Semantic Spatial Reasoning

Developing a Conceptual Framework for Reasoning with Semantic,

Qualitative-Quantitative Spatial Information

Roman Katerinenko

Oracle Labs, Schiffbauergasse 14, Potsdam, Germany

Keywords:

Qualitative Spatial Reasoning, Rule-based Reasoning, CDC, RCC-8, RDF, Semantic Web, OWL.

Abstract:

In recent years, signiﬁcant achievements have been made on handling qualitative spatial relations in the ﬁeld

of qualitative spatial reasoning. These achievements can be utilized to bridge the gap between geometries and

semantics of real-world objects. With this purpose we introduce the Semantic Spatial Reasoning conceptual

framework for reasoning with information of mixed types: qualitative-quantitative spatial and information

described with the help of the Semantic Web technologies. The objective of this framework is not to be a

particular reasoning algorithm but a conceptual decomposition suitable for showing beneﬁts of the combined

reasoning approach, forecasting practical applications and giving a clue for an implementation. Modular

structure of the framework makes it useful to model various tasks in areas, such as, GIS, cognitive vision,

computer-aided design, data integration.

1 INTRODUCTION

In recent years, signiﬁcant achievements have been

made on handling qualitative spatial (QS) relations in

the ﬁeld of qualitative spatial reasoning (QSR). QS

relations are symbol abstractions of geometric repre-

sentations which allow to use qualitative terms to for-

mulate rules in order to describe spatial situations and

actions. Normally, systems dealing with spatial in-

formation also capture it’s semantics. Therefore, we

decided to extend QSR with ability to reason with

semantic information and introduced Semantic Spa-

tial Reasoning (SSR) conceptual framework. In our

investigation, we concluded that the abilities of our

approach broader than often-considered constraint-

based reasoning abilities of QSR because it allows to

generate new spatially-enabled knowledge from ex-

isting knowledge.

Research in the ﬁeld of QSR have been conducted

in different directions, such as, design of and rea-

soning with QS calculi, their combination (De Fe-

lice, 2013) and effective implementation (Schneider,

2002). A wide variety of QS calculi has been de-

veloped to model different aspects of the space like

topology (Region Connection Calculus, RCC-8), car-

dinal directions (Cardinal Directions Calculi, CDC),

relative orientation, distance, visibility, shape, size.

Herewith, there was a relatively small investigation

of using the Semantic Web technologies in combina-

tion with QSR, mostly related to the improvement of

quantiﬁcation with the help of rules (De Felice, 2013).

From the opposite side, there are some efforts

to develop spatial extensions of some Semantic Web

technologies like GeoRDF and GeoSPARQL (Perry

and Herring, 2012) but, regarding incorporation of

QSR into this standards, only topology calculus

(RCC-8) were added. Therefore, our goal is to bridge

this gap by the development of SSR.

In this article we introduce a conceptual frame-

work for SSR which allows reasoning with differ-

ent types of information — semantic, qualitative-

quantitative spatial. The objective of this framework

is not to be a particular reasoning algorithm but a

conceptual decomposition suitable for showing ben-

eﬁts of the combined reasoning approach, forecasting

practical applications and giving a clue for an imple-

mentation.

2 BASIC ELEMENTS

Coad and Yourdon (Coad and Yourdon, 1991) con-

cluded that it is natural for human to use the object-

oriented approach for thinking about real world: dif-

ferentiation of experience into particular objects, dis-

Katerinenko, R..

Semantic Spatial Reasoning - Developing a Conceptual Framework for Reasoning with Semantic, Qualitative-Quantitative Spatial Information.

In Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2015) - Volume 2: KEOD, pages 257-262

ISBN: 978-989-758-158-8

257

tinction between the whole object and it’s part and

distinction between different classes of objects. The

Semantic Web technologies like RDF and OWL have

successfully utilized this approach and added a very

important concept of a relation which is used to re-

ﬂect arbitrary dependencies between real-world ob-

jects. When considering objects having spatial extent

(spatial objects) qualitative spatial (QS) relations are

normally used to handle information which can in-

clude concepts, such as, “inside”, “next-to”, “part-of”

rather than geometrically speciﬁc data with numerical

coordinates. These relations are studied in the ﬁeld of

Artiﬁcial Intelligence called Qualitative Spatial Rea-

soning (QSR). So we can conclude that QSR and the

Semantic Web technologies have a common ground

— object-oriented approach, thus it is a natural thing

to investigate possibilities of the combined approach

which we call Semantic Spatial Reasoning (SSR).

