While dimensional overlap (DO) is a property of sets, consistency is a property of individual trials in a task. The different ways that elements from overlapping dimensions can be combined to construct individual trials gives rise to a variety of types of consistency.
S-S consistency: Consider an ensemble with dimensional overlap between a relevant and an irrelevant stimulus set. Trial draws on the same value from each dimension, then that trial has S-S consistency. For example: in a task where the relevant stimulus is color and the irrelevant stimulus is a color word, the relevant and irrelevant stimulus sets overlap on the dimension of color.
On a trial where the color BLUE is presented with the word “BLUE” the stimulus is S-S consistent. On a trial where the color BLUE is presented with the word “GREEN”, on the other hand, the stimulus is S-S inconsistent.
Irrelevant S-R consistency: Consider an ensemble with a relevant and an irrelevant stimulus set, plus a response set, with dimensional overlap between the irrelevant stimulus and the response. For example, suppose a blue or green light can appear on the left or right side, and the color of the light is assigned to a left or right key press. In this task, the irrelevant stimulus and the response overlap on the dimension of left-right position.
On a trial where the color assigned to a left key press also appears on the left side, the trial is S-R consistent. On a trial where the color assigned to a left key press also appears on the right side, the trial is S-R inconsistent.
Relevant S-R consistency (Congruent/Incongruent mapping): Consider an ensemble with a relevant stimulus and a response set (there may or may not also be an irrelevant stimulus set), and the relevant stimulus and response sets have dimensional overlap. A trial which on which one of the relevant stimuli and now mapped onto one of the responses is called Relevant Consistent.
In the case of relevant S-R consistency, if the instructions map the stimuli onto their corresponding response (e.g. “respond to the left light with the left key, and to the right light with the right key”) that mapping is said to be congruent. If the instructions map the stimuli onto non-corresponding responses keys (e.g. respond to the left light with the right key,and to the right light with the left key), that mapping is said to be incongruent.
The different types of consistencies reflects the functional role that Dimensional Overlap plays at the level of trials. The different patterns of DO found in ensembles, results in different types of tasks. This is captured in the DO taxonomy.