The model elimination calculus is a linear, refutationally complete calculus for first order clause logic. We show how to extend this calculus with aframeworkfor theory reasoning. Theory reasoning m~ans to separate the knowledge of a given domain or theory and treat it by special purpose inference rules. We present two versions of theory model elimination: the one is called total theory model e...

The history of Model Theory can be traced back to the work of Charles Sanders Peirce and Ernst Schröder, when semantics started playing a role in Logic. But the first outcome dates from 1915. It appears in the paper Über Möglichkeiten im Relativkalkül (Math. Ann. 76, 445-470) by Leopold Löwenheim. The period from 1915 to 1935 is, in words of R.L. Vaught, extraordinary. The method of elimination...

Sparse Gaussian Elimination on High Performance Computers

Compiling a solver-independent constraint model to solver input usually involves flattening, the decomposition of complex constraints into simpler expressions to suit the solver, introducing additional variables and constraints. In previous work [8], we have proposed extending flattening with common subexpression elimination (CSE) which can reduce the overhead introduced during flattening. In t...

In this work, we identify and study the presence of extremely intense surface resonances that frustrate the coupling of photons into a photonic crystal over crucial energy ranges. The practical utility of photonic crystals demands the capability to exchange photons with the external medium; therefore, it is essential to understand the cause of these surface resonances and a route to their elimi...

Constraint modelling is difficult, particularly for novices. Hence, automated methods for improving models are valuable. The context of this paper is tailoring, a process where a solver-independent constraint model is adapted to a target solver. Tailoring is augmented with automated enhancement techniques, in particular common subexpression detection and elimination, which, while powerful, can ...