Geodesic
Four-part semigroups - semigroups of Boolean operations
Discussiones Mathematicae. General Algebra and Applications, Tome 32 (2012) no. 1, pp. 115-136.

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Four-part semigroups form a new class of semigroups which became important when sets of Boolean operations which are closed under the binary superposition operation f + g := f(g,...,g), were studied. In this paper we describe the lattice of all subsemigroups of an arbitrary four-part semigroup, determine regular and idempotent elements, regular and idempotent subsemigroups, homomorphic images, Green's relations, and prove a representation theorem for four-part semigroups.
Keywords: four-part semigroup, Boolean operation 
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Jampachon, Prakit; Susanti, Yeni; Denecke, Klaus. Four-part semigroups - semigroups of Boolean operations. Discussiones Mathematicae. General Algebra and Applications, Tome 32 (2012) no. 1, pp. 115-136. http://geodesic.mathdoc.fr/item/DMGAA_2012_32_1_a5/

[1] R. Butkote and K. Denecke, Semigroup Properties of Boolean Operations, Asian-Eur. J. Math. 1 (2008) 157-176.

[2] R. Butkote, Universal-algebraic and Semigroup-theoretical Properties of Boolean Operations (Dissertation Universität Potsdam, 2009).