Three-valued modal logic for theory construction with contradictory data

Abstract

This article refers to theory construction on the basis of binary data, where a configuration of several yes/no-variables is used in order to explain a binary outcome. The methodology proposed for this purpose has been developed by the political scientist Charles Ragin and is known under the name qualitative comparative analysis. It is frequently confronted with situations, where the same configuration of explanatory variables has contradictory yes/no-values for the outcome-variable of different related cases. Since the standard-solutions to this problem are not always satisfactory, the author proposes the use of three-valued modal logic, which was originally developed by the Polish philosopher Jan Lukasiewicz. In this logic there is a third truth-value indeterminate, which serves to code contradictory or missing data. Moreover, by the proposed use of modal operators it becomes possible to differentiate between strict and possible triggers and inhibitors of a given outcome. Since indeterminate outcomes do not really contribute to knowledge accumulation and theory building, the article discusses strategies for promoting scientific progress by minimizing this indeterminacy.