Introduction

Current and next generation wireless communication technologies will encourage widespread use of well-connected sensor-driven devices which in fact produce sensor data by observing and measuring real-world environments. This has already lead to standardisation efforts aiming at facilitating the so-called Sensor Web, such as the ones by the Sensor Web Enablement Working Group1 of the Open Geospatial Consortium (OGC) 2 . The increasing availability of sensor data raises the need to merge such data with formally specified knowledge representations, such as the ones provided by Semantic Web (SW) standards such as OWL [22] or RDF [23]. However, whereas sensor data usually relies on measurements of perceptual characteristics to describe real-world phenomena, ontological knowledge presentations represent realworld entities through symbols. The symbolic approach -i.e. describing symbols by using other symbols, without a grounding in perceptual dimensions of the real worldleads to the so-called symbol grounding problem [2] and does not entail meaningfulness, since meaning requires both the definition of a terminology in terms of a logical structure (using symbols) and grounding of symbols to a perceptual level [2] [13].

In that, in order to facilitate the vision of the Semantic Sensor Web (SSW) [18] the challenge is to bridge between formal symbolic knowledge representations and the measured data collected by sensors by mapping a given set of arbitrary sensor data to a particular set of symbolic representations. This task is particularly challenging due to the potential infinite variety of possible data sets.

Conceptual Spaces (CS) [8] follow a theory of describing knowledge in geometrical vector spaces which are described by so-called quality dimensions to bridge between the perceived and the symbolic world. Representing instances as vectors, i.e. members, in a CS provides a means to compute similarities by means of spatial distance metrics. However, several issues still have to be considered when applying CS. For instance, CS as well as sensor data provide no means to represent arbitrary relations between data sets, such as part-of relations.

In order to overcome the issues introduced above, we propose a two-fold knowledge representation approach which extends symbolic knowledge representations through a refinement based on CS. This is achieved based on an ontology which allows to refine symbolic concepts as CS and to ground instances to so-called prototypical members, i.e. prototypical vectors, in the CS. The resulting set of CS is formally represented as part of the ontology itself. By computing similarities in terms of spatial distances between a given set of sensor measurements and the finite set of prototypical members, the most similar instance can be identified. In that, our approach provides a means to bridge between the real-world -as measured by sensor data -and symbolic representations.

The remainder of the paper is organized as follows: Section 2 introduces the symbol grounding problem in the context of sensor data, while our representational approach based on CS is proposed in Section 3. In Section 4, we introduce an implementation of our approach based on an existing SWS reference model and we introduce first proof-of-concept prototype in Section 5. Finally, we discuss and conclude our work in Section 6.

Sensor Data, Symbol Grounding and Spatial Representations

This section motivates our approach by introducing the so-called symbol grounding problem in the context of the SSW and introduces some background knowledge on metric-based spatial knowledge representation.

Sensor Data and the Symbol Grounding Problem

Sensor data usually consists of measurements which describe observations of phenomena in real-world environments. In order to ensure a certain degree of interoperability between heterogeneous sensor data, recent efforts, such as the OpenGIS Observations and Measurements Encoding Standard (O&M) 3 , propose a standardized approach to represent observed measurements based on a common XML schema. However, in order to provide comprehensive applications capable of reasoning in real-time on observed real-world phenomena, i.e. the contextual knowledge produced by sensor-driven devices, one needs to bridge between the measurements provided by sensors and the formally specified knowledge as, for instance, exploited by the Semantic Web [18]. Figure 1 illustrates the desired progression from observed real-world phenomena, e.g. a certain color, to measurements provided by sensors, e.g. measurements of the hue, saturation and lightness (HSL) dimensions, to symbolic knowledge entities such as a particular OWL individual representing a specific color. However, whereas sensor data usually relies on measurements of perceptual characteristics to describe real-world phenomena, ontological knowledge presentations represent real-world entities through symbols what leads to a representational gap. Hence, several issues have to be taken into account. The symbolic approach -i.e. describing symbols by using other symbols, without a grounding in the real world or perceptual dimensions what is known as the symbol grounding problem [2] -of established SW representation standards, leads to ambiguity issues and does not entail meaningfulness, since meaning requires both the definition of a terminology in terms of a logical structure (using symbols) and grounding of symbols to a perceptual level [2] [13]. Moreover, describing the complex notion of any specific real-world entity in all its facets through symbolic representation languages is a costly task and may never reach semantic meaningfulness.

