A free IPC is a natural logic: Strong completeness for some intuitionistic free logics

Carl J. Posy

doi:10.1007/BF00157539

A free IPC is a natural logic: Strong completeness for some intuitionistic free logics

Carl J. Posy^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

IPC, the intuitionistic predicate calculus, has the property (i) Vc(Γ⊢A^c/x) ⇒ Γ⊢∃xA.Furthermore, for certain important Γ, IPC has the converse property (ii) Γ⊢∃xA ⇒ Vc(Γ⊢A^c/x). (i) may be given up in various ways, corresponding to different philosophic intuitions and yielding different systems of intuitionistic free logic. The present paper proves the strong completeness of several of these with respect to Kripke style semantics. It also shows that giving up (i) need not force us to abandon the analogue of (ii).

Original language	English
Pages (from-to)	30-43
Number of pages	14
Journal	Topoi
Volume	1
Issue number	1-2
DOIs	https://doi.org/10.1007/BF00157539
State	Published - Dec 1982
Externally published	Yes

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A free IPC is a natural logic: Strong completeness for some intuitionistic free logics

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