## 1.3 General Formula

The only Operators that are used by THEAX are logical operators. As
a result, the only formula that is constructed by operators is the logical
formula. For example, such formula as

are allowed; however, similar formulas like -A*B+C cannot be written.
For instance, Add (Prod (-(A) , B), C) can be written for formulas by applying
defined functions other than operators. Applying defined functions, number
formulas are written such as Add (Prod (-(A), B), C) without using operators.
Other than logical operators and functions, sometimes constructing formulas
exploit the preposition of equal sign such as

[A=B]
This indicates the preposition that "A and B are equal". Also,
by combining those mentioned above, such formulas as

not f(u,g(i)) and [h(k)=j]
are allowed. Concerning generalization of formulas, they are so called
Buckus method of writing and its definition is in index 3. In addition,
formulas of predicate logic can be applied; however, it will be explained
later.

To explicate the grammer easily, not in the operator is the strongest
and as it follows from and, or, xor, (exclusive or), imp (implication),
eqv (equivalence) gets weaker. Also, such as preposition of equal sign
[n=m]‚ predicate logic (All x) (f (x)), formulas that are in parentheses
(A or B), and function g(v) are interpreted before the operator not. In
addition, at both sides of = in the preposition of equal signs, in parentheses
of the predicate preposition formula, at the argument of functions, and
inside parentheses, it is acceptable to write general formulas.

Furthermore, if we limit operators to be logical, the restriction maybe
too strong. However, to make the system by assuming treatment of numbers
seems to be overly concerned.