Relevance as Deduction: A Logical View of Information Retrieval

The problem of Information Retrieval is, given a set of documents D and a query q, providing an algorithm for retrieving all documents in D relevant to q. However, retrieval should depend and be updated whenever the user is able to provide as an input a preferred set of relevant documents; this process is known as relevance feedback. Recent work in IR has been paying great attention to models which employ a logical approach; the advantage being that one can have a simple computable characterization of retrieval on the basis of a pure logical analysis of retrieval. Most of the logical models make use of probabilities or similar belief functions in order to introduce the inductive component whereby uncertainty is treated. Their general paradigm is the following: find the nature of conditional d → q and then define a probability on the top of it . We just reverse this point of view; first use the numerical information, frequencies or probabilities, then define your own logical consequence. More generally, we claim that retrieval is a form of deduction. We introduce a simple but powerful logical framework of relevance feedback, derived from the well founded area of nonmonotonic logic. This description can help us evaluate, describe and compare from a theoretical point of view previous approaches based on conditionals or probabilities. The first difficulty one encounters towards a logical approach to Information Retrieval is how one should view the algorithm which returns a set of relevant documents. Our proposal is to see such an algorithm as a proof. However, this proof is not classical because, as it is widely recognized, q → d, where q is a query and d a document relevant to q, is not conveyed by the material implication (see [vR86],[vR89]). Also, as the set of data which this proof is based is subject to updating, nonmotonicity arises. Since there is no need of nesting implications, implication and deduction can be identified and therefore our starting point is to axiomatize a deduction q ∼ d. The consequence relation ∼ will reflect the properties that relevance satisfies. A similar approach where nonmonotonic