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In this article, we describe PrediCalc, a logical spreadsheet that allows for many-to-many constraints and propagation in all directions. We explain PrediCalc’s update mechanism and PrediCalc’s unique approach to handling inconsistencies between the spreadsheet values and the spreadsheet formulas. We have developed a paraconsistent entailment relation for the purpose of computing the consequences of PrediCalc’s value assignments under inconsistency. We close with thoughts on the prospects of logical spreadsheets on the World Wide Web, and describe our initial Websheet prototypes.