Studia Logica 104 (5):1037-1050 (2016)

Guillermo Badia
University of Queensland
Bi-intuitionistic logic is the result of adding the dual of intuitionistic implication to intuitionistic logic. In this note, we characterize the expressive power of this logic by showing that the first order formulas equivalent to translations of bi-intuitionistic propositional formulas are exactly those preserved under bi-intuitionistic directed bisimulations. The proof technique is originally due to Lindstrom and, in contrast to the most common proofs of this kind of result, it does not use the machinery of neither saturated models nor elementary chains.
Keywords bi-intuitionistic logic   van Benthem’s characterization theorem   model theory.
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DOI 10.1007/s11225-016-9664-1
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Model Theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.

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Citations of this work BETA

Infinitary Propositional Relevant Languages with Absurdity.Guillermo Badia - 2017 - Review of Symbolic Logic 10 (4):663-681.
On Generalized Van Benthem-Type Characterizations.Grigory K. Olkhovikov - 2017 - Annals of Pure and Applied Logic 168 (9):1643-1691.
Bi-Intuitionistic Implication Structures.Daniel Skurt - 2018 - Journal of Applied Non-Classical Logics 28 (1):20-34.

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