formal ontologies and uncertainty - input2014
DESCRIPTION
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.TRANSCRIPT
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.
