mUnc Vocabulary Specification

Table of Content

1. An ontology for Uncertainty Representation: mUnc
2. Examples
3. Classes
4. Object Properties
5. Namespace Declarations

An ontology for uncertainty representation: mUnc

The open nature of the Web allow the existence of fuzzy, vague, or uncertain information for which exists no standard on the Semantic Web. The aim from mUnc is to offer a formal, publishable and reusable representation of uncertainty over the web of linked data, and allow the integration of many theories [1-4] about "uncertainty reasoning". Moreover, this vocabulary offer a way to link between the theories and their calculus.

The current version enables uncertainty representation at different levels of granularity. Uncertainty can be linked to a sentence or to a world (context).

The figure below shows the core classes and properties of mUnc.

In the version 2 of mUnc, an extension allowing the representation of translatability of uncertainty theories, as shown in the figure below:

Examples

In this section, we show some examples to illustrate metadata encoding using mUnc.

Example 1

In this example, we represent the probability theory using mUnc. This theory have one feature representing the probability of the assertion to be true (ex:probabilityValue). The value linked to this feature is a decimal and can be manipulated using different operations (for the sake of the example: Conjunction, Disjunction, Negation). The calculus is represented using LDScript functions.

  prefix ex: <http://example.org/>
  prefix munc: <http://ns.inria.fr/munc/>

    ex:Probability  a   munc:UncertaintyApproach;
                    munc:hasUncertaintyFeature  ex:probabilityValue;
                    munc:hasUncertaintyOperator ex:and, ex:or, ex:not.

    ex:probabilityValue a munc:uncertaintyFeature;
                        rdfs:range xsd:decimal.
              
    ex:probabilityValue ex:and  ex:conjunctionFunction;
                        ex:or   ex:disjunctionFunction;
                        ex:not  ex:negationFunction.

The operations are LDScript functions. Each function have a URI enabling its deferenciation.

  function munc:conjunctionFunction(?P1, ?P2){
    ?P1 * ?P2
  }
  

Once the approach, the Features and the calculus are defined, we can define the values. In this example we annotated both context ex:Biology and sentence ex:S1 with probability information.

    ex:S1 munc:hasMeta [a munc:Uncertainty;
                        ex:probabilityValue 0.7]. 

    ex:Biology munc:hasMeta [a munc:Uncertainty;
                        ex:probabilityValue 0.5].

Finally, a SPARQL query engine can translate the code and match each triple with its convenient uncertainty value. We use LDScript to define the operations (functions for calculus) linked to uncertainty theories.

prefix ex: < http://example.org/ > .
prefix munc: < http://ns.inria.fr/munc/ > .

SELECT ?g ?s ?p ?o ?meta WHERE {
  {
    GRAPH ?g {
      ?s ?p ?object
      ?object rdf:value ?o
      ?object munc:hasMeta ?sentenceMeta
    }
  }
  UNION
  {
    GRAPH ?g {
      ?s ?p ?o
      FILTER (!EXISTS {?o rdf:value ?ob. ?o munc:hasMeta ?mm} && !EXISTS{?s a munc:Uncertainty} && !EXISTS{?s rdf:value ?ob})
    }
    BIND(false as ?sentenceMeta)
  }

  ?g munc:hasMeta ?contextMeta
  BIND(munc:metaList(?sentenceMeta, ?contextMeta) AS ?meta)
}

function munc:metaList(?xT, ?xG){
  let(SELECT ?xT ?xG (group_concat(?FV;separator="-") as ?metaD) WHERE
        {
            {
                SELECT ?xT ?xG (CONCAT(?xF,'=',?xV) AS ?FV) WHERE
                {
                ?xG ?xF ?xV1
                OPTIONAL {?xT ?xF ?xV2}
                ?xF rdfs:subPropertyOf munc:uncertaintyFeature
                ?xF ex:and ?xFFunction
                BIND(IF(BOUND(?xV2),funcall(?xFFunction,?xV1,?xV2),?xV1) AS ?xV)
                } GROUP BY ?xT ?xG
            }
            UNION
            {
                SELECT ?xT ?xG (CONCAT(?xF,'=',?xV) AS ?FV) WHERE
                {
                ?xT ?xF ?xV
                ?xF rdfs:subPropertyOf munc:uncertaintyFeature
                FILTER NOT EXISTS {?xG ?xF ?xV2}
                } GROUP BY ?xT ?xG
            }
        }
    )
  {
    ?metaD
  }
}

Classes

• Meta
• Sentence
• Uncertainty
• Uncertainty Approach
• Uncertainty Operation
• Uncertainty Value
• World
• Translation Function

Object Properties

• hasMeta
• hasUncertaintyApproach
• hasUncertaintyFeature
• hasUncertaintyOperator
• statedIn
• uncertaintyFeature
• uncertaintyOperator
• translateFrom
• translateTo
• hasTranslation
• hasIdealTranslation
• hasFullTranslation

Namespace Declarations back to ToC

default namespace

http://ns.inria.fr/munc/

owl

http://www.w3.org/2002/07/owl#

rdf

http://www.w3.org/1999/02/22-rdf-syntax-ns#

rdfs

http://www.w3.org/2000/01/rdf-schema#

v2

http://ns.inria.fr/munc/v2#

xsd

http://www.w3.org/2001/XMLSchema#