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
Temporal reasoning is recognized as a key problem in many Al areas, namely knowledge bases, natural language processing and planning. The ability to deal with partial knowledge is particularly important in a temporal domain. We describe a temporal language that accounts for incompletely specified temporal information about propositions. The language is semantically based on the notion of maximal interval, the denotation of a proposition being a set of maximal intervals where it holds. The main differences between classical formalisms such as those by Allen, McDermott, Shoham and Kowalski and our approach are briefly discussed. In a partial KB, abduction on the temporal order is generally needed to answer a query, and the answer is then conditional on the abduced facts. To comply with the intended semantics, an implicit form of temporal consistency has to be enforced, and this presents the main challenge to the design of the inference mechanism. We present here the syntax and declarative semantics of a propositional version of the language of maximal intervals and a first discussion of the problems in designing an inference system adequate to work with this temporal framework.

Abstract
The ability to deal with partial knowledge is particularly important in a temporal domain. We describe a temporal language that accounts for incompletely specified temporal information about propositions. Temporal terms in the language denote time instants and inequality constraints are used to keep incomplete information about their order. The language is semantically based on the notion of maximal interval, the denotation of a proposition being a set of maximal intervals where it holds. The adequacy of maximal intervals for temporal knowledge representation has been justified elsewhere [5]. In a partial KB, abduction on the temporal order is generally needed to answer a query, and the answer is then conditional on the abduced facts. To comply with the intended semantics, an implicit form of temporal consistency has to be enforced, and this presents the main challenge to the design of the inference mechanism. We present here the syntax and declarative semantics of a propositional version of the language of maximal intervals and a first discussion of the problems in designing an inference system adequate to work with this temporal framework. Rather than presenting a complete solution, we discuss several a roaches.

Abstract

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.