De Finettian Logics of Indicative Conditionals Part II: Proof Theory and Algebraic Semantics

被引：0
作者：
Paul Égré
Lorenzo Rossi
Jan Sprenger
机构：
[1] PSL University,Institut Jean
[2] Ludwig-Maximilians-Universität München,Nicod (CNRS/ENS/EHESS), Département de Philosophie & Département d’études Cognitives, Ecole Normale Supérieure
[3] Università degli Studi di Torino,Munich Center for Mathematical Philosophy (MCMP), Fakultät für Philosophie, Wissenschaftstheorie und Religionswissenschaft
来源：
Journal of Philosophical Logic | 2021年 / 50卷
关键词：
Indicative conditionals; Trivalent logics; Cooper-Cantwell conditional; de Finetti conditional; Proof theory; Algebraic semantics; Connexive logics;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicative conditionals, most notably the proposals by de Finetti (1936) and Reichenbach (1935, 1944) on the one hand, and by Cooper (Inquiry, 11, 295–320, 1968) and Cantwell (Notre Dame Journal of Formal Logic, 49, 245–260, 2008) on the other. Here we provide the proof theory for the resulting logics DF/TT and CC/TT, using tableau calculi and sequent calculi, and proving soundness and completeness results. Then we turn to the algebraic semantics, where both logics have substantive limitations: DF/TT allows for algebraic completeness, but not for the construction of a canonical model, while CC/TT fails the construction of a Lindenbaum-Tarski algebra. With these results in mind, we draw up the balance and sketch future research projects.
引用
收藏
页码：215 / 247
页数：32
相关论文
共 29 条
  • [1] Asenjo FG(1966)A calculus of antinomies Notre Dame Journal of Formal Logic 16 103-105
  • [2] Baratgin J(2013)Uncertainty and the de Finetti tables Thinking & Reasoning 19 308-328
  • [3] Over D(2018)The psychology of uncertainty and three-valued truth tables Frontiers in Psychology 9 1479-191
  • [4] Politzer G(2002)Deduction with uncertain conditionals Information Sciences 147 143-260
  • [5] Baratgin J(2008)The logic of conditional negation Notre Dame Journal of Formal Logic 49 245-320
  • [6] Politzer G(1968)The propositional logic of ordinary discourse Inquiry 11 295-1740
  • [7] Over DE(1994)Conditional objects as nonmonotonic consequence relationships IEEE Transactions on Systems, Man, and Cybernetics 24 1724-329
  • [8] Takahashi T(1995)On Conditionals Mind 104 235-394
  • [9] Calabrese P(1979)Material implication, confirmation, and counterfactuals Notre Dame Journal of Formal Logic 20 383-61
  • [10] Cantwell J(1996)On dialetheism Australasian Journal of Philosophy 74 153-436
123