Boolean document retrieval inhibits any form of partial matching. Algebraic and probabilistic models address this matter by assigning non-binary weights to index terms.
One representative algebraic model is the vector space model. In this approach, the IR system represents documents and queries as vectors in a multi-dimensional vector space. In this space, index terms will likely be features of the vector space, and queries and documents are plotted across this space according to the presence and frequency with which they contain index terms. The IR system computes similarity between a search query and documents according to their proximity in vector space.
There are a number of metrics for determining proximity in a vector space model, such as Jaccard and dot product. Perhaps one of the most common, however, is cosine similarity, represented by the formula:

Here, x and y signify two vectors in the vector space. The cosine similarity score can be any value between -1 and 1. The higher the cosine score, the more alike two items are considered.
The IR vector space model returns documents in order according to their measured degree of similarity. In this way, algebraic IR systems, such as the vector space model, allow for partial matching, potentially providing a more precise or nuanced form of information retrieval.13