Measurements, Models, Systems and Design

531 s.

Neutrality and Many-Valued Logics

In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. On the base of non-Archimedean valued logics, we construct non-Archimedean valued interval neutrosophic logic INL by which we can describe neutrality phenomena.Comment: 119 page

Prototype system for supporting the incremental modelling of vague geometric configurations

In this paper the need for Intelligent Computer Aided Design (Int.CAD) to jointly support design and learning assistance is introduced. The paper focuses on presenting and exploring the possibility of realizing learning assistance in Int.CAD by introducing a new concept called Shared Learning. Shared Learning is proposed to empower CAD tools with more useful learning capabilities than that currently available and thereby provide a stronger interaction of learning between a designer and a computer. Controlled computational learning is proposed as a means whereby the Shared Learning concept can be realized. The viability of this new concept is explored by using a system called PERSPECT. PERSPECT is a preliminary numerical design tool aimed at supporting the effective utilization of numerical experiential knowledge in design. After a detailed discussion of PERSPECT's numerical design support, the paper presents the results of an evaluation that focuses on PERSPECT's implementation of controlled computational learning and ability to support a designer's need to learn. The paper then discusses PERSPECT's potential as a tool for supporting the Shared Learning concept by explaining how a designer and PERSPECT can jointly learn. There is still much work to be done before the full potential of Shared Learning can be realized. However, the authors do believe that the concept of Shared Learning may hold the key to truly empowering learning in Int.CAD