Rooted Hypersequent Calculus for Modal Logic S5

被引:0
|
作者
Hamzeh Mohammadi
Mojtaba Aghaei
机构
[1] Isfahan University of Technology,Department of Mathematical Sciences
来源
Logica Universalis | 2023年 / 17卷
关键词
Proof theory; Hypersequent calculus; Cut-elimination; Modal logic S5; Primary 03F03; Secondary 03F05; 03B45;
D O I
暂无
中图分类号
学科分类号
摘要
We present a rooted hypersequent calculus for modal propositional logic S5. We show that all rules of this calculus are invertible and that the rules of weakening, contraction, and cut are admissible. Soundness and completeness are established as well.
引用
收藏
页码:269 / 295
页数:26
相关论文
共 50 条
  • [31] On modal logics between K x K x K and S5 x S5 x S5
    Hirsch, R
    Hodkinson, I
    Kurucz, A
    [J]. JOURNAL OF SYMBOLIC LOGIC, 2002, 67 (01) : 221 - 234
  • [32] Path calculus in the modal logic S4
    Norgėla S.
    [J]. Lithuanian Mathematical Journal, 2005, 45 (1) : 94 - 101
  • [33] A tableau system for Godel-Dummett logic based on a hypersequent calculus
    Avron, A
    [J]. AUTOMATED REASONING WITH ANALYTIC TABLEAUX AND RELATED METHODS, 2000, 1847 : 98 - 111
  • [34] On fuzzy modal logics S5(C)
    Hajek, Petr
    [J]. FUZZY SETS AND SYSTEMS, 2010, 161 (18) : 2389 - 2396
  • [35] Efficient SAT-Based Minimal Model Generation Methods for Modal Logic S5
    Huang, Pei
    Li, Rundong
    Liu, Minghao
    Ma, Feifei
    Zhang, Jian
    [J]. THEORY AND APPLICATIONS OF SATISFIABILITY TESTING, SAT 2021, 2021, 12831 : 225 - 241
  • [36] AN ALGEBRAIC STUDY OF THE LOGIC S5'(BL)
    Wang, Juntao
    He, Xiaoli
    Wang, Mei
    [J]. MATHEMATICA SLOVACA, 2022, 72 (06) : 1447 - 1462
  • [37] The Situation Calculus: A Case for Modal Logic
    Lakemeyer G.
    [J]. Journal of Logic, Language and Information, 2010, 19 (4) : 431 - 450
  • [38] A SEQUENT CALCULUS FOR THE MODAL LOGIC OF PROVABILITY
    VALENTINI, S
    [J]. JOURNAL OF SYMBOLIC LOGIC, 1984, 49 (02) : 707 - 708
  • [39] Noncommuting (S5, S5)-amalgams
    Bundy, D
    [J]. COMMUNICATIONS IN ALGEBRA, 2006, 34 (03) : 1149 - 1180
  • [40] Hypersequent Calculi for Modal Logics Extending S4
    Kurokawa, Hidenori
    [J]. NEW FRONTIERS IN ARTIFICIAL INTELLIGENCE (JSAI-ISAI 2013), 2014, 8417 : 51 - 68