The formal language of Geometry as a semiotic system. Part II. Advanced syntax

The paper constitutes the second part of the article of 2017, and is devoted to the advanced syntax of the formal language of Geometry. The units of the advanced syntax are divided in two groups: the elementary syntactic units and the units that are built on the elementary ones by special operations called reductions. Those operations are assigned to reduce regular-formed expressions and thus to facilitate their perception. The author specifes two types of reductions being made on the basis of the universal laws of formal logic and being introduced into the language of special new items. At the end of the article the expressive power of the advanced syntax are discussed. The exemplifed fragment of the advanced syntax related to the theory of triangles and quadrilaterals is presented.

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