A Roadmap towards Tuneable Random Ontology Generation Via

Probabilistic Generative Models

Pietro Galliani, Oliver Kutz and Roberto Confalonieri

Free University of Bozen-Bolzano, Faculty of Computer Science, 39100, Bozen-Bolzano, Italy

Keywords:

Ontology Generation, Benchmarking, Testing.

Abstract:

As the sophistication of the tools available for manipulating ontologies increases, so does the need for novel

and rich ontologies to use for purposes such as benchmarking, testing and validation. Ontology repositories

are not ideally suited for this need, as the ontologies they contain are limited in number, may not generally

have required properties (e.g., inconsistency), and may present unwelcome correlations between features. In

order to better match this need, we hold that a highly tuneable, language-agnostic, theoretically principled tool

for the automated generation of random ontologies is needed. In this position paper we describe how a proba-

bilistic generative model (based on features obtained via the analysis of real ontologies) should be developed

for use as the theoretical back-end for such an enterprise, and discuss the role of the DOL metalanguage in it.

1 INTRODUCTION

Due to the ever-increasing practical importance of Se-

mantic Web technologies, in recent years there has

been a remarkable increase in the pacing of the study

and development of algorithms and tools for ma-

nipulating, analyzing or exploring ontologies (Cris-

tani and Cuel, 2005; Katifori et al., 2007). Every

month, sophisticated novel techniques are developed

for identifying and resolving inconsistencies in on-

tologies (Plessers and De Troyer, 2006; Troquard

et al., 2018), representing and answering queries over

them (Wache et al., 2001; Zhang et al., 2018), alig-

ning ontologies (Choi et al., 2006; Granitzer et al.,

2010; Dragisic et al., 2014), and assisting human

users in their creation and manipulation (Choi et al.,

2006; Zablith et al., 2015).

The problem of testing and validating such techni-

ques, as well as the problem of comparing their per-

formance with that of related approaches, cannot be

solved without a steady supply of new, independently

generated ontologies satisfying speciﬁc criteria (e.g.,

language choice, size, height and tree-width of indu-

ced class hierarchy, distribution of the operator depth

in logical expressions and so forth).

The existence of Ontology Repositories (e.g., Bi-

oPortal (Matentzoglu and Parsia, 2018) and Onto-

hub (Codescu et al., 2017)) making publicly available

a number of human-generated ontologies of practical

importance is not, in itself, a satisfactory solution to

this need. In more detail:

1. Although the number of ontologies contained in

such repositories is not small, it is not sufﬁcient

for performing each instance of testing or ben-

chmarking on a truly novel corpus of ontologies.

This is especially problematic in the case of tools

designed to be used for speciﬁc subclasses of on-

tologies, for which few examples may be availa-

ble in such repositories, or for tools that make use

of machine learning methodologies (and which,

therefore, need to be trained, cross-validated and

tested on different corpora of ontologies).

2. Tools for solving certain highly important types of

problems, like ontology repair, operate on ontolo-

gies with properties (e.g inconsistency) which are

not generally shared by the ontologies uploaded

to public repositories. It is, of course, possible to

induce artiﬁcially such properties via ad-hoc met-

hods (e.g., adding random axioms to an ontology

until it is made inconsistent), but it then becomes

rather opaque whether the resulting corpus of on-

tologies bears any resemblance to the typical real

use cases.

3. In many cases, it would be important to be able

to examine how the performance of a tool is af-

fected by various changes in the properties of the

input ontologies. However, it is not generally pos-

sible to sample from repositories adequately rich

corpora of ontologies which differ with respect

Galliani, P., Kutz, O. and Confalonieri, R.

A Roadmap towards Tuneable Random Ontology Generation Via Probabilistic Generative Models.

