Paper Summary - Uncertainty in Ontologies: Dempster-Shafer Theory for Data Fusion Applications

"Uncertainty in Ontologies: Dempster-Shafer Theory for Data Fusion Applications", A.
Bellenger1 and S. Gatepaille, Defence and Security Information Processing, Control and Cognition department, France

This paper is relevant to my work because they use DS to represent uncertainty in ontologies. They do this by creating an upper ontology that contains the DS measures calculated i.e mass, belief, plausibility, etc.


The paper starts with a background in data fusion and gives some examples of how uncertainty is captured in ontologies and why it is important to represent uncertainty. They define uncertainty as "incomplete knowledge, including incompleteness, vagueness, ambiguity, and others". In addition to the natural occurrence of uncertainty in data, it is also a product of fusing data which may be acquired from different sources.

This is an interesting statement: " If the user/application is not able to decide in favor of a single alternative (due to insufficient trust in the respective information sources), the aggregated statement resulting from the fusion of multiple
statements is typically uncertain. The result needs to reflect and weight the different information inputs appropriately, which typically leads to uncertainty."

This is the common in military applications and in general knowledge bases because one attempts to acquire supporting data for entities in the knowledge base from various sources that can be unreliable.

They briefly discuss the shortcomings in current traditional methods to handle uncertainty in ontologies. They state that since ontologies are designed to contain concepts and relations only that describe asserted facts about the world, that they are not designed to handle uncertainty. The facts asserted are assumed to be 'true'. Therefore even information that is not certain to be 'true' are stored and lead to errors or inaccurate information. There is not a standard way to handle uncertainty currently (can read more on this).

They discuss how probability is used as a way to represent uncertainty in ontologies. They discuss some existing work in this area including (BayesOWL). The problem with this approach in particular is that it does not account for OWL properties, instances of the ontologies or the data types. There are also extensions to DL (Pronto is one of them), however performance is a problem. There are also Fuzzy approaches that exist.

They then discuss using DS. DS is presented as a generalized probability theory, however books related to this topic are not exactly is agreement with this representation. Masses are calculated and the sum of these masses make up the beliefs. It is also noted that is supports combining evidence from different sources which makes it especially useful for fusing data from different sources. They note work that actually use DS to handle the inconsistencies produced by mapping ontologies. However it also highlights a relevant paper that translates an OWL taxonomy into a directed evidential network.

The rest of the paper discusses their approach and how they use DS for modeling and reasoning. The point they make about uncertainty and why probabilistic methods can't represent it accurately is p-methods do not represent the absence of information very well. One needs to specify prior and conditional probabilities. They argue this leads to a minimax error due to is nature of symmetry prior probability assignment (.5) when information is not available. With DS missing information is not applied unless obtained indirectly. It allows one to specify a degree of ignorance (some define this as an upper and lower bound). They find this property to be appealing.


Probabilistic approaches use singletons only where DS allows one to use composites in addition to singletons. This is powerful. With probability theory there is a relationship between an event and its negation, DS does not imply a relationship between an event and its negation, it only models beliefs associated with a class.

They mention an additional point that I find makes this approach appealing. DS provides a way to combine evidence from different sources. This makes it especially useful for fusion.

They state, "the evidence theory is much more flexible than the probability theory". This is a strong statement and I'm not sure if it is completely true based on other papers that show how both Bayesian and DS can produce similar results.

Ok the paper ends with their approach. They discuss their proposed model which is an upper ontology representing the uncertainty. A DS_Concept which is a subclass of OWL:Thing has a DS_Mass, DS_Belief, DS_Plausibility, and a DS_Source. The Uncertain_Concept represents a concept that is part of the set. There is an object property is_either which has a range of owl:Thing so that all instances can be used.

This paper isn't cited by anyone else but I think there are good ideas proposed here and I am using this paper in my 601 work.