From Intuitionism to Brouwer's Modal Logic

From Intuitionism to Brouwer's Modal Logic

We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication as modal strict implication, whereas variables and other positive...

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Bibliographic Details
Main Author: Zofia Kostrzycka
Format: Article
Language:English
Published: Lodz University Press 2020-12-01
Series:Bulletin of the Section of Logic
Subjects:
intuitionistic logic
kripke frames
brouwer's modal logic
Online Access:https://czasopisma.uni.lodz.pl/bulletin/article/view/8174
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spelling doaj-04965e117b8a436991a8d03a5012f7502021-01-26T11:28:49ZengLodz University PressBulletin of the Section of Logic0138-06802449-836X2020-12-0149434335810.18778/0138-0680.2020.227176From Intuitionism to Brouwer's Modal LogicZofia Kostrzycka0Opole University of Technology ul. Sosnkowskiego 31 45-272 Opole, PolandWe try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication as modal strict implication, whereas variables and other positive sentences remain as they are. The proposed translation preserves fragments of the Rieger-Nishimura lattice which is the Lindenbaum algebra of monadic formulas in INT. Unfortunately, INT is not embedded by this mapping into KTB.https://czasopisma.uni.lodz.pl/bulletin/article/view/8174intuitionistic logickripke framesbrouwer's modal logic
collection DOAJ
language English
format Article
sources DOAJ
author Zofia Kostrzycka
spellingShingle Zofia Kostrzycka
From Intuitionism to Brouwer's Modal Logic
Bulletin of the Section of Logic
intuitionistic logic
kripke frames
brouwer's modal logic
author_facet Zofia Kostrzycka
author_sort Zofia Kostrzycka
title From Intuitionism to Brouwer's Modal Logic
title_short From Intuitionism to Brouwer's Modal Logic
title_full From Intuitionism to Brouwer's Modal Logic
title_fullStr From Intuitionism to Brouwer's Modal Logic
title_full_unstemmed From Intuitionism to Brouwer's Modal Logic
title_sort from intuitionism to brouwer's modal logic
publisher Lodz University Press
series Bulletin of the Section of Logic
issn 0138-0680
2449-836X
publishDate 2020-12-01
description We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication as modal strict implication, whereas variables and other positive sentences remain as they are. The proposed translation preserves fragments of the Rieger-Nishimura lattice which is the Lindenbaum algebra of monadic formulas in INT. Unfortunately, INT is not embedded by this mapping into KTB.
topic intuitionistic logic
kripke frames
brouwer's modal logic
url https://czasopisma.uni.lodz.pl/bulletin/article/view/8174
work_keys_str_mv AT zofiakostrzycka fromintuitionismtobrouwersmodallogic
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