Analysis of Strategic Knowledge in Back of the Envelope Reasoning

Back of the envelope (BotE) reasoning involves generating quantitative answers in situations where exact data and models are unavailable and where available data is often incomplete and/or inconsistent. A rough estimate generated quickly is more valuable and useful than a detailed analysis, which might be unnecessary, impractical, or impossible because the situation does not provide enough time, information, or other resources to perform one. Such reasoning is a key component of commonsense reasoning about everyday physical situations. We present an implemented system, BotE-Solver, that can solve about a dozen estimation questions like “What is the annual cost of healthcare in USA?” from different domains using a library of strategies and the Cyc knowledge base. BotE-Solver is a general-purpose problem solving framework that uses strategies represented as suggestions, and keeps track of problem solving progress in an AND/OR tree. A key contribution of this paper is a knowledge level analysis [Newell, 1982] of the strategic knowledge used in BotE reasoning. We present a core collection of seven powerful estimation strategies that provides broad coverage for such problem solving. We hypothesize that this is the complete set of back of the envelope problem solving strategies. We present twofold support for this hypothesis: 1) an empirical analysis of all problems (n=44) on Force and Pressure, Rotation and Mechanics, Heat, and Astronomy from Clifford Swartz’s "Back-of-the-Envelope Physics" [Swartz, 2003], and 2) an analysis of strategies used by BotE-Solver.