Formal ontologies have proved to be a very useful tool to manage interoperability among data, systems and knowledge. In this paper we will show how formal ontologies can evolve from a crisp, deterministic framework (ontologies of hard knowledge) to new probabilistic, fuzzy or possibilistic frameworks (ontologies of soft knowledge). This can considerably enlarge the application potential of formal ontologies in geographic analysis and planning, where soft knowledge is intrinsically linked to the complexity of the phenomena under study. The paper briefly presents these new uncertainty-based formal ontologies. It then highlights how ontologies are formal tools to define both concepts and relations among concepts. An example from the domain of urban geography finally shows how the cause-to-effect relation between household preferences and urban sprawl can be encoded within a crisp, a probabilistic and a possibilistic ontology, respectively. The ontology formalism will also determine the kind of reasoning that can be developed from available knowledge. Uncertain ontologies can be seen as the preliminary phase of more complex uncertainty-based models. The advantages of moving to uncertainty-based models is evident: whether it is in the analysis of geographic space or in decision support for planning, reasoning on geographic space is almost always reasoning with uncertain knowledge of geographic phenomena.

1. FORMAL ONTOLOGIES AND
UNCERTAINTY
Matteo CAGLIONI, Giovanni FUSCO
Université de Nice Sophia Antipolis / CNRS ESPACE UMR7300
Eighth International Conference INPUT
Smart City - Planning for Energy, Transportation
and Sustainability of the Urban System
Naples, June 4th
-6th
2014

2. Summary
1. Why Uncertainty?
2. Why Ontologies?
3. Uncertain Ontologies
4. Ontology of Uncertain Relations: an
example

3. Research on Uncertainty at UMR ESPACE
• PEPS HuMaIn 2014 (Geography – Computer Science)
• Interdisciplinary WG University of Nice Sophia Antipolis
• WG within laboratory ESPACE (Nice, Avignon, Aix/Marseille)
• COST TD1202 (VGI and mapping uncertainty)
Growing awareness of the importance of Uncertainty
in Geographic Knowledge

4. Why Uncertainty?
• Assumption of knowability of the real value (theory of measurement)
• Artefact of a deterministic (or binary) logic
• Need of numbers to execute a model
• Need of numbers from the experts
• Model overestimation (calibration of model parameters)
• Precise values often used just for rough classifications
• Apparent precision fooling decision makers
Not a problem but a solution, to overcome several
problems:

5. Uncertainty in Geographic Information
But Geographic Information is not everything:
from Information to Knowledge …

6. Geographic Knowledge
Relations
Descriptive Geography
Explicative Geography
Space
Time
Theme
Domain of
Semantic
Uncertainty Domain of
Syntactic
Uncertainty

7. Ontology: definition
Term borrowed by Artificial Intelligence, in particular in the
Theory of Knowledge.
Computer Science
Ontology: explicit and formal specification of a shared
conceptualisation [Studer, 1998].
• EXPLICIT (concepts, their extent, their significations, explicitly defined)
• FORMAL (machine understandable)
• SHARED (knowledge based on shared agreement in a group)

8. Ontology: content
Surface, Length, …
The domain objects (classes/instances)
Object Proprieties
House, Street, Activity, Theatre, …
IS_A, Near_To, Contain, …
Relations among objects
Opéra Garnier
IS_A
Theatre
Building
IS_A
Av. de l’Opéra
Street
IS_A
Lead_To

9. Ontology: formalisation
Not formal
Ontology
Semi-
formal
Ontology
Formal
Ontology
Protocol on natural language
Ex. City = agglomeration of population and non-agricultural activities
Ex. Thesauri, WordNet
Concept Instance Valeur
relationCATEGORIE
DE RELATION
OWL
(Ontology Web Language)
- Formalism DL (Description
Logic)
- Evolution of xml
owl.org/resources/StarTrek/starship.owl">
<owl:Ontology rdf:about="">
<owl:imports rdf:resource="http://www.pr-owl.org/pr-owl.owl"/>
</owl:Ontology>
<owl:Class rdf:ID="TimeStep">
<owl:disjointWith>
<owl:Class rdf:ID="SensorReport"/>
</owl:disjointWith>
<owl:disjointWith>
<owl:Class rdf:ID="Zone"/>
</owl:disjointWith>
<owl:disjointWith>
<owl:Class rdf:ID="Starship"/>
</owl:disjointWith>
<rdfs:subClassOf rdf:resource="http://www.pr-owl.org/pr-
owl.owl#ObjectEntity"/>
Graphic protocol

