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The object of contextuality analysis is a set of random variables each ofwhich is uniquely labeled by a content and a context. In the measurementterminology, the content is that which the random variable measures, whereasthe context describes the conditions under which this content is measured (inparticular, the set of other contents being measured "together" with this one).Such a set of random variables is deemed noncontextual or contextual dependingon whether the distributions of the context-sharing random variables are or arenot compatible with certain distributions imposed on the content-sharing randomvariables. In the traditional approaches, contextuality is either restricted toonly consistently-connected systems (those in which any two content-sharingrandom variables have the same distribution) or else allinconsistently-connected systems (those not having this property) areconsidered contextual. In the Contextuality-by-Default theory, aninconsistently connected system may or may not be contextual. There are severalarguments for this understanding of contextuality, and this note adds one more.It is related to the fact that generally not each content is measured in eachcontext, so there are "empty" content-context pairs. It is convenient to treateach of these empty pairs as containing a dummy random variable, one that doesnot change the degree of contextuality in a system. These dummy randomvariables are deterministic ones, attaining a single value with probability 1.The replacement of absent random variables with deterministic ones, however,can only be made if one allows for inconsistently-connected systems.  KEYWORDS: contextuality, dummy measurements, inconsistent connectedness,random variables.

Replacing Nothing with Something Special: Contextuality-by-Default and Dummy Measurements