Including Qualitative Knowledge in Semiqualitative Dynamical Systems

A new method to incorporate qualitative knowledge in semiqualitative systems is presented. In these systems qualitative knowledge may be expressed in their parameters, initial conditions and/or vector fields. The representation of qualitative knowledge is made by means of intervals, continuous qualitative functions and envelope functions. A dynamical system is defined by differential equations with qualitative knowledge. This definition is transformed into a family of dynamical systems. In this paper the semiqualitative analysis is carried out by means of constraint satisfaction problems, using interval consistency techniques

Automatic Semiqualitative Analysis: Application to a Biometallurgical System

The aim of this work is the representation and analysis of semiqualitative models. Their qualitative knowledge is represented by means of qualitative operators and envelope functions. A semiqualitative model is transformed into a family of quantitative models. In this paper the analysis of a model is proposed as a constraint satisfaction problem. Constraint satisfaction is an umbrella term for a variety of techniques of Artificial Intelligence and related disciplines. In this paper attention is focused on intervals consistency techniques. The semiqualitative analysis is automatically made by means of consistency techniques. The presented method is applied to a industrial biometallurgical system in order to show how increase the capacity of production

An introduction to interval-based constraint processing.

Constraint programming is often associated with solving problems over finite domains. Many applications in engineering, CAD and design, however, require solving problems over continuous (real-valued) domains. While simple constraint solvers can solve linear constraints with the inaccuracy of floating-point arithmetic, methods based on interval arithmetic allow exact (interval) solutions over a much wider range of problems. Applications of interval-based programming extend the range of solvable problems from non-linear polynomials up to those involving ordinary differential equations. In this text, we give an introduction to current approaches, methods and implementations of interval-based constraint programming and solving. Special care is taken to provide a uniform and consistent notation, since the literature in this field employs many seemingly different, but yet conceptually related, notations and terminology

Novel Approaches to Numerical Software with Result Verification

Traditional design of numerical software with result verification is based on the assumption that we know the algorithm ¦¨§� © ©���� £��������� � that transforms input © ©�� into �� � £��������� � ©���� the output, and we £��������� � know the intervals of possible values of the inputs. Many real-life problems go beyond this paradigm. In some cases, we do not have an algorithm ¦, we only know some relation (constraints) between ©� � and. In other cases, in addition to knowing the intervals, we may know some relations between; we may have some information about the probabilities of different values of © � , and we may know the exact values of some of the inputs (e.g., we may know that © £ ���¨�� �). In this paper, we describe the approaches for solving these real-life problems. In Section 2, we describe interval consistency techniques related to handling constraints; in Section 3, we describe techniques that take probabilistic information into consideration, and in Section 4, we overview techniques for processing exact real numbers

Novel Approaches to Numerical Software with Result Verification

Abstract. Traditional design of numerical software with result verification is based on the assumption that we know the algorithm ¦¨§� © ©���� £��������� � that transforms inputs © ©�� into �� � £��������� � ©���� the output, and we £��������� � know the intervals of possible values of the inputs. Many real-life problems go beyond this paradigm. In some cases, we do not have an algorithm ¦, we only know some relation (constraints) between ©� � and. In other cases, in addition to knowing the intervals, we may know some relations between; we may have some information about the probabilities of different values of © � , and we may know the exact values of some of the inputs (e.g., we may know that © £ ���¨�� �). In this paper, we describe the approaches for solving these real-life problems. In Section 2, we describe interval consistency techniques related to handling constraints