that eta reduction is useful for adapting substitution calculi for practical problems like higher order uni cation. This paper concentrates on rewrite rules for eta reduction in three dierent styles of explicit substitution calculi: , se and the suspension calculus. Both and se when extended with eta

to preserve termination and conuence of the associated substitution calculus and to correspond to the eta-reductions of the other two calculi. Additionally, we prove that and s e as well as and the suspension calculus are non comparable while s e is more adequate than the suspension calculus.

and the suspension calculus; other explicit substitutions calculi can be easily incorporated into the system. An implementation of the η-reduction is provided for each of these explicit substitutions calculi. This system has been of great help for systematically comparing explicit substitutions calculi, as well

, the λs e , the suspension calculus and a refinement of the suspension calculus called combining suspension calculus which allows for combination of steps of β-contraction; other explicit substitutions calculi can be easily incorporated into the system. An implementation of the η-reduction is provided

SUBSEXPL is a system originally developed to visualise reductions, simplifications and normalisations in three important calculi of explicit substitutions and has been applied to understand and explain properties of these calculi and to compare the different styles of making explicit

substitutions proposed by de Bruijn and called Cλξφ. In this paper, we introduce λν, we present Cλξφ in the same framework as λν and we compare both calculi. Moreover, we prove properties of λν; namely &

is the crucial difference with the treatment of equalities in the tableau system for hybrid logic previously proposed by van Eijck [10]. In order to evaluate the impact of the different approaches to nominal equalities of the considered calculi, they have been implemented and their performances compared

. While resolution is much more efficiently implementable (compared to Hilbert-type calculi), the search space is still huge. Thus it was suggested to restrict resolution and apply it to a smaller class of formulae: Horn clauses. This leads to PROLOG as an efficient inference engine for definite logic

eingereicht an der

m]]l]]s¶D]]¿÷mB]iv]b]oD]m¶¨]iv]§]iv]r]j]t¿rv]]irj]]t]]m] / | ap]]r¿]ÎNy]s¶D]]mb¶r]ix} Û]Ix]]rd]mb]} p—N]t]o%ism] in]ty]m] / || Û]Is]¡uÎc]rN]]riv]nd]p]*N]m]st¶ I always bow to Śri ̄ Śāradāmbā, the limitless ocean of the nectar of compassion, who bears a rosary, a vessel of nectar, the symbol of knowledge and a book in Her lotus hands. Dedicated to the Lotus Feet of the revered Sadguru. This thesis presents a new active mask (AM) framework and an algorithm for segmenta-tion of digital images, particularly those of punctate patterns from fluorescence microscopy. Fluorescence microscopy has greatly facilitated the task of understanding complex sys-tems at cellular and molecular levels in recent years. Segmentation, an important yet dif-ficult problem, is often the first processing step following acquisition. Our team previously demonstrated that a stochastic active contour based algorithm together with the concept of