DOI: 10.5220/0006961103510357

In Proceedings of the 10th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2018) - Volume 2: KEOD, pages 351-357

ISBN: 978-989-758-330-8

351

to certain features and are not statistically distin-

guishable with respect to others: instead, diffe-

rent features are generally highly correlated. For

instance: if the larger ontologies of a repository

tend to be little more than taxonomies, having

relatively few complex axioms in comparison to

the smaller ontologies of the repository, then sam-

pling ontologies of different sizes from it in order

to study the effect of ontology dimension on the

performance of an algorithm might lead unwary

researchers to outright incorrect conclusions.

One additional difﬁculty worth mentioning, mo-

reover, is that there does not, at the moment, exist

a truly comprehensive, experimentally validated set

of ontology features with respect to which to validate

and compare tools and algorithms. Certainly, the clas-

siﬁcation of ontologies is not unexplored territory al-

together; but the features thus far studied in the lite-

rature, though certainly interesting and worth of furt-

her analysis, have not for the most part been obtained

through systematic exploration of the available cor-

pora but rather as a result of the researchers’ own in-

terests in certain properties of ontologies.

To bridge this gap, the development of a new

generation of tools, based on principled theoretical

foundations, for the automatic generation of random

ontologies, is required. These tools should be tune-

able with respect to a variety of (logic-agnostic) fe-

atures, and these features should in turn be extracted

and justiﬁed through the study of corpora via network

analysis-inspired techniques and probabilistic model-

ling.

We here outline a possible roadmap towards such

an achievement, discussing furthermore the current

approaches to ontology generation and their limita-

tions.

2 TOWARDS TUNEABLE

RANDOM ONTOLOGY

GENERATION

Against the above mentioned background, it is clear

that extracting a selection of human-readable, com-

prehensive ontology features and using them for the

generation of random ontologies suitable for testing

purposes is a major and challenging task.

Our overall aim is then to:

Develop a tuneable, language-agnostic gene-

rator of random ontologies suitable for the

testing and benchmarking of algorithms and

tools. Relevant features will be extracted semi-

automatically from corpora of ontologies. These

features will be used for the development of

Markov Chain Monte Carlo (MCMC)-like sam-

pling algorithms over ontologies.

The usefulness of the resulting generator for

benchmarking and testing purposes will be ex-

perimentally veriﬁed.

To achieve the general aims outlined above, we be-

lieve that the following three speciﬁc objectives need

to be solved.

Objective 1 – Ontology Features: A fundamental

prerequisite for tuneable ontology generation is

to ﬁrst generate and justify, on empirical grounds,

a set of language-agnostic ontology features and

study their distribution and correlations in corpora

of human-created ontologies. We will then need

to ﬁnd (possibly multiple) choices of default va-

lues for these features that may be used to direct

the generation of realistic random ontologies,

barring users choosing different values for them

(cf. Figure 1, Node 1: Feature Analyzer). It is

worth remarking here that obtaining such features

and classifying real ontologies with respect to

them will result in a product of inherent value

for the scientiﬁc community, even aside from

their intended application to random ontology

generation: indeed, it will provide the basis for a

reliable, empirically grounded, language-agnostic

taxonomy of ontologies.

Objective 2 – Generative Probabilistic Model:

The thus obtained ontology features and statistics

will then serve as the basis for a Generative Pro-

babilistic Model (see Figure 1, Node 3: Ontology

Generator) for ontologies which, for any given

choice of parameters, will provide a mechanism

for producing novel, random ontologies. The

precise structure of such a model will, of course,

depend heavily on the nature of the features

found as well as on their probabilistic distribution

over the corpora; but as a preliminary hypothesis,

we think that an agent-based approach in which

multiple artiﬁcial agents add or remove certain

patterns of expressions to the ontology with

a probability which depends on the values of

certain features is likely to be a proﬁtable one in

this context, in such a way that the overall proba-

bility distribution of features is as required. This

can be seen, after a fashion, as a generalisation

of Markov Chain Monte Carlo approaches to

KEOD 2018 - 10th International Conference on Knowledge Engineering and Ontology Development

352

Real Repositories

– 1 –

Feature

Analyser

Parameter Distribution

– 4 –

DOL

Speciﬁcation

(swappable)

– 2 –

Reasoner

(swappable)

user

– 3 –

Ontology

Generator

Random Ontologies

Samples

Feature Values

Chosen Parameters

Random Ontology

Typical

Parameters

Ontorator

Figure 1: Tuneable Ontology Generation: workﬂow, structure and modules.

random sampling.

