Abstract
The purpose of this paper is to present a first step in a formal study of inheritance systems. The kind of systems considered are those that support overriding (all definitions being taken as defaults) and multiple inheritance. The overriding is based on the explicit statement of negative information. The basic entities are classes and properties. The system is hierarchic because it is made out of classes which are structured as a hierarchy. We consider both the basic case of properties restricted to atomic propositional formulas and their negations, and the extension to properties defined by rules in the Logic Programming style. A formal definition of hierarchic systems is given for which a model-theoretic 3-valued semantics is introduced. This semantics is explicitly stated in terms of sets of individuals. It defines the notion of interpretation, the characterization of models, and what is meant by validity of formulas in such structures. The inheritance mechanism is able to choose from a set of inherited default properties which ones mechanism be overriden in order to guarantee that the local program has a model. The notion of characteristic individuals of classes, introduced in our semantics, turns out to play a clarifying role of the relationship between semantic and syntactic aspects of inheritance systems.

Abstract
The purpose of this paper is to present a first step in a formal study of inheritance systems. The kind of systems considered are those that support overriding (all definitions being taken as defaults) and multiple inheritance. The overriding is based on the explicit statement of negative information. The basic entities are classes and properties. The system is hierarchic because it is made out of classes which are structured as a hierarchy. We consider both the basic case of properties restricted to atomic propositional formulas and their negations, and the extension to properties defined by rules in the Logic Programming style. A formal definition of hierarchic systems is given for which a model-theoretic 3-valued semantics is in roduced. This semantics is explicitly stated in terms of sets of individuals. It defines the notion of interpretation, the characterization of models, and what is meant by validity of formulas in such structures. The inheritance mechanism is able to choose from a set of inherited default properties which ones must be overriden in order to guarantee that the local program has a model. The notion of characteristic individuals of classes, introduced in our semantics, turns out to play a clarifying role of the relationship between semantic and syntactic aspects of inheritance systems. © Springer-Verlag Berlin Heidelberg 1991.

Abstract
The value of the signal in one point of the variable is presented as the component of the vector in the basis vector associated with that point. The decomposition of the signal in its components is called the Dirac transform. The change of the convolution into a multiplication, made by the Fourier transform, is a change of bases in the linear space where the signals are defined.

Abstract
It is shown that in using the Laplace transform one has to start with the condition that imposes f(0-) = 0 in order to avoid errors in the derivative and integral operations. In that case the matrix representation of the circuits using the Laplace transform becomes possible and the resolution of integral-differential equations is straightforward. Nevertheless, it is possible to use the Laplace transform with signals that have no null initial conditions, keeping the mathematical coherence, by choosing between two ways: (1) shifting the origin of time domains to the left to obtain the null initial conditions, and (2) using the superposition theorem to obtain one partial signal with null initial conditions.

Abstract

Abstract
In this paper the work of the Computer Graphics & CAD group at INESC.Norte, in Solid Modelling, Surface Generation, Visibility and other 3D areas, is described. This group has created a working environment, based on a 3D kernel developed at INESC, which allowed the easy integration of other works, ranging from Solid Modelling to Surface Generation to Visibility, ect. The results achieved seem to be good enough to encourage to continue our effort, so that, in the near future, we can have a stronger and more flexible 3D kernel, good enough to be used in industrial developments and as a research starting point, for areas like Image Synthesis, 3D Graphics User Interfaces, and so on. © 1990.