Undecidable iterative propositional calculus

Abstract

In this paper, we consider iterative propositional calculi, which are finite sets of propositional formulas together with the rules of modus ponens and weak substitution (when formula being substituted must be already inferred). We construct an undecidable iterative propositional calculus using axioms in 3 variables. Particulary, we show that the general problem of derivability for these calculi is undecidable.