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ANALYTIC CUT AND INTERPOLATION FOR BI-INTUITIONISTIC LOGIC

  • TOMASZ KOWALSKI (a1) and HIROAKIRA ONO (a2)
Abstract
Abstract

We prove that certain natural sequent systems for bi-intuitionistic logic have the analytic cut property. In the process we show that the (global) subformula property implies the (local) analytic cut property, thereby demonstrating their equivalence. Applying a version of Maehara technique modified in several ways, we prove that bi-intuitionistic logic enjoys the classical Craig interpolation property and Maximova variable separation property; its Halldén completeness follows.

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*DEPARTMENT OF MATHEMATICS AND STATISTICS LA TROBE UNIVERSITY MELBOURNE, VICTORIA 3086 AUSTRALIA E-mail: t.kowalski@latrobe.edu.au
JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY 1-1 ASAHIDAI, NOMI, ISHIKAWA 923-1292 JAPAN E-mail: ono@jaist.ac.jp
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
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