With a view to be semantically close to the object–

oriented approach, we have included the following

basic concepts to our model: objects, classes, prop-

erties of objects and relations between them. We dis-

tinguish two types of objects: the objects with known

spatial extent (SE) and others. In the remainder of

this article we refer to the former objects as O

and

to the latter as O. In the same way we distinguish

two types of relations: QS relations and others which

we call semantic relations for simplicity. QS relation

) could be an arbitrary relation of any QS calculi,

such as, CDC, RCC-8 or OPRA. Semantic relations

sem

) express some other relations between objects,

such as, administrative (“report-to”), family (“parent-

of”), friendship (“who-likes-whom”), etc. Such dis-

tinction to spatial and not spatial elements allows us to

analyze possible translation (mapping) functions be-

tween O

, O, R

, R

sem

in the next section.

3 TRANSLATION OPERATIONS

In this section we introduce the next part of our con-

ceptual framework — translation operations which

perform translation or mapping between different

types of the basic elements. We have analyzed all

possible translation operations between objects, ob-

jects with SE, QS relations, semantic relations and

have selected six meaningful. The quantiﬁcation (see

Section 3.2) and qualiﬁcation (see Section 3.3) opera-

tions have been studied in literature but the others are

our own contribution.

3.1 Translation Operations Sem, Geom

The Sem translation operation is supposed to deﬁne

semantics for an object, so that this semantics could

be used in the rule-based reasoning described in Sec-

tion 4.2. In the Semantic Web technologies semantics

of a real-world object is captured within it’s relations

to another objects. For example, given object’s identi-

ﬁer as an input, the Sem operation could yield the se-

mantic network containing information about object’s

class, properties and relations. Sometimes such se-

mantic information is contained in geographic maps

as a“thematic layer” or, in case of OpenStreetMaps,

is contained in “tags” attached to objects.

The Geom translation operation yields object’s SE

which is used in the QS reasoning and the transla-

tion operations. The result could be a vector geometry

stored in a spatial database or a text description kept

in GeoRDF and turned to a vector geometry.

3.2 Quantiﬁcation

The quantiﬁcation operation was deﬁned in (Wolter

and Wallgr¨un, 2012) as the process of computing a ge-

ometric interpretation of a qualitative relation consid-

ering geometries of the reference objects. The com-

putation is based on the geometric semantics of the

relation. For most qualitative calculi quantiﬁcation

hasn’t been studied yet, but for CDC and RCC-8 it

can be implemented relatively simple.

We have extended this notion to use with objects

and several calculi simultaneously: the quantiﬁcation

operation approximates a possible SE of O

∗

(with as-

terisk we mark objects with unknown SE) by quanti-

fying all QS relations R

∗

, O

, . . . , O

) associated

with it. More precisely the quantiﬁcation of O

∗

computation of a spatial region that the real-world

entity represented by O

∗

can occupy in order to sat-

isfy all QS relations R

∗

, O

, . . . , O

) with respect

to the reference objects O

, . . . , O

. The quantiﬁca-

tion is impossible when SE for all reference objects

are unknown. As a result O

∗

gets not just an exem-

plar region which satisﬁes the relations but the max-

imum region which is union of all possible exemplar

regions.

east,

externally connected

south-west

west

east

south-east

Figure 1: Constraint network for the geometric scene.

KEOD 2015 - 7th International Conference on Knowledge Engineering and Ontology Development

258

For example, if it was required to quantify object

B shown in Figure 1 then the quantiﬁcation operation

could compute the region shown in Figure 2. Obvi-

ously, the quantiﬁed region is less precise than the

real-world object, but the more objects and relations

are involved the more precise the result is. In our nota-

Figure 2: Quantiﬁcation of object B.

tion the quantiﬁcation operation expressed as follows:

Quantification : O

∗

, R

∗

, O

, . . . , O

) 7→ O

3.3 Qualiﬁcation

The opposite to the quantiﬁcation operation is the

qualiﬁcation operation. It yields the QS relation

which holds between objects with SE:

Qualification : O

, . . . , O

7→ R

, . . . , O

)

Given that the system contains several calculi, the

quantiﬁcation operation requires to check the con-

straints which every calculus deﬁnes for the objects

in a all relations. For example, to qualify a relation

in the system containing RCC-8 and CDC calculi the

quantiﬁcation requires to check whether the objects

overlap, disjoint, one object is located to the north of

another, etc.

