Results 181 to 190 of about 1,260 (226)
Cut-elimination theorem and Brouwerian-valued models for intuitionistic type theory
Cut-elimination theorem and Brouwerian-valued models for intuitionistic type theoryopenaire
An Ordinal-Free Proof of the Cut-elimination Theorem for a Subsystem of $\Pi^1_1$-Analysis with $\omega$-rule (Proof theoretical study of the structure of logic and computation)openaire
, 2021 AbstractAll the rules of the sequent calculus have the property that all the formulas that are present in the premises also occur in the conclusion. There is only one exception, the cut rule. In this chapter, it is shown using double induction that every theorem provable in Gentzen’s sequent calculi using the cut rule can also be proved without.
Pietro Mancosu +2 more
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Gentzen’s Cut Elimination Theorem for Non-Logicians
Tulane Studies in Philosophy, 1972 The most important theorem of constructive mathematical logic, Gentzen’s cut elimination theorem, is largely unknown even among those acquainted with mathematical logic. Usual treatments of mathematical logic, oriented to semantics, use formalization only to find a syntactic property (theoremhood) to correspond to the semantic property (validity). What
Larry W. Miller
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Cut‐Elimination Theorem for the Logic of Constant Domains
Mathematical Logic Quarterly, 1994 AbstractThe logic CD is an intermediate logic (stronger than intuitionistic logic and weaker than classical logic) which exactly corresponds to the Kripke models with constant domains. It is known that the logic CD has a Gentzen‐type formulation called LD (which is same as LK except that (→) and (⊃–) rules are replaced by the corresponding ...
Ryo Kashima, Tatsuya Shimura
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Cut-elimination Theorems for Some Infinitary Modal Logics
MLQ, 2001 The well-known Gentzen systems of propositional modal logics K, T, K4, and S4 are extended naturally to their infinitary versions by adjoining the rules for (countably) infinite conjunction and disjunction preserving the cut-elimination property, according to which then the infinitary formula corresponding to the so-called Barcan axiom of predicate ...
Yoshihito Tanaka
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A proof of the cut-elimination theorem in simple type theory
Journal of Symbolic Logic, 1973 In [4], I introduced a quasi-Boolean algebra, and showed that in a formal system of simple type theory, from which the cut rule is omitted, wffs form a quasi-Boolean algebra, and that the cut-elimination theorem can be formulated in algebraic language.
Satoko Titani
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Cut-Elimination Theorem for Higher-Order Classical Logic: An Intuitionistic Proof
, 1987 It is not difficult to see that usual inductive cut-elimination proof fails for higher-order logics. The cause is that the induction goes to the ruin in the case of quantifier rules in logics with the impredicative comprehension shema. In fact, it follows from one Takeuti’s result, that finite proof of cut-elimination is impossible in this case (see ...
A. G. Dragalin
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Applications of the Cut Elimination Theorem to Some Subsystems of Classical Analysis
, 1970 Publisher Summary This chapter discusses the applications of the cut elimination theorem to some subsystems of classical analysis. The principal result presented in the chapter is a constructive consistency proof for the system (Σ 1 2 -ADC) of second order number theory with the Σ 1 2 axiom of dependent choice. It is shown that every derivation in
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