The introduction of sorts to rst-order automated deduction has brought greater conciseness of representation and a considerable gain in eeciency by reducing the search space. It is therefore promising to treat sorts in higher order theorem proving as well. In this paper we present a generalization of Huet's Constrained Resolution to an order-sorted type theory T with term declarations. This sys...

We study the problem of comparing ageing patterns lifetimes k-out-of-n systems with i.i.d. components. Mathematically, this reduces to being able decide about a stochastic ordering relationship between different order statistics. discuss such relationships respect second-order dominance, obtaining characterizations through verification relative convexity suitably chosen reference distribution f...

When processing a data-stream in small space, how important is the order in which the data arrives? Are there problems that are unsolvable when the ordering is worst-case, that can typically be solved in practice? Does the role of ordering become less significant when we permit algorithms to make multiple passes over the data-stream if the stream is not re-ordered between each pass? If we consi...