How is Logical Implication Analyzed and Formulated? A Critical Review of the Article "on Historical Aspects of Hajihosseini’s Logical Systems"

In natural language, we sometimes come across arguments contain non-functional connectives. Classical logic is not able to analyze and formalize these arguments. Moreover, logical implication in a valid argument has four properties: Truth-preservation, Necessity, Formality, and Universality. In classical logic, which evaluates EQT and EFQ as valid and correct, the second property, necessity, is not guaranteed. Hajihosseini in book “A New Outlook on Elements of Logic” has paved the way for solving these two problems by establishing two logical systems, one functional and one non-functional, and extending these systems. In this context, however, Asadollah Fallahi, in his article On Historical Aspects of Hajhosseini’s Logical Systems, published in Knowledge, No. 88/1 (Spring/Summer 2023), has attributed three claims to the author of the book: 1) The separation of functional and non-functional fragments is one of the author's innovations. 2) Classical logic confused material implication and deduction and considered them one. 3) The metatheorem of deduction is incorrect because the relation between the premises is an extensional conjunction. In this article, we demonstrate that none of the above claims were made in the book and that any confusion results from a selective reading of a detailed passage and a lack of understanding Fallahi, also, argues that any contradiction can be derived from a contradiction in the functional system. Moreover, transitive relations in arguments are valid in both functional and non-functional systems, contrary to Tennant's classical relational logic.