Intuitionistic Logic and Elementary Rules
نویسندگان
چکیده
منابع مشابه
Admissible and Derivable Rules in Intuitionistic Logic
A well-known problem in intuitionistic logic is the existence of valid but not derivable rules. This problem seems to be related with some constructive features of intuitionism (disjunction and existence property) but appear also in modal logics. We study here a particular case of this phenomenon, admissible rules in propositional calculus. G.E.Mints in [Mi 72] give sufficients conditions for a...
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The size of shortest cut-free proofs of first-order formulas in intuitionistic sequent calculus is known to be non-elementary in the worst case in terms of the size of given sequent proofs with cuts of the same formulas. In contrast to that fact, we provide an elementary bound for the size of cut-free proofs for disjunction-free intuitionistic logic for the case where the cut-formulas of the or...
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When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them, and are related to nothing they already know, unlike, for instance, the notion of model, that can be seen as a generalization of the notion of algebraic str...
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We present a basis for the admissible rules of intuitionistic proposi-tional logic. Thereby a conjecture by de Jongh and Visser is proved. We also present a proof system for the admissible rules, and give semantic criteria for admissibility.
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Uniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic IPC and its consistent axiomatic extensions (intermediate logics). A Kripke semantics characterization is given for the (hereditarily) structurally complete implication–negation fragments of intermediate logics, and it is shown that ...
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ژورنال
عنوان ژورنال: Mind
سال: 2011
ISSN: 0026-4423,1460-2113
DOI: 10.1093/mind/fzr076