Geodesic
On logical description of geometric figures
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 1191-1197.

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This paper deals with the problem of equivalence of predicate logic formulas, used for description of geometric objects, constructed from a given set of basic figures by set-theoretic operations $\cap,\cup,\overline{\phantom{a}}$. A finite complete system of identities is obtained for a finite basis in the class of the above formulas with finite number of variables. 
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     author = {A. A. Shakirov},
     title = {On logical description of geometric figures},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     volume = {5},
     number = {4},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a13/}
}
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A. A. Shakirov. On logical description of geometric figures. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 1191-1197. http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a13/