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FORMAL ONTOLOGIES AND UNCERTAINTY
Matteo CAGLIONI, Giovanni FUSCO
Université de Nice Sophia Antipolis / CNRS ESPACE UMR7300
Eighth International Conference INPUTSmart City - Planning for Energy, Transportation
and Sustainability of the Urban SystemNaples, June 4th-6th 2014
Summary
1. Why Uncertainty?
2. Why Ontologies?
3. Uncertain Ontologies
4. Ontology of Uncertain Relations: an example
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
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:
Uncertainty in Geographic Information
But Geographic Information is not everything: from Information to Knowledge …
Geographic Knowledge
Relations
Descriptive Geography
Explicative Geography
SpaceTime
Theme
Domain of Semantic
Uncertainty Domain of Syntactic
Uncertainty
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)
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
Ontology: formalisation
Not formal Ontology
Semi-formal Ontology
Formal Ontology
Protocol on natural languageEx. City = agglomeration of population and non-agricultural activitiesEx. 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
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
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
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.
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)
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
Ontology and POSSIBLISTIC LOGIC
Possibility theory: integrating the uncertainty of knowledge from the point of view of the expert
Possibility () = degree of surprise of the expert for an outcomeNecessity (N) = certainty of the outcome
N (C) = 1 – (¬C)
Possibilistic ontologies: reasoning with epistemic uncertainty (ex. max-min composition of and N measures, etc.)
Ontology of Uncertain Relations: an example
Does household preference for individual housing cause sprawl?
Preference for Individual Housing
Preference for Individual Housing
Urban SprawlUrban Sprawl
Truth TablePref. = Ind.
HousingPref. = 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
Ontology of Uncertain Relations: an example
Cond. Probab.Pref. = Ind.
HousingPref. = 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.
HousingPref. = 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
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
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.
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