Model-based Most Specific Concepts in Description Logics with Value Restrictions

Non-standard inferences are particularly useful in the bottom-up construction of ontologies in description logics. One of the more common non-standard reasoning tasks is the most specific concept (msc) for an ABox-individual. In this paper we present similar non-standard reasoning task: most specific concepts for models (model-mscs). We show that, although they look similar to ABox-mscs their computational behaviour can be different. We present constructions for model-mscs in FL₀ and FLE with cyclic TBoxes and for ALC∪∗ with acyclic TBoxes. Since subsumption in FLE with cyclic TBoxes has not been examined previously, we present a characterization of subsumption and give a construction for the least common subsumer in this setting

On the complexity of enumerating pseudo-intents

AbstractWe 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 minimal transversals of a given hypergraph. We introduce the notion of minimal pseudo-intents and show that recognizing minimal pseudo-intents is polynomial. Despite their less complicated nature, surprisingly it turns out that minimal pseudo-intents cannot be enumerated in output-polynomial time unless P=NP

Exploring finite models in the Description Logic ELgfp

In a previous ICFCA paper we have shown that, in the Description Logics EL and ELgfp, the set of general concept inclusions holding in a finite model always has a finite basis. In this paper, we address the problem of how to compute this basis efficiently, by adapting methods from formal concept analysis

Learning Formal Definitions for Snomed CT from Text

Snomed CT is a widely used medical ontology which is formally expressed in a fragment of the Description Logic EL++. The underlying logics allow for expressive querying, yet make it costly to maintain and extend the ontology. Existing approaches for ontology generation mostly focus on learning superclass or subclass relations and therefore fail to be used to generate Snomed CT definitions. In this paper, we present an approach for the extraction of Snomed CT definitions from natural language texts, based on the distance relation extraction approach. By benefiting from a relatively large amount of textual data for the medical domain and the rich content of Snomed CT, such an approach comes with the benefit that no manually labelled corpus is required. We also show that the type information for Snomed CT concept is an important feature to be examined for such a system. We test and evaluate the approach using two types of texts. Experimental results show that the proposed approach is promising to assist Snomed CT development

Expected Numbers of Proper Premises and Concept Intents

We compute the expected numbers of both formal concepts and proper premises in a formal context that is chosen uniformly at random among all formal contexts of given dimensions

A finite basis for the set of EL-implications holding in a finite model

Formal Concept Analysis (FCA) can be used to analyze data given in the form of a formal context. In particular, FCA provides efficient algorithms for computing a minimal basis of the implications holding in the context. In this paper, we extend classical FCA by considering data that are represented by relational structures rather than formal contexts, and by replacing atomic attributes by complex formulae defined in some logic. After generalizing some of the FCA theory to this more general form of contexts, we instantiate the general framework with attributes defined in the Description Logic (DL) EL, and with relational structures over a signature of unary and binary predicates, i.e., models for EL. In this setting, an implication corresponds to a so-called general concept inclusion axiom (GCI) in EL. The main technical result of this report is that, in EL, for any finite model there is a finite set of implications (GCIs) holding in this model from which all implications (GCIs) holding in the model follow

Learning Description Logic Knowledge Bases from Data Using Methods from Formal Concept Analysis

Description Logics (DLs) are a class of knowledge representation formalisms that can represent terminological and assertional knowledge using a well-defined semantics. Often, knowledge engineers are experts in their own fields, but not in logics, and require assistance in the process of ontology design. This thesis presents three methods that can extract terminological knowledge from existing data and thereby assist in the design process. They are based on similar formalisms from Formal Concept Analysis (FCA), in particular the Next-Closure Algorithm and Attribute-Exploration. The first of the three methods computes terminological knowledge from the data, without any expert interaction. The two other methods use expert interaction where a human expert can confirm each terminological axiom or refute it by providing a counterexample. These two methods differ only in the way counterexamples are provided

Axiomatization of General Concept Inclusions from Finite Interpretations

Description logic knowledge bases can be used to represent knowledge about a particular domain in a formal and unambiguous manner. Their practical relevance has been shown in many research areas, especially in biology and the semantic web. However, the tasks of constructing knowledge bases itself, often performed by human experts, is difficult, time-consuming and expensive. In particular the synthesis of terminological knowledge is a challenge every expert has to face. Because human experts cannot be omitted completely from the construction of knowledge bases, it would therefore be desirable to at least get some support from machines during this process. To this end, we shall investigate in this work an approach which shall allow us to extract terminological knowledge in the form of general concept inclusions from factual data, where the data is given in the form of vertex and edge labeled graphs. As such graphs appear naturally within the scope of the Semantic Web in the form of sets of RDF triples, the presented approach opens up the possibility to extract terminological knowledge from the Linked Open Data Cloud. We shall also present first experimental results showing that our approach has the potential to be useful for practical applications

Gödel Description Logics

In the last few years there has been a large effort for analysing the computational properties of reasoning in fuzzy Description Logics. This has led to a number of papers studying the complexity of these logics, depending on their chosen semantics. Surprisingly, despite being arguably the simplest form of fuzzy semantics, not much is known about the complexity of reasoning in fuzzy DLs w.r.t. witnessed models over the Gödel t-norm. We show that in the logic G-IALC, reasoning cannot be restricted to finitely valued models in general. Despite this negative result, we also show that all the standard reasoning problems can be solved in this logic in exponential time, matching the complexity of reasoning in classical ALC

Non-professional phagocytosis: a general feature of normal tissue cells

Non-professional phagocytosis by cancer cells has been described for decades. Recently, non-professional phagocytosis by normal tissue cells has been reported, which prompted us to take a closer look at this phenomenon. Non-professional phagocytosis was studied by staining cultured cells with live-cell staining dyes or by staining paraffin-embedded tissues by immunohistochemistry. Here, we report that each of 21 normal tissue cell lines from seven different organs was capable of phagocytosis, including ex vivo cell cultures examined before the 3rd passage as well as the primary and virus-transformed cell lines. We extended our analysis to an in vivo setting, and we found the occurrence of non-professional phagocytosis in healthy skin biopsies immediately after resection. Using dystrophin immunohistochemistry for membrane staining, human post-infarction myocardial tissue was assessed. We found prominent signs of non-professional phagocytosis at the transition zone of healthy and infarcted myocardia. Taken together, our findings suggest that non-professional phagocytosis is a general feature of normal tissue cells