From Intuitionism to Brouwer's Modal Logic
Bulletin of the Section of Logic (2020)
- Volume: 49, Issue: 4, page 343-358
- ISSN: 0138-0680
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topZofia Kostrzycka. "From Intuitionism to Brouwer's Modal Logic." Bulletin of the Section of Logic 49.4 (2020): 343-358. <http://eudml.org/doc/296794>.
@article{ZofiaKostrzycka2020,
abstract = {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.},
author = {Zofia Kostrzycka},
journal = {Bulletin of the Section of Logic},
keywords = {intuitionistic logic; Kripke frames; Brouwer's modal logic},
language = {eng},
number = {4},
pages = {343-358},
title = {From Intuitionism to Brouwer's Modal Logic},
url = {http://eudml.org/doc/296794},
volume = {49},
year = {2020},
}
TY - JOUR
AU - Zofia Kostrzycka
TI - From Intuitionism to Brouwer's Modal Logic
JO - Bulletin of the Section of Logic
PY - 2020
VL - 49
IS - 4
SP - 343
EP - 358
AB - 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.
LA - eng
KW - intuitionistic logic; Kripke frames; Brouwer's modal logic
UR - http://eudml.org/doc/296794
ER -
References
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