Several extensions of the basic modal language are characterized in terms of interpolation. Our main results are of the following form: Language ℒ' is the least expressive extension of ℒ with interpolation. For instance, let ℳ(D) be the extension of the basic modal language with a difference operator . First-order logic is the least expressive extension of ℳ(D) with interpolation. These characterizations are subsequently used to derive new results about hybrid logic, relation algebra and the guarded fragment.
"Interpolation for extended modal languages." J. Symbolic Logic 70 (1) 223 - 234, March 2005. https://doi.org/10.2178/jsl/1107298517