Uncertain inference was first described by C. J. van Rijsbergen as a way to formally define a query and document relationship in Information retrieval. This formalization is a logical implication with an attached measure of uncertainty.
Rijsbergen proposes that the measure of uncertainty of a document d to a query q be the probability of its logical implication, i.e.:
P(d\toq)
A user's query can be interpreted as a set of assertions about the desired document. It is the system's task to infer, given a particular document, if the query assertions are true. If they are, the document is retrieved.In many cases the contents of documents are not sufficient to assert the queries. A knowledge base of facts and rules is needed, but some of them may be uncertain because there may be a probability associated to using them for inference. Therefore, we can also refer to this as plausible inference. The plausibility of an inference
d\toq
d\toq
By doing this it accomplishes two things:
Multimedia documents, like images or videos, have different inference properties for each datatype. They are also different from text document properties. The framework of plausible inference allows us to measure and combine the probabilities coming from these different properties.
Uncertain inference generalizes the notions of autoepistemic logic, where truth values are either known or unknown, and when known, they are true or false.
If we have a query of the form:
q=A\wedgeB\wedgeC
where A, B and C are query assertions, then for a document D we want the probability:
P(D\to(A\wedgeB\wedgeC))
P((A\wedgeB\wedgeC)|D)
Croft and Krovetz applied uncertain inference to an information retrieval system for office documents they called OFFICER. In office documents the independence assumption is valid since the query will focus on their individual attributes. Besides analysing the content of documents one can also query about the author, size, topic or collection for example. They devised methods to compare document and query attributes, infer their plausibility and combine it into an overall rating for each document. Besides that uncertainty of document and query contents also had to be addressed.
Probabilistic logic networks is a system for performing uncertain inference; crisp true/false truth values are replaced not only by a probability, but also by a confidence level, indicating the certitude of the probability.
Markov logic networks allow uncertain inference to be performed; uncertainties are computed using the maximum entropy principle, in analogy to the way that Markov chains describe the uncertainty of finite state machines.