Magnitude Monadic Logic over Words and the Use of Relative Internal Set Theory

Cost monadic logic extends monadic second-order logic with the ability to measure the cardinality of sets and comes with decision procedures for boundedness related questions. We provide new decidability results allowing the systematic investigation of questions involving "relative boundedness&...

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Bibliographic Details
Published in:2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science p. 123
Main Author: Colcombet, Thomas
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2013
Subjects:
Automata
Context
Games
Set theory
Syntactics
Upper bound
ISBN:1479904139, 9781479904136
ISSN:1043-6871
Online Access:Get full text
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Summary:Cost monadic logic extends monadic second-order logic with the ability to measure the cardinality of sets and comes with decision procedures for boundedness related questions. We provide new decidability results allowing the systematic investigation of questions involving "relative boundedness". We first introduce a suitable logic, magnitude monadic logic. We then establish the decidability of this logic over finite words. We finally advocate that developing the proofs in the axiomatic system of "relative internal set theory", a variant of nonstandard analysis, entails a significant simplification of the proofs.
ISBN:1479904139
9781479904136
ISSN:1043-6871
DOI:10.1109/LICS.2013.17