Results 11 to 20 of about 1,260 (226)

The cut elimination theorem in the unary second order language [PDF]

Proceedings of the American Mathematical Society, 1966
ln [T], Takeuti has conjectured that the cut elimination theorem holds for the simple theory of types cast in the sequent calculus. This conjecture is true for the first order language, as Gentzen had shown in [G]. (Indeed, the conjecture was made after Gentzen had proved his "Hauptsatz.") The purpose of this Note is to show that the conjecture is true
Mitsuru Yasuhara
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Lattice-valued representation of the cut-elimination theorem [PDF]

Tsukuba Journal of Mathematics, 1991
Let \(L\) be a relatively pseudo-complemented complete lattice, \(F\) a set of formulas of a formal system (classical or intuitionistic). The author considers mappings \(m,M: F\to L\) satisfying a series of conditions. For such pairs of mappings he proves, as his main theorem: \(m(A)\leq M(B)\) for any provable sequent \(A\to B\). In the final section,
Shôji Maehara
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Correction to: Kripke-Completeness and Cut-elimination Theorems for Intuitionistic Paradefinite Logics With and Without Quasi-Explosion [PDF]

Journal of Philosophical Logic, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Norihiro Kamide
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Cut Elimination Theorem for Non-Commutative Hypersequent Calculus

Bulletin of the Section of Logic, 2017
Hypersequent calculi (HC) can formalize various non-classical logics. In [9] we presented a non-commutative variant of HC for the weakest temporal logic of linear frames Kt4.3 and some its extensions for dense and serial flow of time. The system was proved to be cut-free HC formalization of respective temporal logics by means of Schütte/Hintikka-style ...
Andrzej Indrzejczak
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Normalization and cut-elimination theorems for some logics of evidence and truth [PDF]

Journal of Logic and Computation
Abstract In this paper, we investigate proof-theoretic aspects of the logics of evidence and truth $LET_{J}$ and $LET_{F}$. These logics extend, respectively, Nelson’s logic N4 and the logic of first-degree entailment, also known as Belnap–Dunn four-valued logic, with a classicality operator ${{\circ }}$ that recovers classical logic for
Marcelo E. Coniglio, Martín Figallo, Abílio Rodrigues   +2 more
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The Cut-Elimination Theorem for Differential Nets with Promotion

, 2009
Recently Ehrhard and Regnier have introduced Differential Linear Logic, DiLL for short -- an extension of the Multiplicative Exponential fragment of Linear Logic that is able to express non-deterministic computations. The authors have examined the cut-elimination of the promotion-free fragment of DiLL by means of a proofnet-like calculus: differential ...
Michele Pagani
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A cut elimination theorem for stationary logic

Annals of Pure and Applied Logic, 1987
We develop a complete cut-free labelled sequent calculus for stationary logic and prove that in the given formalization, this logic has the subformula property. The necessary parameter restrictions on the rules of inference involved explain the compatibility of this result with the known failure of interpolation for stationary logic.
M. E. Szabo
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Kripke-Completeness and Cut-elimination Theorems for Intuitionistic Paradefinite Logics With and Without Quasi-Explosion [PDF]

Journal of Philosophical Logic, 2020
The original version of this article unfortunately contains several errors introduced by the typesetter during the publishing process. It has been corrected.
Norihiro Kamide
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A uniform cut-elimination theorem for linear logics with fixed points and super exponentials [PDF]

In the realm of light logics deriving from linear logic, a number of variants of exponential rules have been investigated. The profusion of such proof systems induces the need for cut-elimination theorems for each logic, the proof of which may be redundant. A number of approaches in proof theory have been adopted to cope with this need.
Esaïe Bauer, Alexis Saurin
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An algebraic formulation of cut-elimination theorem [PDF]

Journal of the Mathematical Society of Japan, 1965
Satoko Titani
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