What is the "presumption of validity" as it relates to claim interpretation?

This is another principle of claim interpretation that patent claims should, if possible, be read in a manner that preserves their validity.  The underlying assumption here is that a claim approved by the Patent Office should be presumed valid, and so if a claim is subject to multiple interpretations, the interpretation that supports validity (i.e., the one that avoids the prior art) must be the one that the Patent Office had in mind.  However, this principle has limits:  it does not justify a claim interpretation that is unreasonable or contrary to the weight of the evidence.