Abstract
Incidence geometries of dimension two and three, miquelian geometry and projective geometry are defined through conditional equational axioms. The mechanization of these geometries is done using their associated positive/negative conditional term rewriting systems. To any figure and to any property of the figure are associated two terms t 1 and t 2 such that the figure possesses the property if and only if t 1 and t2 have a same normal form for the conditional term rewriting system corresponding to the considered geometry.
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Balbiani, P. (1995). Equation solving in geometrical theories. In: Dershowitz, N., Lindenstrauss, N. (eds) Conditional and Typed Rewriting Systems. CTRS 1994. Lecture Notes in Computer Science, vol 968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60381-6_3
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DOI: https://doi.org/10.1007/3-540-60381-6_3
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