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https://doi.org/10.1...arrow_drop_down
https://doi.org/10.1016/s0049-...
Part of book or chapter of book . 1965 . Peer-reviewed
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Semantical Analysis of Intuitionistic Logic I

Authors: Saul A. Kripke;

Semantical Analysis of Intuitionistic Logic I

Abstract

Publisher Summary The chapter discusses a semantical analysis of intuitionistic logic I. The chapter presents a semantical model theory for Heyting's intuitionist predicate logic and proves the completeness of that system relative to the modeling. The semantics for modal logic that is announced and developed together with the known mappings of intuitionistic logic into the modal system, S4, inspired the present semantics for intuitionist logic. It is important to develop the semantics of intuitionistic logic independently of that of S4; this procedure helps to obtain somewhat more information about intuitionistic logic, including the mapping into S4 as a consequence thereof. In addition to giving a simple decision procedure for Heyting's propositional calculus, the chapter presents the undecidability of monadic intuitionistic quantification theory. The proof is based on the semantics previously developed. Beth semantic tableaux for intuitionistic logic is developed in the chapter. The chapter describes consistency property: in a standard formalization of Heyting's predicate calculus, the axioms are all valid, and the rules preserve validity.

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Microsoft Academic Graph classification: Discrete mathematics Truth value Minimal logic Many-valued logic Calculus Dynamic logic (modal logic) Kripke semantics Intermediate logic Intuitionistic logic Higher-order logic Mathematics

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  • citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    393
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 1%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 0.1%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Top 10%
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Found an issue? Give us feedback
citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
393
Top 1%
Top 0.1%
Top 10%