In this article we first show how the functional and the optimized functional translation from modal logic to many-sorted first-order logic can be naturally extended to the hybrid language H(@, ↓). The translation is correct not only when reasoning over the class of all models, but for any firstorder definable class. We then show that sorts can be safely removed (i.e., without affecting the sat...

In this note, we show by a proof-theoretical argument that in full linear logic the set of formulas for which contraction and weakening are admissible (the set of saturated formulas) does not coincide (up to equivalences) with the set of exponentiated formulas. This solves an open problem of Schellinx.

We present BFL, a hybrid logic for representing uncertain knowledge. BFL attaches a quantified notion of belief based on Dempster-Shafer’s theory of belief functions to classical first-order logic. The language of BFL is composed of objects of the form F:[a,b], where F is a first-order sentence, and Q and b are numbers in the [O,l] interval (with c&b). Intuitively, a measures the strength of ou...