Objective 3 – Implementation and Validation: We

will then implement the thus obtained theoretical

model. The implementation will also be language

agnostic, in the sense that it will be applicable to

ontologies described in any language as long as a

DOL speciﬁcation and a suitable reasoner will be

provided (see Nodes 2 and 4 of Figure 1, as well

as the discussion below). This implementation

will then be validated by means of comparing

the performance of algorithms over real-world

ontologies and over synthetic ones.

3 THE ROLE OF DOL

The Distributed Ontology, Modeling, and Speciﬁca-

tion Language (DOL) (Mossakowski et al., 2015) was

submitted in November 2015 to the Object Manage-

ment Group (OMG), and formally adopted in 2016 as

an international standard. The ﬁnalisation of this lan-

guage for heterogeneous logical speciﬁcation invol-

ved more than 50 international experts overall.

DOL

has support for logical heterogeneity, structuring, lin-

king, and modularisation, i.e., crucial features to orga-

nise a large number of ontologies into structured re-

positories. Also, several key technologies have been

developed in the DOL ecosystem, most importantly

the OntoHub repository and reasoning platform (Co-

descu et al., 2017).

See http://ontoiop.org

See http://ontohub.org

The availability of DOL is thus essential to the

overall feasibility of the research proposed here, for

at least three different reasons:

• In its role as a unifying meta-language, it allows

our approach to be truly language-agnostic, in that

it will be able to generate random ontologies (or

estimate feature parameter distributions given cor-

pora) for any formalisms for which DOL speci-

ﬁcations and reasoners can be provided (see Fi-

gure 1);

• The OntoHub repository, which, as already men-

tioned, is part of the DOL ecosystem and provides

a rich collection of ontologies in various speciﬁ-

cation languages, will be essential for our work in

feature selection over ontologies as well as for the

testing of the resulting framework.

• The rich linking and modularisation constructs of

DOL support speciﬁcally two crucial operations:

1) the systematic build-up of larger ontologies

from smaller parts, and 2) the recording of rela-

tionships between ontologies in different logical

formalisms, e.g. recording the approximation of

an ontology in a less expressive language, via a

theory interpretation. Note that operationalising

this structural information is non-destructive, i.e.,

the parts of a larger ontology can be recovered

from the structural links.

A Roadmap towards Tuneable Random Ontology Generation Via Probabilistic Generative Models

353

4 EXTRACTING FEATURES

FROM ONTOLOGY CORPORA

As the size and the practical importance of ontologies

increased, it is not surprising that the interest in the

development of ontology metrics – that is, numerical

quantities that summarize the overall features of on-

tologies – has also grown (Lozano-Tello and G

omez-

erez, 2004; Garc

ıa et al., 2010; Kang et al., 2012;

Sicilia et al., 2012; McDaniel et al., 2018).

Such metrics have been introduced for different

purposes, such as assessing the quality of an ontology

(McDaniel et al., 2018), predicting the performance

of reasoners (see e.g., (Tempich and Volz, 2003;

Kang et al., 2012)) or measuring the cognitive com-

plexity of OWL justiﬁcations (Horridge et al., 2011).

Approaches along these lines seem to have been

fairly effective in predicting the results of benchmarks

in real ontologies. Their effectiveness for evaluating

ontology quality seems more limited, owing to some

degree to the greater intangibility and complexity of

the concept, but nonetheless such metrics can have a

useful role in this context (Tartir and Arpinar, 2007;

Duque-Ramos et al., 2011; Sicilia et al., 2012; Neu-

haus et al., 2013; McDaniel et al., 2018).

