It is well-known that intuitionistic propositional logic Int may be faithfully embedded not just into the modal logic S4 but also into the provability logics GL and Grz of Gödel-Löb and Grzegorczyk, and also that there is a similar embedding of Grz into GL. Known proofs of these faithfulness results are short but model-theoretic and thus non-constructive. Here a labelled sequent system Grz for ...

This paper presents two sufficient conditions to ensure a faithful evaluation of polynomial in IEEE-754 floating point arithmetic. Faithfulness means that the computed value is one of the two floating point neighbours of the exact result; it can be satisfied using a more accurate algorithm than the classic Horner scheme. One condition here provided is an a priori bound of the polynomial conditi...

We consider the Burau and Gassner representations of the braid groups B„ . A sufficient condition for faithfulness, involving just a pair of arcs, is shown to be necessary as well for all but at most two values of n. In the Burau case, this implies nonfaithfulness for n > 10 . Alexander showed in [6] that any knot K can be made by connecting the ends of some braid b. The Alexander polynomial A(...