An Approach to Glivenko’s Theorem in Algebraizable Logics

Studia Logica ◽  
2008 ◽  
Vol 88 (3) ◽  
pp. 349-383 ◽  
Author(s):  
Antoni Torrens
Keyword(s):  
Algebraizable Logics ◽  
Glivenko’S Theorem

Algebraizable logics

1989 ◽  
Vol 77 (396) ◽  
pp. 0-0 ◽  
Author(s):  
W. J. Blok ◽  
Don Pigozzi
Keyword(s):  
Algebraizable Logics

scholarly journals Order algebraizable logics

2013 ◽  
Vol 164 (3) ◽  
pp. 251-283 ◽  
Author(s):  
J.G. Raftery
Keyword(s):  
Algebraizable Logics

On second order intuitionistic propositional logic without a universal quantifier

2009 ◽  
Vol 74 (1) ◽  
pp. 157-167 ◽  
Author(s):  
Konrad Zdanowski
Keyword(s):  
Propositional Logic ◽  
Second Order ◽  
Universal Quantifier ◽  
Intuitionistic Propositional Logic ◽  
Glivenko’S Theorem ◽  
Free Variables ◽  
Universal Quantification

AbstractWe examine second order intuitionistic propositional logic, IPC2. Let ℱ∃ a be the set of formulas with no universal quantification. We prove Glivenko's theorem for formulas in ℱ∃ that is, for φ ∈ ℱ∃, φ is a classical tautology if and only if ┐┐φ is a tautology of IPC2. We show that for each sentence φ ∈ ℱ∃ (without free variables), φ is a classical tautology if and only if φ is an intuitionistic tautology. As a corollary we obtain a semantic argument that the quantifier ∀ is not definable in IPC2 from ⊥, ⋁, ⋀, →, ∃.

scholarly journals Combining Algebraizable Logics

1996 ◽  
Vol 37 (2) ◽  
pp. 366-380 ◽  
Author(s):  
A. Jánossy ◽  
Á. Kurucz ◽  
Á. E. Eiben
Keyword(s):  
Algebraizable Logics

scholarly journals Glivenko theorems for substructural logics over FL

2006 ◽  
Vol 71 (4) ◽  
pp. 1353-1384 ◽  
Author(s):  
Nikolaos Galatos ◽  
Hiroakira Ono
Keyword(s):  
Propositional Logic ◽  
Substructural Logics ◽  
Residuated Lattices ◽  
Substructural Logic ◽  
Classical Propositional Logic ◽  
Double Negation ◽  
Glivenko’S Theorem

AbstractIt is well known that classical propositional logic can be interpreted in intuitionistic prepositional logic. In particular Glivenko's theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko's theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via a double negation interpretation. Our presentation is algebraic and is formulated in the context of residuated lattices. In the last part of the paper, we also discuss some extended forms of the Koltnogorov translation and we compare it to the Glivenko translation.

Postponement of $$\mathsf {raa}$$ raa and Glivenko’s Theorem, Revisited

Studia Logica ◽  
2018 ◽  
Vol 107 (1) ◽  
pp. 109-144 ◽  
Author(s):  
Giulio Guerrieri ◽  
Alberto Naibo
Keyword(s):  
Glivenko’S Theorem
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