3.4 Translation Operations TO

, TO

Previously, we have considered four elements of our

framework: objects in general, objects with known

SE, QS relations and translation operations between

them (quantiﬁcation, qualiﬁcation). Now we are

adding the rest part of our model — semantic objects,

rules, relations and considering possible translation

operations between whole elements of the model.

At ﬁrst, we consider the mapping between an arbi-

trary semantic relation and a QS relation for the same

objects: R

, . . . , O

) ↔ R

sem

, . . . , O

). The Se-

mantic Web technologies allows to deﬁne any ar-

bitrary relation but we do think the restriction for

this translation operation is those semantic relations

which have synonymic QS relations. For example,

one could deﬁne an RDF relations, such as, “next-

to”,“close-to”, “near” which, could be mapped to the

“externally connected” RCC-8 relation. So CDC re-

lations, such as,“north”, “east” could be mapped to

the “in-front-of” and “to-the-right” RDF relations. In

other words, this translation operation allows to uti-

lize QS relations during the rule-based reasoning and

utilize semantic relations during the QS reasoning.

For more thorough analysis we divide this transla-

tion operation into two separate operations (TO):

: R

, . . . , O

) 7→ R

sem

, . . . , O

)

: R

sem

, . . . , O

) 7→ R

, . . . , O

)

In general, TO

should be treated not just as a

mapping but as the operation which deﬁnes semantics

of an object taking into account it’s QS relations with

another objects. An exemplar implementation could

accept inputs as: a geometric scene; QS relations be-

tween the objects of the scene; geographic or admin-

istrative semantics for some of them, such as, “build-

ing”, “bridge”, “river”; etc. Afterwards, TO

yields

a semantic description of the scene, such as, “An un-

known object O

∗

is connected to particular road and

overlaps particular river” but in the form of a seman-

tic network. This semantic network could be turned

into a SPARQL query to search the RDF concept for

∗

in some RDF graph. This RDF concept could be

treated as semantics of O

∗

We admit that some geographic feature recogni-

tion or image analysis algorithms could do this job as

well and decide that O

∗

is likely a “bridge”, but our

approach could ﬁnd the name of the bridge if the RDF

graph is detailed enough. Also probabilistic machine

learning models could be utilized for TO

implemen-

tation.

Considering TO

, there are two cases. In case

when all SEs of O

, . . . , O

are known, TO

is just

a mapping between synonymic relations . In case,

there is an object O

∗

with unknown SE this operation

(in combination with quantiﬁcation) could determine

it. As an exemplar scenario, let us consider the fol-

lowing news message: “Undeﬁned object is between

the church and the railroad and close to the bus stop”.

This information could be captured as an RDF graph.

Moreover, SE of the church, the railroad and the bus

stop are known from the map of the city. So after-

wards, TO

yields constraint network (similar to the

one shown in Figure 1) consisting of QS relations and

one object with unknown SE, which could be com-

puted later by the quantiﬁcation operation.

Mentioned scenario is related to the task of com-

putation of quantitative spatial scene by it’s text, video

or speech description. In general, the result geometry

is not a perfect match with the real-world geometry of

the object but this approximations is especially useful

in case of observations when precise coordinates of

the observable object are not available or not needed,

such as, “crowd movement” observation.

Semantic Spatial Reasoning - Developing a Conceptual Framework for Reasoning with Semantic, Qualitative-Quantitative Spatial

Information

259

Comparing to a conventional quantiﬁcation, the

combination of Sem, TO

and quantiﬁcation can

achieve a better result and compute SE more precisely

because it is possible to utilize semantic information

about object’s geometry, such as, shape or size. In

our framework this information could be kept in the

class of an object. For example, the information that

the target object is instance of a car-like shape class

could be accounted during the quantiﬁcation process.

We think that investigation of this possibility is related

to the idea of using real algebraic geometry for the

quantiﬁcation suggested here (Wolter and Wallgr¨un,

2012).

