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This paper concerns notions of Booleanness in the setting of partial frames, which, in contrast to full frames, do not necessarily have all joins. Examples of these include bounded distributive lattices,  σ - and  κ -frames. We provide four distinct conditions which all reduce in the case of full frames to each element having a complement. These concepts depend heavily on the free frame over a partial frame, the congruence frame of a partial frame and the relations between them. We also examine the adjoint situation between the congruences of a partial frame and those of its free frame.

Variants of Booleanness: Congruences of a partial frame versus those of its free frame