These metrics, in general, are hand-crafted by re-

searchers on the basis of their intuitions and expe-

rience with ontologies. We think that, in this con-

text, it would be instead useful to take inspiration

from approaches to representation learning on graphs

(see (Hamilton et al., 2017b) for a survey) such as

node2vec (Grover and Leskovec, 2016) and Grap-

hSAGE (Hamilton et al., 2017a) to automatically ex-

tract the salient features from a corpus of ontologies.

Automatically extracted features, however, will

not sufﬁce for our needs: indeed, for our purposes we

need to ﬁnd not only features over ontologies which

are suitable for clustering and prediction tasks or for

ontology generation, but also those features which

can be understood and used as parameters by humans.

Therefore, we envision a two-stage approach to

the extraction of features from ontologies:

1. Automated feature learning techniques can be

used to extract statistically signiﬁcant (but not ne-

cessarily human-readable) features from ontology

corpora;

2. These features can then be further analysed, at-

tempting to either (a) ﬁnd intuitively comprehen-

sible, human-readable analogues or (b) decom-

pose them in terms of multiple human-readable

features.

5 A GENERATIVE

PROBABILISTIC MODEL FOR

ONTOLOGIES

A natural source of inspiration for the study of ge-

nerative models for ontologies is the study of such

models for graphs. This is a very rich topic, and

many such models, like Exponential Random Graphs

(Erd

os and R

enyi, 1959; Robins et al., 2007), the Ba-

rab

asi-Albert model (Albert and Barab

asi, 2002), sto-

chastic block models (Airoldi et al., 2008) and Kro-

necker graphs (Leskovec et al., 2010) have been ex-

tensively studied in the literature.

It is difﬁcult to predict in advance the exact struc-

ture of the model which we will develop, as much will

of course depend on the results of our previous inves-

tigation about ontology features.

We think, in analogy with some recent works on

graph generation (see e.g., (You et al., 2018)), that

a potentially fruitful approach might be to create a

MCMC-like model in which various transformations

(e.g., axiom additions, deletions and modiﬁcations)

might be applied to an ontology with a probability

that depends on the current values of its features.

By assigning correct weights to the probability of

each transformation, it would be then possible to en-

sure that the probability distribution over the features

would indeed match the speciﬁed one; and, by sam-

pling from this distribution, we could indeed obtain

random ontologies for any choice of parameter value.

As an added advantage, this type of model - repre-

sented as a set of possible transformation over ontolo-

gies, with pre-requisites and weights - would be fairly

human-interpretable and could be modiﬁed manually

if desired.

6 IMPLEMENTATION, TESTING

AND COMPARISON

The best known and most used frameworks for the

benchmarking of tools over ontologies are the Lehigh

University Benchmark (LUBM) (Guo et al., 2005)

and the University Ontology Benchmark (UOBM)

(Ma et al., 2006). Albeit certainly useful, the general

applicability of these two frameworks for generating

ontologies is hindered by at least three factors:

1. The languages of the ontologies generated

through these two frameworks are ﬁxed (to a sub-

set of OWL Lite and to the complete OWL Lite or

OWL DL respectively) and not easy to change;

2. The structure of the TBoxes obtained via these ap-

proaches are fairly static, and not necessarily re-

KEOD 2018 - 10th International Conference on Knowledge Engineering and Ontology Development

354

ﬂective of that of all real ontologies;

3. Although there are options for changing somew-

hat the properties of the ontologies generated via

these approaches, the amount of ﬁne-tuning that

is possible to perform with respect to the features

of the ontology is very limited.

The programme sketched in this work is thus con-

siderably more ambitious than LUBM and UOBM:

indeed, as we argued before, it would be highly desi-

rable to develop a tool for the generation of random

ontologies that was highly tuneable, language agnos-

tic, theoretically well founded, and capable of gene-

rating ontologies whose statistical features are ana-

logous to those of arbitrary real world ontologies.

Despite their undeniable practical success, LUBM

and UOBM are quite far indeed from this mark.