Hence, in order to facilitate the vision of the SSW, the challenge is, to map a given set of sensor observation data to semantic (symbolic) instances which most appropriately represent the observed real-world entity within an ontology. In this respect, it is particularly obstructive that a potentially infinite amount of real-world phenomena, i.e. measurement data, needs to be mapped to a finite set of knowledge representations, e.g. ontological concepts or instances.

Exploiting Measurements through spatial Knowledge Representations

Sensor data usually consists of sets of measurements being observed from the surrounding environment. In that, spatially oriented approaches to knowledge representation which exploit metrics to describe knowledge entities naturally appear to be an obvious choice when attempting to formally represent sensor data. Conceptual Spaces (CS) [8] follow a theory of describing entities in terms of their quality characteristics similar to natural human cognition in order to bridge between the perceived and the symbolic world. CS foresee the representation of concepts as multidimensional geometrical Vector Spaces which are defined through sets of quality dimensions. Instances are supposed to be represented as vectors, i.e. particular points in a CS. For instance, a particular color may be defined as point described by vectors measuring HSL or RGB dimensions. Describing instances as points within vector spaces where each vector follows a specific metric enables the automatic calculation of their semantic similarity by means of distance metrics such as the Euclidean, Taxicab or Manhattan distance [11] or the Minkowsky Metric [19]. Hence, semantic similarity is implicit information carried within a CS representation what is perceived as one of the major contribution of the CS theory. Soft Ontologies (SO) [10] follow a similar approach by representing a knowledge domain D through a multi-dimensional ontospace A, which is described by its so-called ontodimensions. An item I, i.e. an instance, is represented by scaling each dimension to express its impact, presence or probability in the case of I. In that, a SO can be perceived as a CS where dimensions are measured exclusively on a ratio-scale.

However, several issues have to be taken into account. For instance, CS as well as SO do not provide any notion to represent any arbitrary relations [17], such as part-of relations which usually are represented within symbolic knowledge models. Moreover, it can be argued, that representing an entire knowledge model through a coherent CS might not be feasible, particularly when attempting to maintain the meaningfulness of the spatial distance as a similarity measure. In this regard, it is even more obstructive that the scope of a dimension is not definable, i.e. a dimension always applies to the entire CS/SO [17].

Grounding Ontological Concepts in Conceptual Spaces

We propose the grounding of ontologies in multiple CS in order to bridge between the measurements provided by sensor-driven devices and symbolic representations of the SW.

Approach: Spatial Groundings for Symbolic Ontologies

We claim that CS represent a particularly promising model when being applied to individual concepts instead of representing an entire ontology in a single CS. By representing instances as so-called prototypical members in CS, arbitrary sensor-data can be associated with specific ontology instances in terms of the closest -i.e. the most similar -prototypical member representation.

We propose a two-fold representational approach -combining SW vocabularies with corresponding representations based on CS -to enable similarity-based matchmaking between a given set of sensor data and ontological representations. In that, we consider the representation of a set of n concepts C of an ontology O through a set of n Conceptual Spaces CS. Instances of concepts are represented as prototypical members in the respective CS. The following Figure 2 depicts this vision:

Instance I1j Instance I1i Concept C1x is-a refined-as-cs refined-as-prototypical-member refined-as-prototypical-member d1 d2 d3 is-a Ontology O1

Conceptual Space CS1x

Fig. 2. Representing ontology instances through prototypical members in CS.

While benefiting from implicit similarity information within a CS, our hybrid approach allows overcoming CS-related issues by maintaining the advantages of ontology-based knowledge representations and provides a means to ground knowledge entities to cognitive dimensions based on measurements. To give a rather obvious example, a concept describing the notion of a geospatial location could be grounded to a CS described through quality dimensions such as its longitude and latitude. In previous work [3][4], we provided more comprehensive examples, even for rather qualitative notions, such as particular subjects or learning styles.

