Decidability of Logical Theories and Their Combination by João Rasga & Cristina Sernadas

Author:João Rasga & Cristina Sernadas
Language: eng
Format: epub
ISBN: 9783030565541
Publisher: Springer International Publishing

be the translation map defined inductively as follows: is the formula ;

is the formula

is the formula

is the formula ;

is the formula ;

is the formula .

The translation of B(x, y, z) reflects the fact that if , and are collinear then the slope of the lines determined by and by should be the same. Moreover, the translation of B(x, y, z) expresses that y is in between x and z. The translation of E(x, y, z, w) states that the distance from x to y should be the same as the distance from z to w. We are ready to prove that is decidable.

Proposition 3.13

Theory is decidable.

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