The product of implication and counter-implication systems.
Rangaswamy V. Setlur · Notre Dame Journal of Formal Logic · 1970
Introduction.*Rasiowa has obtained in [1] a finite axiomatization of the product system of "implication" and ''equivalence".In this paper, we show that the logic system based on the single binary connective O with the logical matrixthat is the product connective of implication (C) and counter-implication (D) is finitely axiomatizable.The axiom and the rules of inference have been obtained by combining the axioms and the rules of inference of the complete axiomatizations of the implication system (C-system) and of the counterimplication system (O-system).2. Preliminary definitions.In these definitions Δ and Δ x are arbitrary binary connectives.2.1.^-formulas.Δ-formulas are defined recursively as follows:i) a sentential variable, a small Roman letter, is a Δ-formula;*The material for this paper has been extracted from the author's Thesis "The Product of Implication and Counter-Implication Systems'* written under the direction of Professor Henryk Hiz