In Classical Logic, it is not possible to conclude from "If P then Q" that "It is not the case that if P then ∼Q". This argument, whose conditional counterpart is known as Boethius' thesis, is abundantly attested in the realm of causal, conceptual, and logical relations. Aristotle's thesis "It is not the case that if P then P" is not a theorem in this logic. Furthermore, in Classical Logic, each of the two propositions P and Q is derived from "It is not the case that if P then ∼Q", against which there is a lot of evidence. The Non-Truth Functional System of Propositional Logic is an answer to these problems, in which causal, conceptual, and logical relations are analyzed, formulated, and evaluated in accordance with natural intuition without exception.
In article "Hajhosseini's Non-Truth Functional Logic", Asadollah Fallahi makes three specific criticisms of this system: "The number of inference rules are reducible", "Every propositional variable is a theorem, and this system and its extension are trivial" and "The extension of the Non-Truth Functional System reduces to classical logic". In this article, we show that the first criticism is based on some incorrect proofs. Also, the second criticism arises from the incorrect definition of some non-truth functional combinations or the incorrect proof of some arguments. Finally, the third criticism is solved by reducing the rules of distributivity. For our answer to his repeated criticisms we refer to the article "Critical Review of a Criticism on the Theory of Truth-Functional System".