Provided our refinement of ontology concepts as CS and of instances as prototypical members, a given set of sensor data which measures the quality dimensions of a particular CS i represents a vector v in CS i which can be mapped to an appropriate ontology instance I in terms of the spatial distance of the prototypical member of I and v. Figure 3 illustrates the approach based on the color example introduced in Section 2.1. While measurements obtained from sensors are well-suited to be represented as vectors, i.e. members, in a CS, we facilitate similarity-based computation between a given set of sensor data and sets of prototypical members which represent ontological instances. For instance, the example in Figure 3 depicts the utilisation of a CS based on the HSL dimensions to map between color measurements obtained through sensors and prototypical members representing certain color instances. Based on the spatial distance between one measured color vector and different prototypical members, the closest vector, i.e. the most similar one, can be identified. In that, CS provide a means to bridge between observed sensor data and symbolic ontological representations.

A formal Ontology to represent Conceptual Spaces

In order to be able to refine and represent ontological concepts through CS, we formalised the CS model into an ontology, currently being represented through OCML [12]. Hence, a CS can simply be instantiated in order to represent a particular concept.

Referring to [16][8], we formalise a CS as a vector space defined through quality dimensions d i of CS. Each dimension is associated with a certain metric scale, e.g. ratio, interval or ordinal scale. To reflect the impact of a specific quality dimension on the entire CS, we consider a prominence value p for each dimension. Therefore, a CS is defined by

( ) { } ℜ ∈ ∈ = i i n n n p CS d d p d p d p CS , ,..., , 2 2 1 1

where P is the set of real numbers. However, the usage context, purpose and domain of a particular CS strongly influence the ranking of its quality dimensions. This clearly supports our position of describing distinct CS explicitly for individual concepts. Please note that we do not distinguish between dimensions and domains [8] but enable dimensions to be detailed further in terms of subspaces. Hence, a dimension within one space may be defined through another CS by using further dimensions [16]. In this way, a CS may be composed of several subspaces and consequently, the description granularity can be refined gradually. Dimensions may be correlated. For instance, when describing an apple the quality dimension describing its sugar content may be correlated with the taste dimension. Information about correlation is expressed through axioms related to a specific quality dimension instance.

A particular (prototypical) member M -representing a particular instance -in the CS is described through valued dimension vectors v i :

( ) { } M v v v v M i n n ∈ = ,..., , 2

With respect to [16], we define the semantic similarity between two members of a space as a function of the Euclidean distance between the points representing each of the members. Hence, with respect to [16], given a CS definition CS and two members V and U, defined by vectors v 0 , v 1 , …,v n and u 1 , u 2 ,…,u n within CS, the distance between V and U can be calculated as:

∑ = − − − = n i v i u i i s v v s u u p v u dist 1 2 )) ( ) (( ) , (

where u is the mean of a dataset U and u s is the standard deviation from U. The formula above already considers the so-called Z-transformation or standardization [13] which facilitates the standardization of distinct measurement scales utilised by different quality dimensions in order to enable the calculation of distances in a multidimensional and multi-metric space. Please note, as mentioned in Section 2.2, different distance metrics could be applied depending on the nature and purpose of the CS.

Representing Ontologies through Conceptual Spaces

The derivation of an appropriate space CS i to represent a particular concept C i of a given ontology O is understood a non-trivial task which aims at the creation of a CS instance which most appropriately represents the real-world entity represented by C i . We particularly foresee a transformation procedure consisting of the following steps: which is aimed at instantiating all elements of a CS, such as dimensions and prominence values (S1 -S3). S1 aims at representing each concept property pc ij of C i as a particular dimension instance d ij together with a corresponding prominence p ij of a resulting space CS i :

( ) { } ( ) { } ℜ ∈ ∈ ⇒ ∈ ij i ij in in i i i i i ij in i i p CS d d p d p d p PC pc pc pc pc trans , ,..., , ,..., , : 2 2 1 1 2 1

Please note that we particularly distinguish between data type properties and relations. While the latter represent relations between concepts, these are not represented as dimensions since such dimensions would refer to a range of concepts (instances) instead of quantified metrics, as required by S2. Therefore, in the case of relations, we propose to maintain the relationships represented within the original ontology O without representing these within the resulting CS i . In that, the complexity of CS i is reduced to enable the maintainability of the spatial distance as appropriate similarity measure. The assignment of metric scales to dimensions (S2) which naturally are described using quantitative measurements, such as size or weight, is rather straightforward. In such cases, interval scale or ratio scale, could be used, whereas otherwise, a nominal scale might be required. S3 is aimed at assigning a prominence value p ij -chosen from a predefined value range -to each dimension d ij . Since the assignment of prominences to quality dimensions is of major importance for the expressiveness of the similarity measure within a CS, most probably this step requires incremental ex-post re-adjustments until a sufficient definition of a CS is achieved.

