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&...

Full description

Saved in:
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
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract 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.
AbstractList 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.
Author Colcombet, Thomas
Author_xml – sequence: 1
  givenname: Thomas
  surname: Colcombet
  fullname: Colcombet, Thomas
  email: thomas.colcombet@liafa.univ-paris-diderot.fr
  organization: LIAFA, Univ. Paris-Diderot, Paris, France
BookMark eNotzEFLwzAUwPGAE9ymN29e8gVa32vSZDlKUVfoFNyGx_HavG6VmUhbB_v2Cnr5_27_mZiEGFiIW4QUEdx9VRbrNANUKdoLMUNtnQONyk3EFEGrxCwsXonZMHwAQGY0TMXLivahG789y1UM5LtGVnH_23jiXr7H3g-SgpfjgeV2YBlb-cZHGrsTyzKM3Ac6yjWPcnPg2J-vxWVLx4Fv_p2L7dPjplgm1etzWTxUCWUax8RADeib2vrW5QZb2zBQZi163SoHzi-YG0usa1ODqb1jsqwV1QunyGGj5uLu79sx8-6r7z6pP-9MbjHXSv0AVVZOmA
CODEN IEEPAD
ContentType Conference Proceeding
DBID 6IE
6IH
CBEJK
RIE
RIO
DOI 10.1109/LICS.2013.17
DatabaseName IEEE Electronic Library (IEL) Conference Proceedings
IEEE Proceedings Order Plan (POP) 1998-present by volume
IEEE Xplore All Conference Proceedings
IEEE Electronic Library (IEL)
IEEE Proceedings Order Plans (POP) 1998-present
DatabaseTitleList
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Electronic Library (IEL)
  url: https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EndPage 123
ExternalDocumentID 6571543
Genre orig-research
GroupedDBID --Z
23M
29P
6IE
6IF
6IH
6IK
6IL
6IM
6IN
AAJGR
AAWTH
ADZIZ
ALMA_UNASSIGNED_HOLDINGS
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
CBEJK
CHZPO
IEGSK
IJVOP
IPLJI
M43
OCL
RIE
RIL
RIO
RNS
ID FETCH-LOGICAL-a241t-60b01dcb7df9561f7ce0a2771d4f3909d8eec7ae4b6b06bd9ea7e43ab893a91c3
IEDL.DBID RIE
ISBN 1479904139
9781479904136
ISICitedReferencesCount 2
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000326815000016&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1043-6871
IngestDate Wed Aug 27 04:17:06 EDT 2025
IsPeerReviewed false
IsScholarly true
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-a241t-60b01dcb7df9561f7ce0a2771d4f3909d8eec7ae4b6b06bd9ea7e43ab893a91c3
PageCount 1
ParticipantIDs ieee_primary_6571543
PublicationCentury 2000
PublicationDate 2013-June
PublicationDateYYYYMMDD 2013-06-01
PublicationDate_xml – month: 06
  year: 2013
  text: 2013-June
PublicationDecade 2010
PublicationTitle 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
PublicationTitleAbbrev lics
PublicationYear 2013
Publisher IEEE
Publisher_xml – name: IEEE
SSID ssj0002640
ssj0001035133
Score 1.8530318
Snippet Cost monadic logic extends monadic second-order logic with the ability to measure the cardinality of sets and comes with decision procedures for boundedness...
SourceID ieee
SourceType Publisher
StartPage 123
SubjectTerms Automata
Context
Games
Set theory
Syntactics
Upper bound
Title Magnitude Monadic Logic over Words and the Use of Relative Internal Set Theory
URI https://ieeexplore.ieee.org/document/6571543
WOSCitedRecordID wos000326815000016&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3Pa8IwFH6o7LCT23TsNznsuGjatElzlskGmwhO5k3y4xWEoUOrf_-StiqDXXZrSw4lIe_Le_m-9wE8MinzTCWMIs9Smmg01MTa0MiKVHFtWISsNJuQo1E2m6lxA54OWhhELMln2AuP5V2-W9ltKJX1RSo94vMmNKUUlVbrWE8JV2L8GIU90NedCDgVPisoRV3Sx14ftdW-11P9Lg6MeNV_ex1MAuOL96Lfjisl4Azb__vVM-gelXtkfMCkc2jg8gLae-sGUu_kDozedaANbR0Sv6u1W1gSXJctCYxO8ukz0g3RS0f88ZBMN0hWOaloczskdRHxi0ywIJW2vwvT4fPH4IXW1gpUe8guqAj1T2eNdHlQtubSItOxlJFLcq6YchmilRoTIwwTxinUEhO_dv54o1Vk-SW0lqslXgFhJvPZeZa5PFWJH6yZ9TlKjEKnhsWOXUMnTM_8u-qeMa9n5ubvz7dwGleGE5RFd9Aq1lu8hxO7Kxab9UO55D9oKqWk
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1NawIxEA3WFtqTbbX0uzn02Gj2K9mcpaJUF0Gl3iQfsyCUtejq72-yuyqFXnrbXXJYEjIvM3lvHkKvlPM0FiElEMQRCSUoonypiKdZJAKpqAe0MJvgSRLP52JcQ28HLQwAFOQzaLvH4i7frPTWlco6LOIW8YMTdBqFoU9LtdaxouIuxYJjHLZQX_UiCAizeUEh6-I2-tq4Lfbdnqp3duDEi85w0J04zlfQ9n57rhSQ02v872cvUeuo3cPjAypdoRpk16ixN2_A1V5uomQkHXFoawDbfS3NUmPnu6yx43TiT5uTbrDMDLYHRDzbAF6luCTO7QBXZcQvPIEcl-r-Fpr13qfdPqnMFYi0oJ0T5iqgRituUqdtTbkGKn3OPROmgaDCxACaSwgVU5QpI0ByCO3q2QOOFJ4OblA9W2VwizBVsc3P49ikkQjtYEm1zVJ8YDJS1Df0DjXd9Cy-y_4Zi2pm7v_-_ILO-9PRcDEcJB8P6MIv7ScI9R5RPV9v4Qmd6V2-3Kyfi-X_ATvOqOs
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=proceeding&rft.title=2013+28th+Annual+ACM%2FIEEE+Symposium+on+Logic+in+Computer+Science&rft.atitle=Magnitude+Monadic+Logic+over+Words+and+the+Use+of+Relative+Internal+Set+Theory&rft.au=Colcombet%2C+Thomas&rft.date=2013-06-01&rft.pub=IEEE&rft.isbn=9781479904136&rft.issn=1043-6871&rft.spage=123&rft.epage=123&rft_id=info:doi/10.1109%2FLICS.2013.17&rft.externalDocID=6571543
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1043-6871&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1043-6871&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1043-6871&client=summon