Interpolation for extended modal languages

Abstract

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 [7]. 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.