Representation

Formal representation of uncertain knowledge

Sometimes it is useful to look at a knowledge base as a map. This map can be partitioned according to different criteria, e.g. the source of the facts or their domain. While on such a map the knowledge is usually locally consistent, it is almost impossible and practically infeasible to maintain a global consistency. Experience in developing the Cyc ontology demonstrated this challenge. Hence, a system must be able to identify sources of inconsistency and deal with contradicting statements in such a way that it can still produce derivations that are reliable

In the traditional bivalent-logic based formalisms we, that is the users or the systems, have to make a decision. Once two contradictory statements are identified, one has to be chosen as the right one. While this is possible in domains that are axiomatized, fully explored or in which statements are true by definition, it is not possible for most scientific domains. In the life sciences for instance, hypotheses have to be evaluated, contradicting statements have promoting data, etc. Decisions have to be deferred until enough data is available that either verifies or falsifies the hypothesis. Nevertheless, it is desirable to express these hypotheses formally to have means to computationally evaluate them on the one hand and to exchange them between different systems on the other.

In order to allow the sort of reasoning that would allow this, the expressiveness of the formalism needs to be increased. It is known that increasing the expressive power of a KR language causes problems relating to computability. This has been the main reason for limiting the expressive power of KR languages. The real power behind human reasoning however is the ability to do so in the face of imprecision, uncertainty, inconsistencies, partial truth, and approximation.

Some related literature
• Umberto Straccia, e.g. A Fuzzy Description Logic
• Rosalba Giugno, Thomas Lukasiewicz. P-SHOQ(D): A Probabilistic Extension of SHOQ(D) for Probabilistic Ontologies in the Semantic Web
• Lotfi A. Zadeh. Zadeh, L.A. (2002). Toward a perception based theory of probabilistic reasoning with imprecise probabilities. Journal of Statistical Planning and Inference, 105, 233-264.
• Amit Sheth, Cartic Ramakrishnan and Christopher Thomas. Semantics for the Semantic Web: The Implicit, the Formal and the Powerful (to appear in Int’l Journal on Semantic Web & Information Systms, 1(1), 1-18, Jan-March 2005)