3.5 Translation Operations TO

, TO

These two translation operations are different from

the others because their purpose is to produce new

objects. Introduction of new objects during reasoning

process is not a typical situation for a reasoner. For

instance, Semantic Web reasoners are supposed to in-

troduce new relations between entities, but not new

entities. Datalog-style reasoners are the same. But,

sometimes, such feature is needed for the application

purposes. So that Oracle Database supports this fea-

ture in combination with user-deﬁned rule reasoning.

In our notation TO

, TO

are expressed as fol-

lows:

: R

sem

, . . . , O

) 7→ O

: R

, . . . , O

) 7→ O

The idea of both operations is the same, but TO

is designed to compose a new object by semantic re-

lations while TO

accepts QS relations. New object

is the result of application of geometric operations to

, . . . , O

input objects with known SE. The geomet-

ric operations could be of any kind, such as, compu-

tation of union, difference, convex hull, etc.

For example, in a particular application TO

could

be implemented in the following way: if O

is a

“house”, O

is a “garden” and R

is “externally-

connected” RCC-8 relation between O

and O

then

yields new object O

“household” which SE is

geometric union of O

and O

regions.

4 SEMANTIC SPATIAL

REASONER

In this section we introduce architecture of the seman-

tic spatial reasoner. We have developed it with the

aim to show great possibilities of combined reasoning

process utilizing the translation operations described

in Section 3.The reasoner (see Figure 3) consists of

two major modules: QSR and rule-based reasoner.

They run in a loop until ﬁxpoint state is reached and

no new information can be inferred anymore.

Rulebase

Figure 3: Semantic spatial reasoner architecture.

4.1 Qualitative Spatial Reasoner

This module was introduced in (De Felice, 2013) as a

system for integration of quantitative and QS infor-

mation. For this purpose it contains three compo-

nents: qualiﬁcation, quantiﬁcation components and

qualitative reasoner. We have added QS reasoner to

our framework in it’s original meaning but with one

extension — we added ability to inﬂuence the quan-

tiﬁcation component by semantic rules. The reason

for that will be discussed in Section 4.3.

All three components operate on the same data

structure — the constraint network in which the edges

are labeled with relations from QS calculi; the nodes

correspond to the objects with known or unknown SE.

The quantiﬁcation component applies the quantiﬁca-

tion operations (see Section 3.2) to every object with

unknown SE in order to ﬁnd it’s possible geometry

with respect to the constraints (relations). Afterwards,

the qualiﬁcation component applies qualiﬁcation op-

eration (see Section 3.3) to every object in order to

deduce it’s QS relations with the others. The next turn

is for qualitative reasoner which is based on algebraic

closure or path consistency algorithm (Mackworth,

1977) that applies composition and permutation op-

erations deﬁned in a calculus to propagate the con-

straints through the network and infer as much newre-

lations as possible. Main loop continues while infor-

mation in the constraint network is changing. When

ﬁxpoint is reached the rule-based reasoner steps into

the reasoning process.

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260

4.2 Rule based Reasoner

By the rule-based reasoner we mean a reasoner which

applies rules to some informationand deduces newin-

formation complied with the rules. This type of rea-

soning is known as a forward chaining inference or

bottom-up inference. Such reasoning process ﬁnishes

at a ﬁxpoint state. A rule is an IF — THEN construc-

tion. If some condition (the IF part) that is checkable

in some dataset holds, then the conclusion (the THEN

part) is processed.

There are many types of rules with different syn-

tax and semantics. In our framework we are us-

ing the Datalog-style rules (Katerinenko and Bess-

mertnyi, 2011). Such rules contain relations in both

parts. For example, the fact that a car is parked

in a parking might be expressed with relation like

parkedIn(car, parking). Adding the notion of vari-

ables, a rule could be something like:

IFparkedIn(?x, ?y)THENntpp(?x, ?y)

where “ntpp” stands for “non-tangential-proper-part”

RCC-8 relation. It is expected that for every pair

of ?x and ?y for which parkedIn relation holds, the

rule-based reasoner can conclude that the ntpp re-

lation holds as well and the corresponding relation

ntpp(car, parking) is added to the dataset.

4.3 Rules as Constraints

Qualitative representations enable capturing concep-

tual knowledge while abstracting of complexity of

real-world numeric information. Thus, it is a natu-

ral choice to use QS reasoning in conjunction with

rule-based reasoning. But there is another possibil-

ity for cooperation — rules can be used as constraints

to guide quantiﬁcation. For example, it is possible to

compose a rule from the statement “A river can not

intersect a house” and use this rule during computa-

tion of SE for the house. This idea was presented in

(De Felice, 2013) as additional to QS reasoner “the-

matic reduction” component, but in our case it is an

integral part of the framework. Thus, the same rule-

base could be used for this purpose and for rule-based

reasoning.

