Abstract
Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula ϕ in the language {∨, ∧, →, ⊤, ⊥, ∀, ∃}, we associate two sequences of formulas 〈ϕ0,ϕ1,...〉 and 〈ϕ0,ϕ1,...〉 in the same language. We prove that for every sequent ϕ ⇒ ψ, there are natural numbers m, n, such that IQC ⊢ ϕ ⇒ ψ, iff BQC ⊢ ϕn ⇒ ψm. Some applications of this translation are mentioned.
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Ardeshir, M. A Translation of Intuitionistic Predicate Logic into Basic Predicate Logic. Studia Logica 62, 341–352 (1999). https://doi.org/10.1023/A:1005196310070
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DOI: https://doi.org/10.1023/A:1005196310070