Logic without contraction as based on inclusion and unrestricted abstraction

DOI10.1023/A:1005293713265zbMath0954.03023OpenAlexW1570665400MaRDI QIDQ1577364

Uwe Petersen

Publication date: 14 February 2001

Published in: Studia Logica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1005293713265

zbMATH Keywords

contraction free logicfoundation of the notion of natural numbertype free logicunrestricted abstraction

Mathematics Subject Classification ID

Cut-elimination and normal-form theorems (03F05) Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47) Subsystems of classical logic (including intuitionistic logic) (03B20)

Related Items (16)

Is cut-free logic fit for unrestricted abstraction? ⋮ Non-monotonic set theory as a pragmatic foundation of mathematics ⋮ Stability and paradox in algorithmic logic ⋮ CONTRACTIONS OF NONCONTRACTIVE CONSEQUENCE RELATIONS ⋮ NAIVE SET THEORY AND NONTRANSITIVE LOGIC ⋮ Systems for non-reflexive consequence ⋮ (I can't get no) antisatisfaction ⋮ ON ZARDINI’S RULES FOR MULTIPLICATIVE QUANTIFICATION AS THE SOURCE OF CONTRA(DI)CTIONS ⋮ On contraction and the modal fragment ⋮ TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY ⋮ REPLY TO BJØRDAL ⋮ Extensionality and restriction in naive set theory ⋮ Variations on a theme of Curry ⋮ MODAL LOGIC WITHOUT CONTRACTION IN A METATHEORY WITHOUT CONTRACTION ⋮ A NOTE ON THE CUT-ELIMINATION PROOF IN “TRUTH WITHOUT CONTRA(DI)CTION” ⋮ Enhancing induction in a contraction free logic with unrestricted abstraction: from \(\mathbf{Z}\) to \(\mathbf{Z}_2\)

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