With respect to S4, one has to represent all instances I ki of a concept C i as member instances in the created space CS i :

ik ik M I trans ⇒ :

This is achieved by transforming all instantiated properties pi ikl of I ik as valued vectors in CS i .

( ) { } ( ) { } ik ikl ikn ik ik ik ikl ikn ik ik M v v v v PI pi pi pi pi trans ∈ ⇒ ∈

,..., , ,..., , :

2 1 2 1

Hence, given a particular CS, representing instances as members becomes just a matter of assigning specific measurements to the dimensions of the CS. In order to represent all concepts C i of a given ontology O, the transformation function consisting of the steps S1-S4 has to be repeated iteratively for all C i which are element of O. The accomplishment of the proposed procedure results in a set of CS instances which each refine a particular concept together with a set of member instances which each refine a particular instance. Please note that applying the procedure proposed here requires additional effort which needs to be further investigated within future work.

Implementation -Exploiting Sensor Data for Semantic Web Service Discovery

In previous work [3][4], we applied our two-fold approach to Semantic Web Services (SWS) technology [6] which aims at the automated discovery, orchestration and invocation of Web services based on comprehensive semantic annotations of services. Current results of SWS research are available in terms of reference models such as OWL-S [14], SAWSDL 4 or WSMO [24]. In [3][4], our CS representation was deployed to refine instances which are part of SWS annotations in order to enable interoperability between heterogeneous SWS and SWS requests. In contrast, here we propose the utilization of our CS-based representational approach to facilitate interoperability between observations and measurements provided by sensors and symbolic SWS representations based on extensions which are described in this section.

The representational model described above had been implemented by and aligned to established SWS technologies based on WSMO [24] and the Internet Reasoning Service IRS-III [1]. Further details on the IRS-III Service Ontology and its extension through our CS formalisation can be found in [5]. However, please note that in principle the representational approach described above could be applied to any SWS reference model and is particularly well-suited to support rather light-weight approaches such as SAWSDL or WSMO Lite [21].

In order to facilitate the representational approach described in Section 3, we aligned the CS Ontology (Section 3.2) with the IRS-III Service Ontology to allow for the refinement of individual concepts -used as part of formal SWS descriptions -as formally expressed CS. In that, instances being used to represent SWS characteristics such as interfaces or capabilities can be refined as vectors. Figure 4 depicts the core concepts of CSO and their alignment with the IRS-III Service Ontology. Concepts (instances) as being used by IRS service or goal descriptions are refined as CS (members) within the CSO. In that, following the procedure proposed in Section 3.3, service capabilities are refined in multiple CS. To take into account the representational gap between measurement data as provided by sensors and symbolic SWS goal representations, we introduced a novel way of requesting goal achievements through IRS-III. Instead of simply invoking a goal by providing the goal achievement request SWS i , including the actual input data, we also foresee the on-the-fly provisioning of underlying assumptions in terms of sets of measurements, i.e. vectors {V 1 , V 2 ,…, V n }, which in fact describe the actual contextual environment of the request.

