships between classes of the application domain and extend the ontology accordingly. We present basis for efficient and formally well-founded techniques an...

Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and obtained differ significantly between these two research areas. Despite these differences, there have been severa...

We intoduce the ELepHant reasoner, a consequence-based reasoner for the EL+ fragment of DLs. We present optimizations, implementation details and experimental results for classification of several large bio-medical knowledge bases.

Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and obtained differ significantly between these two research areas. Despite these differences, there have been severa...

We investigate whether the pseudo-intents of a given formal context can efficiently be enumerated. We show that they cannot be enumerated in a specified lexicographic order with polynomial delay unless P=NP. Furthermore we show that if the restriction on the order of enumeration is removed, then the problem becomes at least as hard as enumerating m...

We investigate possible improvements to the existing algo- rithm for classifying EL+ TBoxes.We present a modi�ed algorithm based on the well-known linear closure algorithm from relational databases. De- spite its better worst-case complexity, surprisingly it turns out that this algorithm does not perform well in practice. We discuss optimizations t...

Business Intelligence solutions provide different means like OLAP, data mining or case based reasoning to explore data. Standard BI means are usually based on mathematical statistics and provide a quanti- tative analysis of the data. In this paper, a qualitative approach based on a mathematical theory called "Formal Concept Analysis" (FCA) is used...

Classical Business Intelligence (BI) solutions provide different means like OLAP, data mining or case based reasoning to explore structured data. The data is usually stored in dedicated repositories like data warehouses and then explored by standard BI means, which are usually based on mathematical statistics and provide a quantitative analysis of...

In the present work we investigate the complexity of axiom pinpointing in the other family of tractable DLs, namely the DL-Lite family, which has been very popular due to its success in efficiently accessing large data and answering complex queries on this data. We investigate in detail the complexity of enumerating MinAs in a DL-Lite TBox for a gi...

We investigate the complexity of axiom pinpointing for different members of the DL-Lite family of Description Logics. More precisely, we consider the problem of enumerating all minimal subsets of a given DL-Lite knowledge base that have a given consequence. We show that for the DL-LiteHcore, DL-LiteHkrom and DL-LiteHNhorn fragments such minimal sub...

Pseudo-intents play a key rôle in Formal Concept Analysis. They are the premises of the implications in the Duquenne-Guigues Base, which is a minimum cardinality base for the set of implications that hold in a formal context. It has been shown that checking whether a set is a pseudo-intent is in conp. However, it is still open whether this problem...

Pseudo-intents play a key rôle in Formal Concept Analysis. They are the premises of the implications in the Duquenne-Guigues Base, which is a minimum cardinality base for the set of implications that hold in a formal context. It has been shown that checking whether a set is a pseudo-intent is in conp. However, it is still open whether this problem...

We describe OntoComP, a Protégé4 plugin that supports ontology engineers in completing OWL ontologies. More precisely, OntoComPsupports an ontology engineer in checking whether an ontology contains all the relevant information about the application domain, and in extending the ontology appropriately if this is not the case. It acquires complete kno...

We investigate the computational complexity of several decision, enumeration and counting problems related to pseudo-intents. We show that given a formal context and a subset of its set of pseudo-intents, checking whether this context has an additional pseudo-intent is in conp, and it is at least as hard as checking whether a given simple hypergrap...

We investigate the computational complexity of several decision, enumeration and counting problems related to pseudo-intents. We show that given a formal context and a subset of its set of pseudo-intents, checking whether this context has an additional pseudo-intent is in conp, and it is at least as hard as checking whether a given simple hypergrap...

In a previous paper, we have introduced an approach for extending both the terminological and the assertional part of a Description Logic knowledge base by using information provided by the assertional part and by a domain expert. This approach, called knowledge base completion, was based on an extension of attribute exploration to the case of part...

We investigate the complexity of several decision, enumera- tion and counting problems in axiom pinpointing in Description Logics. We prove hardness results that already hold for the propositional Horn fragment. We show that for this fragment, unless p = np, all minimal subsets of a given TBox that have a given consequence, i.e. MinAs, can- not be...

We describe OntoComP, a PROTE´GE´ 4 plugin that supports knowledge engineers in completing DL-based ontologies. More precisely, OntoComP supports a knowledge engineer in checking whether an ontology contains all the relevant information about the application domain, and in extending the ontology appropriately if this is not the case. It acquires co...

We investigate the computational complexity of some decision and counting problems related to generators of closed sets fundamental in Formal Concept Analysis. We recall results from the literature about the problem of checking the existence of a generator with a specified cardinality, and about the problem of determining the number of minimal gene...

Knowledge base completion is a method for extending both the terminological and assertional part of a Description Logic knowledge base by using information provided by a domain expert. It ensures that the extended knowledge base is complete w.r.t. a fixed interpretation in a certain, well-defined sense. Here we consider the problem of explaining us...

This work presents mainly two contributions to Description Logics (DLs) research by means of Formal Concept Analysis (FCA) methods: supporting bottom-up construction of DL knowledge bases, and completing DL knowledge bases. Its contribution to FCA research is on the computational complexity of computing generators of closed sets.

Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive Description Logics (DLs) whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to re-use concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend...

We propose an approach for extending both the terminological and the assertional part of a Description Logic knowledge base by using information provided by the assertional part and by a domain expert. The use of techniques from Formal Concept Analysis ensures that, on the one hand, the interaction with the expert is kept to a minimum, and, on the...

In a series of previous work, we have presented how attribute exploration can be used in the bottom-up construction of DL knowledge bases to compute a concept lattice that is isomorphic to the subsumption hierarchy of all conjunctions of concept names occurring in a knowledge base, and the negations of these concept names. This work is a con-tinuat...

This paper presents a machine-checked proof of the Basic Theorem on Concept Lattices, which appears in the book “Formal Concept Analysis” by Ganter and Wille, in the Isabelle/HOL Proof Assistant. As a by-product, the underlying lattice theory by Kammueller has been extended.

Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive Description Logics (DLs) whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to re-use concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend...

Given a finite set C : = { C1, ¼, Cn}\mathcal{C} := \{ C_1, \ldots, C_n\} of description logic concepts, we are interested in computing the subsumption hierarchy of all least common subsumers of subsets of C\mathcal{C} as well as the hierarchy of all conjunctions of subsets of C\mathcal{C}. These hierarchies can be used to support the bottom-up con...

Keywords: Formal concept analysis, Isabelle, Higher Order Logic, formalized mathematics. Thesis (M.S.)--Middle East Technical University, 2003.

Business Intelligence solutions provide different means like OLAP, data mining or case based reasoning to explore data. Standard BI means are usually based on mathematical statistics and provide a quantitative analysis of the data. In this paper, a qualitative approach based on a mathematical theory called ”Formal Concept Analysis” (FCA) is used in...

In our previous work we have developed a method for com-pleting a Description Logic knowledge base w.r.t. a fixed interpretation by asking questions to a domain expert. Our experiments showed that during this process the domain expert sometimes gives wrong answers to the questions, which cause the resultant knowledge base to have un-wanted conseque...