Expressing Second-order Sentences in Intuitionistic Dependence Logic

Studia Logica 101 (2):323-342 (2013)

Abstract

Intuitionistic dependence logic was introduced by Abramsky and Väänänen [1] as a variant of dependence logic under a general construction of Hodges’ (trump) team semantics. It was proven that there is a translation from intuitionistic dependence logic sentences into second order logic sentences. In this paper, we prove that the other direction is also true, therefore intuitionistic dependence logic is equivalent to second order logic on the level of sentences

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References found in this work

Compositional Semantics for a Language of Imperfect Information.W. Hodges - 1997 - Logic Journal of the IGPL 5 (4):539-563.
Finite Partially-Ordered Quantification.Wilbur John Walkoe Jr - 1970 - Journal of Symbolic Logic 35 (4):535-555.
On Definability in Dependence Logic.Juha Kontinen & Jouko Väänänen - 2009 - Journal of Logic, Language and Information 18 (3):317-332.
From If to Bi.Samson Abramsky & Jouko Väänänen - 2009 - Synthese 167 (2):207 - 230.
Finite Partially‐Ordered Quantifiers.Herbert B. Enderton - 1970 - Mathematical Logic Quarterly 16 (8):393-397.

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Citations of this work

Questions and Dependency in Intuitionistic Logic.Ivano Ciardelli, Rosalie Iemhoff & Fan Yang - 2020 - Notre Dame Journal of Formal Logic 61 (1):75-115.
Propositional Logics of Dependence.Fan Yang & Jouko Väänänen - 2016 - Annals of Pure and Applied Logic 167 (7):557-589.

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