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.