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Embedding theorems for LTL and its variants†

Published online by Cambridge University Press:  02 December 2014

NORIHIRO KAMIDE
NORIHIRO KAMIDE*
Affiliation:
Department of Human Information Systems, Faculty of Science and Engineering, Teikyo University, Toyosatodai 1-1, Utsunomiya-shi, Tochigi 320-8551, Japan Email: [email protected]
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Abstract

In this paper, we prove some embedding theorems for LTL (linear-time temporal logic) and its variants: viz. some generalisations, extensions and fragments of LTL. Using these embedding theorems, we give uniform proofs of the completeness, cut-elimination and/or decidability theorems for LTL and its variants. The proposed embedding theorems clarify the relationships between some LTL-variations (for example, LTL, a dynamic topological logic, a fixpoint logic, a spatial logic, Prior's logic, Davies' logic and an NP-complete LTL) and some traditional logics (for example, classical logic, intuitionistic logic and infinitary logic).

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 25 , Issue 1 , January 2015 , pp. 83 - 134
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

†

Sections 2, 4, 5, 6.1 and 6.3 in the current paper are based on some refinements of technical parts of the conference presentations Kamide (2009; 2010b; 2010d; 2010e; 2011).

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