Axiomatizing Jaśkowski’s Discussive Logic D2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {D_2}$$\end{document}

被引:0
|
作者
Hitoshi Omori
Jesse Alama     
机构
[1] Kyoto University,Department of Philosophy
[2] Vienna University of Technology,Theory and Logic Group
关键词
Discussive logic; Discursive logic; Modal logic; Automated theorem proving; Counter model; Matrices;
D O I
10.1007/s11225-017-9780-6
中图分类号
学科分类号
摘要
We outline the rather complicated history of attempts at axiomatizing Jaśkowski’s discussive logic D2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {D_2}$$\end{document} and show that some clarity can be had by paying close attention to the language we work with. We then examine the problem of axiomatizing D2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {D_2}$$\end{document} in languages involving discussive conjunctions. Specifically, we show that recent attempts by Ciuciura are mistaken. Finally, we present an axiomatization of D2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {D_2}$$\end{document} in the language Jaśkowski suggested in his second paper on discussive logic, by following a remark of da Costa and Dubikajtis. We also deal with an interesting variant of D2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {D_2}$$\end{document}, introduced by Ciuciura, in which negation is also taken to be discussive.
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页码:1163 / 1180
页数:17
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