Evaluating atomic formulas.

Take any string S representing some atomic formula. We want to compute the truth value of S, or decide that S is an open formula without a fixed truth value. We first replace round brackets by square brackets, because Mathematica notation requires square brackets. We replace <=, >=, ==,!= with the special symbols ≤, ≥, ==,≠. These special symbols are considered, in Mathematica,  different from <=, >=, ==,!=, as we check below:

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Then every = not occurring in some <=, >=, = =, != in S is replaced by the special symbol ==.

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Eventually we can evaluate S, or decide it has no fixed truth value, using ternary ``if'' of Mathematica. If S is neither true nor false, we say that the truth value of S is open.

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Some examples.

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Mathematica can recognize some simple algebraic identities, like x^2 = (-x)^2. Do not rely too much on it.

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Created by Mathematica  (October 17, 2006)