On Boolean Algebraic Structure of Proofs: Towards an Algebraic Semantics for the Logic of Proofs

被引:0
|
作者
Farahmand Parsa, Amir [1 ]
Ghari, Meghdad [2 ]
机构
[1] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran
[2] Univ Isfahan, Fac Literature & Humanities, Dept Philosophy, Esfahan, Iran
关键词
Logic of proofs; Algebraic semantics; Completeness; Representation theorem;
D O I
10.1007/s11225-022-10033-2
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on proof terms and equality predicate on terms. Moreover, the completeness theorem and certain generalizations of Stone's representation theorem are obtained for all proposed algebras.
引用
收藏
页码:573 / 613
页数:41
相关论文
共 50 条
  • [31] Categorical Abstract Algebraic Logic: Algebraic Semantics for π-Institutions
    Voutsadakis, George
    MATHEMATICAL LOGIC QUARTERLY, 2013, 59 (03) : 177 - 200
  • [32] Categorical Abstract Algebraic Logic: Referential Algebraic Semantics
    George Voutsadakis
    Studia Logica, 2013, 101 : 849 - 899
  • [33] Calculational relation-algebraic proofs in Isabelle/Isar
    Kahl, W
    RELATIONAL AND KLEENE-ALGEBRAIC METHODS IN COMPUTER SCIENCE, 2003, 3051 : 178 - 190
  • [34] Interactive Oracle Proofs of Proximity to Algebraic Geometry Codes
    Bordage, Sarah
    Lhotel, Mathieu
    Nardi, Jade
    Randriam, Hugues
    Leibniz International Proceedings in Informatics, LIPIcs, 2022, 234
  • [35] Defining Logical Systems via Algebraic Constraints on Proofs
    Gheorghiu, Alexander, V
    Pym, David J.
    JOURNAL OF LOGIC AND COMPUTATION, 2023,
  • [36] Two new proofs concerning the intrinsic algebraic entropy
    Salce, Luigi
    Virili, Simone
    COMMUNICATIONS IN ALGEBRA, 2018, 46 (09) : 3939 - 3949
  • [37] Towards an Algebraic Semantics for Implicatives
    Zuber, R.
    JOURNAL OF LOGIC LANGUAGE AND INFORMATION, 2020, 29 (04) : 525 - 538
  • [38] Towards an Algebraic Semantics for Implicatives
    R. Zuber
    Journal of Logic, Language and Information, 2020, 29 : 525 - 538
  • [39] ALGEBRAIC SEMANTICS FOR MODAL PREDICATE LOGIC
    FREEMAN, JB
    ZEITSCHRIFT FUR MATHEMATISCHE LOGIK UND GRUNDLAGEN DER MATHEMATIK, 1976, 22 (06): : 523 - 552
  • [40] Algebraic Semantics for Dynamic Dynamic Logic
    Ma, Minghui
    Seligman, Jeremy
    LOGIC, RATIONALITY, AND INTERACTION (LORI 2015), 2015, 9394 : 255 - 267