Generalizing completeness results for loop checks in logic programming

AbstractLoop checking is a mechanism for pruning infinite SLD-derivations. In (Bol, Apt and Klop, 1991) simple loop checks were introduced and their soundness, completeness and relative strength was studied. Since no sound and complete simple loop check exists even in the absence of function symbols, subclasses of programs were determined for which the (sound) loop checks introduced by Bol are complete.In this paper, the Generalization Theorem is proved. This theorem presents a method to extend (under certain conditions) a class of programs for which a given loop check is complete to a larger class, for which the loop check is still complete. Then this theorem is applied to the results of Bol, giving rise to stronger completeness theorems.It appears that unnecessary complications in the proof of the theorem can be avoided by introducing a normal form for SLD-derivations, allowing only certain most general unifiers. This normal form might have other applications than those in the area of loop checking

An analysis of loop checking mechanisms for logic programs

AbstractWe systematically study loop checking mechanisms for logic programs by considering their soundness, completeness, relative strength and related concepts. We introduce a natural concept of a simple loop check and prove that no sound and complete simple loop check exists, even for programs without function symbols. Then we introduce a number of sound simple loop checks and identify natural classes of Prolog programs without function symbols for which they are complete. In these classes a limited form of recursion is allowed. As a by-product we obtain an implementation of the closed world assumption of Reiter (1978) and a query evaluation algorithm for these classes of logic programs

Theory of Luminescent Emission in Nanocrystal ZnS:Mn with an Extra Electron

We consider the effect of an extra electron injected into a doped quantum dot $ZnS:Mn^{2+}$. The Coulomb interaction and the exchange interaction between the extra electron and the states of the Mn ion will mix the wavefunctions, split the impurity energy levels, break the previous selection rules and change the transition probabilities. Using this model of an extra electron in the doped quantum dot, we calculated the energy and the wavefunctions, the luminescence probability and the transition lifetime and compare with the experiments. Our calculation shows that two orders of magnitudes of lifetime shortening can occur in the transition $^4T_1-^6A_1$ when an extra electron is present.Comment: 15 pages, 2 Figs No change in Fig