Measuring Relations Between Concepts In Conceptual Spaces

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. Our recent mathematical formalization of this framework is capable of representing correlations between different domains in a geometric way. In this paper, we extend our formalization by providing quantitative mathematical definitions for the notions of concept size, subsethood, implication, similarity, and betweenness. This considerably increases the representational power of our formalization by introducing measurable ways of describing relations between concepts.Comment: Accepted at SGAI 2017 (http://www.bcs-sgai.org/ai2017/). The final publication is available at Springer via https://doi.org/10.1007/978-3-319-71078-5_7. arXiv admin note: substantial text overlap with arXiv:1707.05165, arXiv:1706.0636

Formalized Conceptual Spaces with a Geometric Representation of Correlations

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a similarity space and concepts are represented by convex regions in this space. After pointing out a problem with the convexity requirement, we propose a formalization of conceptual spaces based on fuzzy star-shaped sets. Our formalization uses a parametric definition of concepts and extends the original framework by adding means to represent correlations between different domains in a geometric way. Moreover, we define various operations for our formalization, both for creating new concepts from old ones and for measuring relations between concepts. We present an illustrative toy-example and sketch a research project on concept formation that is based on both our formalization and its implementation.Comment: Published in the edited volume "Conceptual Spaces: Elaborations and Applications". arXiv admin note: text overlap with arXiv:1706.06366, arXiv:1707.02292, arXiv:1707.0516

Bridging between sensor measurements and symbolic ontologies through conceptual spaces

The increasing availability of sensor data through a variety of sensor-driven devices raises the need to exploit the data observed by sensors with the help of formally specified knowledge representations, such as the ones provided by the Semantic Web. In order to facilitate such a Semantic Sensor Web, the challenge is to bridge between symbolic knowledge representations and the measured data collected by sensors. In particular, one needs to map a given set of arbitrary sensor data to a particular set of symbolic knowledge representations, e.g. ontology instances. This task is particularly challenging due to the potential infinite variety of possible sensor measurements. Conceptual Spaces (CS) provide a means to represent knowledge in geometrical vector spaces in order to enable computation of similarities between knowledge entities by means of distance metrics. We propose an ontology for CS which allows to refine symbolic concepts as CS and to ground instances to so-called prototypical members described by vectors. By computing similarities in terms of spatial distances between a given set of sensor measurements and a finite set of prototypical members, the most similar instance can be identified. In that, we provide a means to bridge between the real-world as observed by sensors and symbolic representations. We also propose an initial implementation utilizing our approach for measurement-based Semantic Web Service discovery

Blending the physical and the digital through conceptual spaces

The rise of the Internet facilitates an ever increasing growth of virtual, i.e. digital spaces which co-exist with the physical environment, i.e. the physical space. In that, the question arises, how physical and digital space can interact synchronously. While sensors provide a means to continuously observe the physical space, several issues arise with respect to mapping sensor data streams to digital spaces, for instance, structured linked data, formally represented through symbolic Semantic Web (SW) standards such as OWL or RDF. The challenge is to bridge between symbolic knowledge representations and the measured data collected by sensors. In particular, one needs to map a given set of arbitrary sensor data to a particular set of symbolic knowledge representations, e.g. ontology instances. This task is particularly challenging due to the vast variety of possible sensor measurements. Conceptual Spaces (CS) provide a means to represent knowledge in geometrical vector spaces in order to enable computation of similarities between knowledge entities by means of distance metrics. We propose an approach which allows to refine symbolic concepts as CS and to ground ontology instances to so-called prototypical members which are vectors in the CS. By computing similarities in terms of spatial distances between a given set of sensor measurements and a finite set of CS members, the most similar instance can be identified. In that, we provide a means to bridge between the physical space, as observed by sensors, and the digital space made up of symbolic representations

Exploiting conceptual spaces for ontology integration

The widespread use of ontologies raises the need to integrate distinct conceptualisations. Whereas the symbolic approach of established representation standards – based on first-order logic (FOL) and syllogistic reasoning – does not implicitly represent semantic similarities, ontology mapping addresses this problem by aiming at establishing formal relations between a set of knowledge entities which represent the same or a similar meaning in distinct ontologies. However, manually or semi-automatically identifying similarity relationships is costly. Hence, we argue, that representational facilities are required which enable to implicitly represent similarities. Whereas Conceptual Spaces (CS) address similarity computation through the representation of concepts as vector spaces, CS rovide neither an implicit representational mechanism nor a means to represent arbitrary relations between concepts or instances. In order to overcome these issues, we propose a hybrid knowledge representation approach which extends FOL-based ontologies with a conceptual grounding through a set of CS-based representations. Consequently, semantic similarity between instances – represented as members in CS – is indicated by means of distance metrics. Hence, automatic similarity detection across distinct ontologies is supported in order to facilitate ontology integration

Two-fold Semantic Web service matchmaking – applying ontology mapping for service discovery

Semantic Web Services (SWS) aim at the automated discovery and orchestration of Web services on the basis of comprehensive, machine-interpretable semantic descriptions. Since SWS annotations usually are created by distinct SWS providers, semantic-level mediation, i.e. mediation between concurrent semantic representations, is a key requirement for SWS discovery. Since semantic-level mediation aims at enabling interoperability across heterogeneous semantic representations, it can be perceived as a particular instantiation of the ontology mapping problem. While recent SWS matchmakers usually rely on manual alignments or subscription to a common ontology, we propose a two-fold SWS matchmaking approach, consisting of (a) a general-purpose semantic-level mediator and (b) comparison and matchmaking of SWS capabilities. Our semantic-level mediation approach enables the implicit representation of similarities across distinct SWS by grounding service descriptions in so-called Mediation Spaces (MS). Given a set of SWS and their respective grounding, a SWS matchmaker automatically computes instance similarities across distinct SWS ontologies and matches the request to the most suitable SWS. A prototypical application illustrates our approach

Using latent-semantic analysis and network analysis for monitoring conceptual development

This paper describes and evaluates CONSPECT (from concept inspection), an application that analyses states in a learner’s conceptual development. It was designed to help online learners and their tutors monitor conceptual development and also to help reduce the workload of tutors monitoring a learner’s conceptual development. CONSPECT combines two technologies - Latent Semantic Analysis (LSA) and Network Analysis (NA) into a technique called Meaningful Interaction Analysis (MIA). LSA analyses the meaning in the textual digital traces left behind by learners in their learning journey; NA provides the analytic instrument to investigate (visually) the semantic structures identified by LSA. This paper describes the validation activities undertaken to show how well LSA matches first year medical students in 1) grouping similar concepts and 2) annotating text

What are natural concepts? A design perspective

Conceptual spaces have become an increasingly popular modeling tool in cognitive psychology. The core idea of the conceptual spaces approach is that concepts can be represented as regions in similarity spaces. While it is generally acknowledged that not every region in such a space represents a natural concept, it is still an open question what distinguishes those regions that represent natural concepts from those that do not. The central claim of this paper is that natural concepts are represented by the cells of an optimally designed similarity space