A theory of interactions: Unifying qualitative and quantitative algebraic reasoning
type: Item
instance of: scholarly article
title: A theory of interactions: Unifying qualitative and quantitative algebraic reasoning
zbMATH Open document ID: 0753.68084
DOI: 10.1016/0004-3702(91)90108-V
author: Brian C. Williams
published in: Artificial Intelligence
publication date: 1992-09-26T00:00:00Z
review text: In order to develop a model-based theory of design for continuous, lumped parameter devices, the author proposed three hybrid algebras that capture qualitative and quantitative information about interactions and implemented a qualitative symbolic algebra system, called Minima, that provides improved facilities for composing and comparing equations. The paper concentrates on the SR1 hybrid algebra, that merges the signs and reals into a single domain, on its expressive power, as well as the capacity of SR1 and Minima: (1) to select the right level of abstraction; and (2) to efficiently combine qualitative and quantitative reasoning. This is achieved by embodying: a weaker relation of qualitative equality, substitution of equals, qualitative composition and hybrid resolution, inference rules needed for design and verification, qualitative arithmetic reasoning, composition of monotonicity relations etc. Implemented on a Symbolics 3600 (using Symbolics and DOE Macsyma), the Minima system (and SR1 algebra) demonstrated a progress in the design of a better theory of interactions, and proved to be useful in a variety of fluid regulation devices.
Mathematics Subject Classification ID: 68T20
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 68T30
zbMATH DE Number: 55598
zbMATH Keywords: hybrid algebraic reasoning
zbMATH Keywords: engineering
zbMATH Keywords: problem solving
zbMATH Keywords: theory of interactions
describes a project that uses: MACSYMA
MaRDI profile type: Publication
cites work: Qualitative simulation
cites work: Q5655228
cites work: Q3207999
cites work: Algebraic simplification
cites work: Forward reasoning and dependency-directed backtracking in a system for computer-aided circuit analysis
cites work: Task-dependent qualitative domain abstraction
cites work: Q5750453
full work available at URL: 0004-3702(91)90108-v
OpenAlex ID: W2005003668
description: scientific article; zbMATH DE number 55598