In this paper we consider the partial many-sorted first-order logic and its extension to the subsorted partial many-sorted first-order logic that underly the Casl specification formalism. First we present counterexamples showing that the generalization of the Craig Interpolation Property does not hold for these logics in general (i.e., with respect to arbitrary signature morphisms). Then we for...

In order to directly address the potential dangers of estimating rather than measuring GFR in transplantation research protocols, we performed several simulations from a previously described cohort of 500 inulin clearances [5]. This cohort was split into two groups of n=250 each, either according to the date of transplantation (sorted by chronological order, simulation #1) or according to the r...

1 I n t r o d u c t i o n This paper argues that some very significant benefits are available to logic programming from using certain concepts from first order model theory, namely: • order-sorted logic and models; • initial models; • interpretation into rLxed models for certain fLxed sorts, functions and relations; and • true semantic equality. These techniques, which are all standard in the t...

Consider the following scheme to solve the sorting problem: given n numbers to be sorted, after the ith of n (1 ≤ i ≤ n), we will make sure that we have i of input numbers in a sorted list. Clearly these i sorted numbers will partition the ranks of the remaining n− i unsorted numbers into i + 1 intervals. The (i + 1)th step consists of choosing one of the n − i unsorted numbers uniformly at ran...

Some kind of practical problems such as security veri cation of cryptographic protocols can be described as a problem to accomplish a given purpose by using limited operations and limited materials only. To model such problems in a natural way, uni cation problems under constrained substitutions have been proposed. This paper is a collection of results on the decidability and the computational ...