10. Reasoner = tool to perform automatic reasoning with
description logic (≈ 1st
order). It allows to:
• classify object in functional hierarchies,
• verify ontology coherence and consistence,
• infer new knowledge.
It uses an ontology language (OWL) for the specification
of the inference rules.
Reasoning automation:
the Semantic Reasoner

11. Why Ontologies ?
To solve the
problem of the
semantic
difference of
information coming
from different
sources.
To allow automatic
reasoning and the
interaction between
human / machine
To reduce/integrate
the uncertainty of
knowledge in a
study field

12. Ontologies and Uncertainty
Traditional goal: reduce uncertainty through ontologies
of hard knowledge (taxonomies with crisp concepts,
knowledge bases with if-then rules, etc.)
New goal: integrate uncertainty through ontologies of
soft knowledge (probabilistic, fuzzy, possibilistic, ...)
Soft Knowledge widespread in geography and planning.
In this context, even automatic reasoning can benefit
from uncertainty-based approaches.

13. Ontology and PROBABILISTC LOGIC
Subjective Bayesian Probability Theory, the first attempt
to overcome the assumption of frequentist probabilities.
Probabilities = degrees of
belief or rational experts
Conditional probabilities to
represent non-deterministic
relations.
Bayesian Networks (BNs) as
complex probabilistic models.
Probability axioms must be
respected.
Ontologies formalizing probabilistic knowledge for the development of
BNs : OWLOntoBayes (Yi Yang), PR-OWL (Paulo Costa)

14. Ontology and FUZZY LOGIC
Theory of gradual
belonging to concepts,
well suited for
geographic knowledge
(Ch. Rolland-May, B.
Plewe)
Fuzzy OWL and Fuzzy
DL (Bobilo and Straccia):
introducing fuzziness in
taxonomies, relations
among concepts and
reasoning

15. Ontology and POSSIBLISTIC LOGIC
Possibility theory: integrating the uncertainty of knowledge from
the point of view of the expert
Possibility (Π) = degree of
surprise of the expert for
an outcome
Necessity (N) = certainty
of the outcome
N (C) = 1 – Π(¬C)
Possibilistic ontologies: reasoning with epistemic uncertainty (ex.
max-min composition of Π and N measures, etc.)

16. Ontology of Uncertain Relations: an example
Does household preference for individual housing cause sprawl?
Preference for
Individual
Housing
Preference for
Individual
Housing
Urban
Sprawl
Urban
Sprawl
Truth Table
Pref. = Ind.
Housing
Pref. = Coll.
Housing
Sprawl = True True True
Sprawl = False False True
Household Preference Urban Sprawl
causes
has value
Individual Housing Collective Housing
has value
True False
A crisp ontology:
Reasoner can infer
truth value of Urban
Sprawl

17. Ontology of Uncertain Relations: an example
Cond. Probab.
Pref. = Ind.
Housing
Pref. = Coll.
Housing
Sprawl = True 0.8 0.5
Sprawl = False 0.2 0.5
A probabilistic ontology:
Household Preference Urban Sprawl
Probably causes
with parameters …
has value with probability
parameters …
Individual Housing Collective Housing True False
has value with probability
parameters …
Cond. Possib.
Pref. = Ind.
Housing
Pref. = Coll.
Housing
Sprawl = True 1 1
Sprawl = False 0.3 1
A possibilistic ontology:
Household Preference Urban Sprawl
Possibly causes
with parameters …
has value with possibility
parameters …
Individual Housing Collective Housing True False
has value with possibility
parameters …
Reasoner can infer
probability of Urban Sprawl
Reasoner can infer
possibility and necessity
of Urban Sprawl

18. Ontology of Certain/Uncertain Relations
The crisp approach :
Semantic
certainty on the
antecedent
Semantic
certainty on the
antecedent
Semantic
certainty on the
consequent
Semantic
certainty on the
consequent
Syntactic Certainty
on the Relation
The uncertain approach :
Semantic
(un)certainty on
the antecedent
Semantic
(un)certainty on
the antecedent
Semantic
uncertainty on
the consequent
Semantic
uncertainty on
the consequent
Syntactic Uncertainty
on the Relation

19. CONCLUSIONS
• Crisp Ontologies traditionally reduce uncertainty in
phenomena conceptualisation
• Uncertain Ontologies can integrate uncertainty in knowledge
sharing and automated reasoning
• Uncertain Ontologies (probabilistic, fuzzy, possibilistic, ...)
can become building blocks for developping models
• Open question: how to combine uncertain ontologies using
different formalisms.
Reasoning on geographic space is almost always
reasoning with uncertain knowledge on geographic
phenomena.

20. Thanks for your attention!
matteo.caglioni@unice.fr
giovanni.fusco@unice.fr