Similarity search is becoming popular in even more disciplines, such as multimedia databases, bioinformatics, social networks, to name a few. The existing indexing techniques often assume the metric space model that could be too restrictive from the domain point of view. Hence, many modern applications that involve complex similarities do not use any indexing and use just sequential search, so they are applicable only to small databases. In this paper we revisit the assumptions which persist in the mainstream research of content-based retrieval. Leaving the traditional indexing paradigms such as the metric space model, our goal is to propose alternative methods for indexing that shall lead to high-performance similarity search. We introduce the design of the algorithmic framework SIMDEX for exploration of analytical properties (axioms) useful for indexing that hold in a given complex similarity space but were not discovered so far. Consequently, the known axioms will be localized as a subset within the universe of all axioms suitable for indexing. Speaking in a hyperbole, for database research the discovery of new axioms valid in some similarity space might have an impact comparable to the discovery of new laws of physics holding in parallel universes.
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