Aspects of analytic deduction
For any set of formulae \(\Gamma\cup\{A\}\), the deduction \(\Gamma\lvdash A\) is called analytic, if, roughly, every atomic subformula of \(A\) is already contained in the set of subformulae of \(\Gamma\). In this paper, the author gives a formal description of an analytic subrelation of the classical first-order logic consequence relation. This formalization is presented as a subsystem of Gentzen's sequent calculus \({\mathbf L}{\mathbf K}\) for classical logic by the corresponding restrictions on non-analytic rules of \({\mathbf L}{\mathbf K}\). The main result of the paper, regarding the correct axiomatization of the analytic classical consequence relation, can be considered as a new fine example of Gentzen's cut-elimination theorem application. The relationship between the semantic and syntactic aspects of the analytic deduction relation is discussed as well.
subsystem of Gentzen's sequent calculus \({\mathbf L}{\mathbf K}\)
scientific article; zbMATH DE number 980787