It’s true, I guess, that faceted search won’t let you form attribute-combinations that aren’t lexicalized, since faceted navigation is always restricted to attributes of documents found in the search result. In other words, you can never navigate into zero-hits.

Do you think it’s possible to use concept lattices for search result visualization?

In search for your reference on this, Formal Concept Analysis (FCA) is a very nice framework for looking at concept spaces and exploring combinations of properties that are determinant for a concept. In short, FCA implies that a concept is constituted by a set of binary attributes.

A concept space is thus constituted by a matrix of objects and attributes. Imagine attributes such as “acidic”, “round”, “oval”, “yellow”, and “orange” as a set of properties (attributes) to determine a bunch of fruits (objects). By applying (i.e. combining) them, we have a way of telling e.g. a lemon from a grapefruit or orange.

What’s really nice about FCA is the fact that you can visualize the matrix as a concept lattice thus providing a nice tool for exploring concept spaces: You can easily see which attribute-combinations constitute an object and (maybe even more important) what attribute-combinations are not lexicalized, i.e. do not have a name of their own. In my example, we’d see that the acidic fruits could be called something like citrus-fruits, while oval fruits (or yellow ones) do not have a name per se.

Combining the available concepts beforehand and see how combinations are (or are not) realized could be really useful for search – for example when it comes to avoiding unfavorable zero-hit experiences.