DFKI Research Report-94-10
by Knut Hinkelmann, Helge Hintze
Computing Cost Estimates for Proof Strategies
In this paper we extend work of Treitel and Genesereth for calculating cost estimates for alternative proof methods of logic programs. We consider four methods: (1) forward chaining by semi-naive bottom-up evaluation, (2) goal-directed forward chaining by semi-naive bottom-up evaluation after Generalized Magic-Sets rewriting, (3) backward chaining by OLD resolution, and (4) memoing backward chaining by OLDT resolution. The methods can interact during a proof. After motivating the advantages of each of the proof methods, we show how the effort for the proof can be estimated. The calculation is based on indirect domain knowledge like the number of initial facts and the number of possible values for variables. From this information we can estimate the probability that facts are derived multiple times. An important valuation factor for a proof strategy is whether these duplicates are eliminated. For systematic analysis we distinguish between in costs and out costs of a rule. The out costs correspond to the number of calls of a rule. In costs are the costs for proving the premises of a clause. Then we show how the selection of a proof method for one rule influences the effort of other rules. Finally we discuss problems of estimating costs for recursive rules and propose a solution for a restricted case.
This document is available as Postscript.
The next abstract is here, and the previous abstract is here.
Note: This page was written to look best with CSS stylesheet support Level 1 or higher. Since you can see this, your browser obviously doesn't support CSS, or you have turned it off. We highly recommend you use a browser that supports and uses CSS, and review this page once you do. However, don't fear, we've tried to write this page to still work and be readable without CSS.