"Commonsense" Arithmetic Reasoning

Reid Simmons

"Arithmetic reasoning" can range in complexity from simple integer arithmetic to powerful symbolic algebraic reasoning of the sort done by MACSYMA. We describe an arithmetic reasoning system of intermediate complexity called the Quantity Lattice. In a computationally efficient manner the Quantity Lattice integrates qualitative and quantitative reasoning, and combines inequality reasoning with reasoning about simple arithmetic expressions, such as addition or multiplication. The system has proven useful in doing simulation and analysis in several domains, including geology and semiconductor fabrication, by supporting useful forms of reasoning about time and the changes that happen when processes occur.

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