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Published in:
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2010 | OriginalPaper | Chapter

9. Logics of Linear Frames

Author : Dr. Andrzej Indrzejczak

Published in: Natural Deduction, Hybrid Systems and Modal Logics

Publisher: Springer Netherlands

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Abstract

Logics of linear frames, called here for short linear logics form a particularly interesting and important class, especially in temporal interpretation. But we devote a separate Chapter for their treatment not because of their importance but rather because of special problems generated by their formalization in the setting of labelled systems.

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previous chapter Labelled Systems in Modal Logics
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Footnotes
1
It shouldn't cause any misunderstanding, since in this book we do not deal with Girard's linear logic.
 
2
Note that we do not apply superscripts with “{” in monomodal case.
 
3
An additional effect of identifying a new state with every one already present.
 
4
The latter feature was in fact present also in our labelled rules for weak logics introduced in Section 8.​6.
 
5
Actually, it is performed for labelled KE-system with \((\nu 3^{\prime})\) not for LAND1 but that is not the point.
 
6
Analytic labelled system for these logics may be found in Leszczy'nska [175] but it is based on the rules of different character.
 
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Metadata
Title
Logics of Linear Frames
Author
Dr. Andrzej Indrzejczak
Copyright Year
2010
Publisher
Springer Netherlands
Book
Natural Deduction, Hybrid Systems and Modal Logics

Print ISBN: 978-90-481-8784-3

Electronic ISBN: 978-90-481-8785-0

Copyright Year: 2010

DOI
https://doi.org/10.1007/978-90-481-8785-0_9

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