In order to facilitate automated similarity computation between SWS and SWS requests, we extended the matchmaking capabilities of IRS-III through a set of additional functionalities: F1. Instantiation of member M i in CSO for each V i provided as part of SWS i F2. Similarity computation between goal request SWS i and potentially relevant SWS

Given the ontological refinement of SWS descriptions into CS as introduced in Section 3.2 this new functionality enables to automatically achieve IRS-III goals without being restricted to complete matches between a particular goal achievement request and the available SWS. When attempting to achieve a goal, our new function is provided with the actual goal request SWS i , named base, and the SWS descriptions of all x available services that are potentially relevant for the base -i.e. linked through a dedicated mediator:

} ,..., , { 2 1 x i SWS SWS SWS SWS ∪

Each SWS contains a set of concepts C={c 1 ..c m } and instances I={i 1 ..i n }. We first identify all members M(SWS i ) -in the form of valued vectors {v 1 ..v n } refining the instance i l of the base as proposed in Section 3.2. In addition, for each concept c within the base the corresponding conceptual space representations MS={MS 1 ..MS m } are retrieved. Similarly, for each SWS j related to the base, prototypical members M(SWS j ) -which refine capabilities of SWS j and are represented in one of the conceptual spaces CS 1 ..CS m , -are retrieved:

)} ( ),..., ( ), ( { ) ( 2 1 x i SWS M SWS M SWS M SWS M CS ∪ ∪

Based on the above ontological descriptions, for each member v l within M(SWS i ), the Euclidean distances to any prototypical member of all M(SWS j ) which is represented in the same space MS j as v l are computed. In case one set of prototypical members M(SWS j ) contains several members in the same MS -e.g. SWS j targets several instances of the same kind -the algorithm just considers the closest distance since the closest match determines the appropriateness for a given goal. For example, if one SWS supports several different locations, just the one which is closest to the one required by SWS i determines the appropriateness.

Consequently, a set of x sets of distances is computed as follows Dist(SWS i )={Dist(SWS i ,SWS 1 ), Dist(SWS i ,SWS 2 ) .. Dist(SWS i ,SWS x )} where each Dist(SWS i ,SWS j ) contains a set of distances {dist 1 ..dist n } where any dist i represents the distance between one particular member v i of SWS i and one member refining one instance of the capabilities of SWS j . Hence, the overall similarity between the base SWS i and any SWS j could be defined as being reciprocal to the mean value of the individual distances between all instances of their respective capability descriptions and hence, is calculated as follows:

( )1 1 1 ) ( ) , ( ) , ( −= −             = = ∑ n dist SWS SWS Dist SWS SWS Sim n k k j i j i

Finally, a set of x similarity values -computed as described above -which each indicates the similarity between the base SWS i and one of the x target SWS is computed:

)} , (),.., ( ), ( { 2 , 1 ,x i i i SWS SWS Sim SWS SWS Sim SWS SWS Sim

As a result, the most similar SWS j , i.e. the closest associated SWS, can be selected and invoked. In order to ensure a certain degree of overlap between the actual request and the invoked functionality, we also defined a threshold similarity value T which determines the similarity threshold for any potential invocation.

Application: Measurement-based SWS discovery of Weather Forecast Web Services

Our measurement-based SWS discovery approach (Section 4) was actualised within an initial proof-of-concept prototype application which mediates between different weather forecast Web services. This example use case illustrates how measurements can be dynamically mapped to symbolic representations, SWS in this case, by means of similarity-computation within CS.

Here, SWS 1 , SWS 2 and SWS 3 provide weather forecast information for different locations. Each service has distinct constraints, and thus distinct SWS descriptions. In detail, SWS 1 is able to provide forecasts for France and Spain while SWS 2 and SWS 3 are providing forecasts for the United Kingdom. All services show different Quality of Service (QoS) parameters. Three distinct service ontologies O 1 , O 2 , and O 3 had been created, each defining the capability of the respective service by using distinct vocabularies. For example, SWS 2 considers concepts representing the notions of location and QoS together with corresponding instances (see also By applying the representational approach proposed in Section 3, each concept of the involved heterogeneous SWS representations had been refined as a shared CS, while instances -defining the capabilities of available SWS -were defined as prototypical members. For example, a simplified CS (CS 1 : Location Space in Figure 5) was utilized to refine geographical notions (e.g. country) by using two dimensions indicating the geospatial position of the location:

{ } { } 1 2 2 1 1 ) , ( ) , ( CS longitude latitude l p l p = =

The two dimensions latitude and longitude are equally ranked, and hence, a prominence value of 1 has been applied to each dimension. Note that each of the depicted concepts and instances, such as O 2 :UK and O 3 :UK, are distinct and independent from each other, and thus might show heterogeneities, such as distinct labels, for instance United Kingdom and Great Britain. In the case of O 2 :UK and O 3 :UK, these two instances are refined by two distinct prototypical members:

( ) { } 1 2 1 2 1 -3.435973 , 55.378051 ) ( CS v v v SWS L i ∈ = = = and ( ) { } 1 2 1 3 1 -3.435963 , 55.378048 ) ( CS v v v SWS L i ∈ = = =

. Each member has been defined by different individuals applying similar, but non-equivalent geodata.

