Löb’s Logic Meets the μ-Calculus

In this paper, we prove that Löb’s Logic is a retract of the modal μ-calculus in a suitable category of interpretations. We show that various salient properties like decidability and uniform interpolation are preserved over retractions. We prove a generalization of the de Jongh-Sambin theorem.

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Bibliographic Details
Published inProcesses, Terms and Cycles: Steps on the Road to Infinity pp. 14 - 25
Main Author Visser, Albert
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2005
SeriesLecture Notes in Computer Science
Subjects
Free Variable
Modal Logic
Monotonic Operator
Propositional Logic
Propositional Variable
Online AccessGet full text
ISBN354030911X
9783540309116
ISSN0302-9743
1611-3349
DOI10.1007/11601548_3

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Summary:In this paper, we prove that Löb’s Logic is a retract of the modal μ-calculus in a suitable category of interpretations. We show that various salient properties like decidability and uniform interpolation are preserved over retractions. We prove a generalization of the de Jongh-Sambin theorem.
ISBN:354030911X
9783540309116
ISSN:0302-9743
1611-3349
DOI:10.1007/11601548_3