Geodesic
The main semantics of equality for partial algebras correspond to the basic operators
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 338-340.

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For partial algebras, we demonstrate a natural correspondence between the main semantics of equality and the basic operators of homomorphic images and sub-algebras.
Keywords: partial algebras, semantics of equality. 
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M. S. Sheremet. The main semantics of equality for partial algebras correspond to the basic operators. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 338-340. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a8/

[1] V. A. Gorbunov, M. S. Sheremet, “Horn classes of predicate systems and varieties of partial algebras”, Algebra and Logic, 39:1 (2000), 12–25 | Zbl

[2] M. S. Sheremet, “Completeness theorem for the Evans logic of identities”, Siberian Electronic Mathematical Reports, 1 (2004), 24–34 (Russian, English abstract) | Zbl