In addition, a second space (CS 2 : QoS Space in Figure 5) has been defined by three dimensions -latency (in ms), throughput (number of Web services), availability (in Potential service consumers define a goal (e.g. SWS 4 in Figure 5) together with the set of input parameters and the underlying assumptions in terms of measurements. After accomplishment of F.1, i.e. the dynamic instantiation of members in their corresponding CS to represent the sensor data provided with the actual goal request SWS 4 , all involved goals and SWS were grounded in the same set of CS as depicted in Figure 5.

%): { } ( ) { }

In that, assumptions of available SWS had been described independently in terms of simple conjunctions of instances which were individually refined in shared CS as shown in Table 1. As shown in Table 1, the request SWS 4 assumes a SWS which provides weather forecast for the location UK (L 1 (SWS 4 )) and ideal QoS (Q 1 (SWS 4 )) demanding zero latency but high throughput and availability. Given these similarities, our introduced goal achievement method automatically selects the most similar SWS (i.e. SWS 2 in the example above) and triggers its invocation.

Q Q Q L L L Ass ∪ ∪ ∪ ∪ ∪ ∪ ∪ = Members Li in CS1 (locations) Members Cj in CS2 (QoS) SWS1 L1(

Discussion and Conclusions

In order to contribute to the vision of the SSW, i.e. the convergence of sensor data and formal knowledge representations as part of the Semantic Web, we proposed a representational model which grounds ontological representations in CS to overcome the symbol grounding problem. The latter is perceived to be as one of the major obstacles towards the SSW. While ontological instances are represented as prototypical members within a CS, arbitrary sensor data which measures the dimensions of the CS can be associated with the most appropriate instance by identifying the most similar, i.e. the closest, prototypical member to the vector which represents the sensor data. Our approach is facilitated through a dedicated CS Ontology which allows to refine any arbitrary concept (instance) as CS (prototypical member). In that, our representational model allows to bridge between sensor measurements and symbolic knowledge representations by means of similarity computation between vectors within CS.

In addition, we implemented our approach by applying it to the field of SWS and utilising it for measurement-based SWS discovery while bridging between symbolic SWS representations and sensor-based measurement data. Therefore, we extended the matchmaking algorithm of an existing SWS Broker, IRS-III, with new capabilities allowing for measurement-based matchmaking based on our two-fold representational model. A first proof-of-concept prototype application utilises our approach to enable measurement-based discovery of weather forecast Web services based on measured parameters such as the geospatial location and the service QoS.

The proposed approach has the potential to further support interoperability between heterogeneous sensor data and symbolic knowledge representations. While our approach supports automatic mapping between ontology instances and sensor-based measurements it still requires a common agreement on shared CS. In addition, incomplete similarities are computable between partially overlapping CS.

However, the authors are aware that our approach requires considerable effort to establish CS-based representations. Future work has to investigate on this effort in order to further evaluate the potential contribution of the proposed approach. Moreover, while overcoming issues introduced in Section 2, further issues remain. For example, whereas defining instances, i.e. vectors, within a given CS appears to be a straightforward process of assigning specific quantitative values to quality dimensions, the definition of the CS itself is not trivial. Nevertheless, distance calculation relies on the fact that resources are described in equivalent geometrical spaces. However, particularly with respect to the latter, traditional ontology and schema matching methods could be applied to align heterogeneous spaces. In addition, we would like to point out that the increasing usage of upper level ontologies, such as DOLCE [9] or SUMO [15], and emergence of common schemas for sensor data such as the OpenGIS Observations and Measurements Encoding Standard, leads to an increased sharing of ontologies at the concept level. As a result, our proposed hybrid representational model becomes increasingly applicable by further contributing to the vision of the SSW.