Defining and dealing with contradictory truth table rows

The notion of a contradictory truth table row is easier to understand with crisp sets. It describes a situation in which those cases that are members in a truth table row do not share the same membership in the outcome. Put differently, the same row leads to both the occurrence and the non-occurrence of the outcome. Since truth table rows are, in essence, statements of sufficiency, such an empirical situation suggests a logical contradiction, for it would mean that the very same combination of conditions (aka truth table row) produces both Y and ͠Y. The analytic problem is that, based on the empirical evidence, it is not straightforward to decide whether this row is sufficient for Y, ͠Y, or neither and, consequently, whether it should be included in the logical minimization for outcome Y, outcome ͠Y, or neither. It cannot, however, be included in both minimization procedures.

There are several, mutually non-exclusive strategies for dissolving logically contradictory truth table rows in either csQCA or fsQCA prior to the logical minimization, and there is another set of strategies for handling such contradictory rows during the minimization procedure (Ragin 1987: 113–18; Rihoux and De Meur 2009). Let us first turn to the strategies for dissolving the contradiction.