Modelling an Information Retrieval Systems (IRS) consists on building a formal description of an IRS module (Analysis, Indexing, Matching, or Ranking). This modelling activity is essential to understand the behavior of existing IRS, and it can be a way to proposed alternative and better IRS solutions. We work on modelling the matching and ranking IRS activity by using logical models. The use of logic for this modelling, rises from the following hypothesis:
A document is an answer to a query, if there exists a logical deduction chain that starts from the document and ends to the query.
This deduction chain can be a fuzzy one, i.e. a probability to deduce the query from the documents and used for ranking. We have proposed a new IR logic matching model using logical Boolean lattice mixed with a probabilistic function over this lattice.This modelling enables matching functions to be decomposed into a direct matching function (deduction from the document to the query), and a reverse matching function, that evaluate the strength of the deduction from the query to the document. Moreover we have shown that most IR matching function can be decomposed into these two more basic matching functions. This work as conducted to a PhD thesis (Mr. Abdulahhad), and as also being published as short paper in the top conference ACM-SIGIR 2013.