A theory of interactions: Unifying qualitative and quantitative algebraic reasoning.

*(English)*Zbl 0753.68084In 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.

(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.

Reviewer: I.Pavaloi (Iaşi)

##### MSC:

68T20 | Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) |

68W30 | Symbolic computation and algebraic computation |

68T30 | Knowledge representation |

##### Software:

MACSYMA
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\textit{B. C. Williams}, Artif. Intell. 51, No. 1--3, 39--94 (1991; Zbl 0753.68084)

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