5 COMBINED REASONING

WITH THE TRANSLATION

OPERATIONS

In this section we demonstrate how the translation op-

erations enable mutually compliment reasoning. Let

us consider an exemplar dataset of mixed information

in order to demonstrate one iteration of the semantic

spatial reasoner. For the simplicity we are consider-

ing dataset which has been converted to the form of

a constraint network brieﬂy discussed in Section 4.1.

This network is shown in Figure 4, in which black

circle nodes represent objects, square nodes represent

objects with known SE, straight line edges represent

QS relations and dashed edges represent semantic re-

lations. For simplicity, we have omitted directions on

the edges and considering only binary relations. Also

let’s assume that this network is the result of the ﬁrst

application of the QS reasoner to the dataset. For de-

tails of this process refer to (De Felice, 2013).

As it is expected, after QS reasoning all objects

which have at least one relation with the object with

known SE were quantiﬁed. Otherwise, the quantiﬁca-

tion operation are not able to compute geometry for

it, like in case with triangular subnetwork in the left

part (see Figure 4). The same way, all QS relations

between objects with known SE were found. Ap-

plication of the TO

, TO

translation operations have

added two new edges E

, E

to the network (see Fig-

ure 5). The E

edge represents a QS relation appeared

after application of TO

to the semantic relation of

the E

edge. Now E

is adjacent to the object with

known SE that means that SE for the second adjacent

object will be found on the next invocation of the QS

reasoner. In contrast to the E

, edge E

appeared after

application of TO

to the corresponding QS relation.

Figure 4: Exemplar constraint network.

Figure 5: The network after TO

, TO

application.

The next modiﬁcations are done by the Sem and

Geom operations as shown in Figure 6. Geom has

found SE for O

and Sem decided semantics for O

As it was mentioned in Section 3.1, in the Semantic

Web technologies semantics of a real-world object is

captured within it’s relations to another objects, there-

fore new semantic edge was attached to O

. This edge

connects it to the semantic subnetwork, which could

Semantic Spatial Reasoning - Developing a Conceptual Framework for Reasoning with Semantic, Qualitative-Quantitative Spatial

Information

261

Figure 6: The network after Sem, Geom application.

be a subject for the QS reasoner on the next iterations,

because O

has known SE.

On the next step new objects O

, O

with known

SE have been introduced by application of TO

, TO

to the E

, E

edges respectively (see Figure 7). Here-

with, the E

edge has been introduced shortly be-

fore which demonstrates that the translation opera-

tions could be combined with each other in a mean-

ingful ways.

Figure 7: The network after TO

, TO

application.

6 CONCLUSIONS

The aim of this work was to investigate reason-

ing with information of mixed types: qualitative-

quantitative spatial and information described with

the help of the Semantic Web technologies to bridge

the gap between geometries and semantics of real-

world objects. As a result we have introduced a con-

ceptual framework called semantic spatial reasoning.

We have developed the translation operations which

are the main part of the framework that enables com-

bined reasoning. Each operation opens a new direc-

tion for further research of it’s software implemen-

tation and practical application in the context of the

combined reasoning. We provided an exemplar idea

for each operation.

The modular structure of the framework is ﬂex-

ible enough to model different practical tasks. For

example, for the task of computing quantitative scene

by it’s text description one might need to implement

the following elements of the framework: qualitative

spatial reasoner, TO

and Geom translation opera-

tions. Such an easy decomposition makes the frame-

work useful in different application areas, such as,

GIS, cognitivevision, computer-aided design, data in-

tegration. Since declarative rules are the ﬁrst class

citizens of the framework, it makes possible to gen-

erate new spatially-enabled knowledge from existing

knowledge, such as, generating implicit consequences

of some spatial events like earthquakes, industrial dis-

asters.

We plan to incorporate all elements of the frame-

work into software application using existed reason-

ers and investigate reasoning capabilities of the result

on real-world tasks in GIS area. We will also investi-

gate how the framework could be generalized to adopt

qualitative temporal reasoning.

ACKNOWLEDGEMENTS

This work was carried out in the framework of the

ALErT project, European Union grant no. 607996.

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