This paper gives an overview on translation methods we have developed for nonclassical logics, in particular for modal logics. Optimized ’functional’ and semi-functional translation into predicate logic is described. Using normal modal logic as an intermediate logic, other logics can be translated into predicate logic as well. As an example, the translation of modal logic of graded modalities i...

A double-normal pair of a finite set S of points from R is a pair of points {p, q} from S such that S lies in the closed strip bounded by the hyperplanes through p and q perpendicular to pq. A double-normal pair pq is strict if S \ {p, q} lies in the open strip. The problem of estimating the maximum number Nd(n) of double-normal pairs in a set of n points in R, was initiated by Martini and Solt...