Similarity is some degree of symmetry in either analogy and resemblance between two or more concepts or objects. The notion of similarity rests either on exact or approximate repetitions of patterns in the compared items. In the case of approximate repetitions we talk about statistical similarity as found in a fractal and its parts. Finding similarities or distinguishing between dissimilarities depends on the faculties of pattern recognition and disambiguation, respectively.
A general method to calculate probability of an event based on another similar event is called relative probability
If A, B are different events
Probability of A = P(A)
Then P(B) = P(A) x R where R is the similarity ratio between A,B
If A=B --> R=1
If A<>B --> R=0
Specific definitions
Different fields provide differing definitions of similarity:
In philosophy, similarity is defined as sharing properties or characteristic traits. The sky is similar to the sea, for example, because the sky and the sea both share the property of being blue. This definition has some interesting consequences. First, it follows that resemblance is reflexive, since everything shares its own properties. Second, it follows that resemblance is symmetric, since if x shares properties with y then y shares those same properties with x. Third, qualitative identity turns out to be a limiting case of resemblance, since qualitative identity is defined as sharing all rather than some properties.
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