Quantitative Methods for Similarity in Description Logics

Description Logics (DLs) are a family of logic-based knowledge representation languages used to describe the knowledge of an application domain and reason about it in formally well-defined way. They allow users to describe the important notions and classes of the knowledge domain as concepts, which formalize the necessary and sufficient conditions for individual objects to belong to that concept. A variety of different DLs exist, differing in the set of properties one can use to express concepts, the so-called concept constructors, as well as the set of axioms available to describe the relations between concepts or individuals. However, all classical DLs have in common that they can only express exact knowledge, and correspondingly only allow exact inferences. Either we can infer that some individual belongs to a concept, or we can't, there is no in-between. In practice though, knowledge is rarely exact. Many definitions have their exceptions or are vaguely formulated in the first place, and people might not only be interested in exact answers, but also in alternatives that are "close enough". This thesis is aimed at tackling how to express that something "close enough", and how to integrate this notion into the formalism of Description Logics. To this end, we will use the notion of similarity and dissimilarity measures as a way to quantify how close exactly two concepts are. We will look at how useful measures can be defined in the context of DLs, and how they can be incorporated into the formal framework in order to generalize it. In particular, we will look closer at two applications of thus measures to DLs: Relaxed instance queries will incorporate a similarity measure in order to not just give the exact answer to some query, but all answers that are reasonably similar. Prototypical definitions on the other hand use a measure of dissimilarity or distance between concepts in order to allow the definitions of and reasoning with concepts that capture not just those individuals that satisfy exactly the stated properties, but also those that are "close enough"

Similarity Measures for Computing Relaxed Instances w.r.t. General EL-TBoxes

The notion of concept similarity is central to several ontology tasks and can be employed to realize relaxed versions of classical reasoning services. In this paper we investigate the reasoning service of answering instance queries in a relaxed fashion, where the query concept is relaxed by means of a concept similarity measure (CSM). To this end we investigate CSMs that assess the similarity of EL-concepts defined w.r.t. a general EL-TBox. We derive such a family of CSMs from a family of similarity measures for finite interpretations and show in both cases that the resulting measures enjoy a collection of formal properties. These properties allow us to devise an algorithm for computing relaxed instances w.r.t. general EL-TBoxes, where users can specify the „appropriate“ notion of similarity by instanciating our CSM appropriately

Relaxed lightweight assembly retrieval using vector space model

International audienceAssembly searching technologies are important for the improvement of design reusability. However, existing methods require that assemblies possess high-level information, and thus cannot be applied in lightweight assemblies. In this paper, we propose a novel relaxed lightweight assembly retrieval approach based on a vector space model (VSM). By decomposing the assemblies represented in a watertight polygon mesh into bags of parts, and considering the queries as a vague specification of a set of parts, the resilient ranking strategy in VSM is successfully applied in the assembly retrieval. Furthermore, we take the scale-sensitive similarities between parts into the evaluation of matching values, and extend the original VSM to a relaxed matching framework. This framework allows users to input any fuzzy queries, is capable of measuring the results quantitatively, and performs well in retrieving assemblies with specified characteristics. To accelerate the online matching procedure, a typical parts based matching process, as well as a greedy strategy based matching algorithm is presented and integrated in the framework, which makes our system achieve interactive performance. We demonstrate the efficiency and effectiveness of our approach through various experiments on the prototype system

Knowledge Base Population using Semantic Label Propagation

A crucial aspect of a knowledge base population system that extracts new facts from text corpora, is the generation of training data for its relation extractors. In this paper, we present a method that maximizes the effectiveness of newly trained relation extractors at a minimal annotation cost. Manual labeling can be significantly reduced by Distant Supervision, which is a method to construct training data automatically by aligning a large text corpus with an existing knowledge base of known facts. For example, all sentences mentioning both 'Barack Obama' and 'US' may serve as positive training instances for the relation born_in(subject,object). However, distant supervision typically results in a highly noisy training set: many training sentences do not really express the intended relation. We propose to combine distant supervision with minimal manual supervision in a technique called feature labeling, to eliminate noise from the large and noisy initial training set, resulting in a significant increase of precision. We further improve on this approach by introducing the Semantic Label Propagation method, which uses the similarity between low-dimensional representations of candidate training instances, to extend the training set in order to increase recall while maintaining high precision. Our proposed strategy for generating training data is studied and evaluated on an established test collection designed for knowledge base population tasks. The experimental results show that the Semantic Label Propagation strategy leads to substantial performance gains when compared to existing approaches, while requiring an almost negligible manual annotation effort.Comment: Submitted to Knowledge Based Systems, special issue on Knowledge Bases for Natural Language Processin

Approximation in Description Logics: How Weighted Tree Automata Can Help to Define the Required Concept Comparison Measures in FL₀

Recently introduced approaches for relaxed query answering, approximately defining concepts, and approximately solving unification problems in Description Logics have in common that they are based on the use of concept comparison measures together with a threshold construction. In this paper, we will briefly review these approaches, and then show how weighted automata working on infinite trees can be used to construct computable concept comparison measures for FL₀ that are equivalence invariant w.r.t. general TBoxes. This is a first step towards employing such measures in the mentioned approximation approaches.Accepted to LATA 201