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A free IPC is a natural logic: Strong completeness for some intuitionistic free logics
Topoi 1 (1-2):30-43 (1982)
Abstract
IPC, the intuitionistic predicate calculus, has the property(i) Vc(A c /x) xA.Furthermore, for certain important , IPC has the converse property (ii) xA Vc(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).Author's Profile
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Citations of this work
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The infinite, the indefinite and the critical turn: Kant via Kripke models.Carl Posy - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6):743-773.
The language of appearances and things in themselves.Carl J. Posy - 1981 - Synthese 47 (2):313 - 352.
References found in this work
Singular terms, truth-value gaps, and free logic.Bas C. van Fraassen - 1966 - Journal of Philosophy 63 (17):481-495.
On the strong semantical completeness of the intuitionistic predicate calculus.Richmond H. Thomason - 1968 - Journal of Symbolic Logic 33 (1):1-7.
Disjunction and existence under implication in elementary intuitionistic formalisms.S. C. Kleene - 1962 - Journal of Symbolic Logic 27 (1):11-18.
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