by Alexandra Pavlova
Abstract:
In this paper, we define a class of dialogue games for Johansson’s minimal logic and prove that it corresponds to the validity of minimal logic. Many authors have stated similar results for intuitionistic and classical logic either with or without actually proving the correspondence. Rahman, Clerbout and Keiff [17] have already specified dialogues for minimal logic; however, they transformed it into Fitch-style natural deduction only. We propose a different specification for minimal logic with the proof of correspondence between the existence of winning strategies for the Proponent in this class of games and the sequent calculus for minimal logic.
Reference:
Dialogue Games for Minimal LogicAlexandra PavlovaLogic and Logical Philosophy, volume 30, number 2, pages 281–309, 2020.
Bibtex Entry:
@article{LLPLLP.2020.022,
author = {Alexandra Pavlova},
title = {Dialogue Games for Minimal Logic},
journal = {Logic and Logical Philosophy},
volume = {30},
number = {2},
year = {2020},
keywords = {dialogue logic; sequent calculi; minimal logic},
abstract = {In this paper, we define a class of dialogue games for Johansson’s minimal logic and prove that it corresponds to the validity of minimal logic. Many authors have stated similar results for intuitionistic and classical logic either with or without actually proving the correspondence. Rahman, Clerbout and Keiff [17] have already specified dialogues for minimal logic; however, they transformed it into Fitch-style natural deduction only. We propose a different specification for minimal logic with the proof of correspondence between the existence of winning strategies for the Proponent in this class of games and the sequent calculus for minimal logic.},
issn = {2300-9802},
url = {https://apcz.umk.pl/czasopisma/index.php/LLP/article/view/LLP.2020.022},
pages = {281--309}
}