A basic free logic (Q1115422)

The paper provides a Fitch-style proof-theory for a universally free logic. Proofs and subproofs are tagged by terms, and the quantifier rules are formulated in terms of the tagging. Intuitively, the tagged terms are those which may be assumed to denote existent objects within the (sub)proof. Modifications to remove the universality and the freeness of the logic are indicated. The system of proof is shown to be as strong as the free logic \(QC^*\) of \textit{K. Lambert} [ibid. 4, 288-292 (1963; Zbl 0139.244)]. It is claimed (but not shown) that the system is complete with respect to standard semantics for \(QC^*\). See, e.g., \textit{H. Leblanc} and \textit{R. K. Meyer} ``On prefacing (\(\forall x)A\supset A(y/x)\) with (\(\forall y):\) A free quantification theory without identity'' [Existence, truth and provability, 58-75 (1982; Zbl 0502.03003)].