A more general approach, much closer in con-

cept to our research perspectives, is the one employed

by the OTAGen ontology generator (Ongenae et al.,

2008). In short, given a number of parameter choi-

ces (e.g., number of classes, number of logically de-

ﬁned classes, number of individuals, minimum and

maximum number that non-functional object proper-

ties are instantiated and so forth), OTAGen genera-

tes a random ontology ex novo. Still, the selection of

adjustable parameters is arguably somewhat idiosyn-

cratic in that it reﬂects the structure of the ontology

generation algorithm employed (rather than conside-

rations regarding the importance of these speciﬁc pa-

rameters for the testing and benchmarking of ontolo-

gies); and, furthermore, the ontologies thus generated

are not necessarily “typical” or structurally similar to

real-world ontologies with the same parameter values.

Another work worth mentioning in this context is

Mips Benchmark (Zhang et al., 2015), an automatic

generator of incoherent ontologies for the purpose of

measuring the effectiveness of tools for solving the

minimal incoherence preserving sub-terminologies

(Mips) problem (Schlobach et al., 2007). This is

more special-purpose than our intended approach, and

while experimental evaluation suggests that the tune-

able parameters of this generator are relevant to the

analysis of the complexity of the Mips problem once

more there is no particular concern about whether the

ontologies thus generated are structurally analogous

to real-world use cases.

After devoting some effort to the principled search

for relevant ontological features and to the develop-

ment of a generative probabilistic mathematical mo-

del of ontology generation, we believe that it would be

possible to build and validate a general-purpose, the-

oretically sound, highly tuneable generator of struc-

turally plausible (in the sense of “having statistical

structural properties close to those of real ontologies”)

random ontologies; and, as mentioned before, such a

generator - aside from its direct possible application

to the testing and benchmarking of algorithms over

ontologies - would constitute a useful step towards

the integration of statistical and symbolic reasoning

via probabilistic inference.

Our generator will also need to be validated. In or-

der for this validation to be successful, we will require

the following three requirements to be all satisﬁed:

Correctness: The probability distribution of the fea-

tures of the generated ontologies will match the

predictions of the probabilistic model (in other

words, our generator will be a correct implemen-

tation of our probabilistic model);

Suitability: The ontologies generated by our tool

will be suitable for use in testing, benchmarking

and algorithm validation purposes (as veriﬁed, for

instance, by comparison with other benchmarking

approaches and with real ontologies);

Verisimilitude: For adequate choices of parameters,

the ontologies generated will be structurally close

to real ones, as veriﬁed both by direct inspection

and by automated exploration of relevant proper-

ties.

7 CONCLUSION

In this work we presented a roadmap towards the

automated generation of random ontologies for tes-

ting/benchmarking purposes.

This preliminary discussion left several open is-

sues in need of further exploration, and it is a foregone

conclusion that many ulterior difﬁculties and insights

(quite possibly, ones which would prove themselves

valuable in a much wider scope than that of the spe-

ciﬁc problem of random ontology generation) will be

encountered in the process of developing the theoreti-

cally principled, tuneable, practically useable tool that

we envision.

Nonetheless, we hope to have convinced the rea-

der that the problem of random ontology generation is

a surprisingly complex, subtle, and potentially fruitful

one, and to have provided some insights regarding the

difﬁculties inherent to it and the possible ways to sur-

pass them.

As a ﬁnal comment, we further speculate that re-

solving the problem of random ontology generation

– and, in particular, doing so via the generative pro-

babilistic approach discussed here – has the potential

to provide a useful avenue towards the integration of

symbolic and statistical reasoning. Indeed, genera-

tive probabilistic models such as the ones envisioned

A Roadmap towards Tuneable Random Ontology Generation Via Probabilistic Generative Models

355

in this roadmap can in principle be also used for in-

ferential reasoning over ontologies: very brieﬂy, the

probability distributions over ontologies provided by

such a model can be used to calculate quantities such

as e.g. the probability that an axiom will be contained

in an ontology given that certain other axioms are in

it and so forth. It is not possible to say much more at

this juncture regarding the feasibility of this type of

approach to statistical inference over ontologies; but

it is an intriguing idea that would certainly be deser-

ving of further examination after the development of

an adequate model for the generation of random on-

tologies.

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