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ANALYTIC CUT AND INTERPOLATION FOR BI-INTUITIONISTIC LOGIC

Published online by Cambridge University Press:  06 December 2016

TOMASZ KOWALSKI  and
HIROAKIRA ONO
TOMASZ KOWALSKI*
Affiliation:
Department of Mathematics and Statistics, La Trobe University
HIROAKIRA ONO*
Affiliation:
Japan Advanced Institute of Science and Technology
*
*DEPARTMENT OF MATHEMATICS AND STATISTICS LA TROBE UNIVERSITY MELBOURNE, VICTORIA 3086 AUSTRALIA E-mail: [email protected]
†JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY 1-1 ASAHIDAI, NOMI, ISHIKAWA 923-1292 JAPAN E-mail: [email protected]
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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.

Keywords

analytic cutsubformula propertyinterpolation03F0303B4703F52
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 2 , June 2017 , pp. 259 - 283
Copyright
Copyright © Association for Symbolic Logic 2016 

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