From Frame Properties to Hypersequent Rules in Modal Logics

We provide a general method for generating cutfree and/or analytic hypersequent Gentzen-type calculi for a variety of normal modal logics. The method applies to all modal logics characterized by Kripke frames, transitive Kripke frames, or symmetric Kripke frames satisfying some properties, given by...

Full description

Saved in:
Bibliographic Details
Published in:2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 408 - 417
Main Author: Lahav, Ori
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2013
Subjects:
Calculus
Computer science
Context
cut-admissibility
Educational institutions
frame properties
hypersequent calculi
modal logic
proof theory
Semantics
Syntactics
ISBN:1479904139, 9781479904136
ISSN:1043-6871
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract We provide a general method for generating cutfree and/or analytic hypersequent Gentzen-type calculi for a variety of normal modal logics. The method applies to all modal logics characterized by Kripke frames, transitive Kripke frames, or symmetric Kripke frames satisfying some properties, given by first-order formulas of a certain simple form. This includes the logics KT, KD, S4, S5, K4D, K4.2, K4.3, KBD, KBT, and other modal logics, for some of which no Gentzen calculi was presented before. Cut-admissibility (or analyticity in the case of symmetric Kripke frames) is proved semantically in a uniform way for all constructed calculi. The decidability of each modal logic in this class immediately follows.
AbstractList We provide a general method for generating cutfree and/or analytic hypersequent Gentzen-type calculi for a variety of normal modal logics. The method applies to all modal logics characterized by Kripke frames, transitive Kripke frames, or symmetric Kripke frames satisfying some properties, given by first-order formulas of a certain simple form. This includes the logics KT, KD, S4, S5, K4D, K4.2, K4.3, KBD, KBT, and other modal logics, for some of which no Gentzen calculi was presented before. Cut-admissibility (or analyticity in the case of symmetric Kripke frames) is proved semantically in a uniform way for all constructed calculi. The decidability of each modal logic in this class immediately follows.
Author Lahav, Ori
Author_xml – sequence: 1
  givenname: Ori
  surname: Lahav
  fullname: Lahav, Ori
  email: orilahav@post.tau.ac.il
  organization: Sch. of Comput. Sci., Tel Aviv Univ., Tel Aviv, Israel
BookMark eNotj0tLw0AURgesYFPduXMzfyDx3swrwZUE0xYiLT7WZZrcSCTJ1Jl00X9vQFcf5ywOfBFbjG4kxu4REkTIH6tt8Z6kgCKR5opFKE2eg0SRL9gSQYpYZwZvWBTCNwCkWsKSPZXeDbz0diC-9-5Efuoo8MnxzWWGQD9nGif-du5n24381TW255X76upwy65b2we6-98V-yxfPopNXO3W2-K5im0qcYpr1LVRNiUp1LHVR6hla63RllBDaynNdYOaQDemUUJkmSGaT0jUKmsbm4kVe_jrdkR0OPlusP5y0MqgMkL8AhM0R2k
CODEN IEEPAD
ContentType Conference Proceeding
DBID 6IE
6IH
CBEJK
RIE
RIO
DOI 10.1109/LICS.2013.47
DatabaseName IEEE Electronic Library (IEL) Conference Proceedings
IEEE Proceedings Order Plan (POP) 1998-present by volume
IEEE Xplore All Conference Proceedings
IEEE Xplore
IEEE Proceedings Order Plans (POP) 1998-present
DatabaseTitleList
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Xplore
  url: https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EndPage 417
ExternalDocumentID 6571573
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-c16c75a2e435bf6b0c4faa76ae160fae296d16e06d7d533887ee01341658fda83
IEDL.DBID RIE
ISBN 1479904139
9781479904136
ISICitedReferencesCount 35
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000326815000046&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 04:17:07 EDT 2025
IsPeerReviewed false
IsScholarly true
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-a241t-c16c75a2e435bf6b0c4faa76ae160fae296d16e06d7d533887ee01341658fda83
PageCount 10
ParticipantIDs ieee_primary_6571573
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 2.0403683
Snippet We provide a general method for generating cutfree and/or analytic hypersequent Gentzen-type calculi for a variety of normal modal logics. The method applies...
SourceID ieee
SourceType Publisher
StartPage 408
SubjectTerms Calculus
Computer science
Context
cut-admissibility
Educational institutions
frame properties
hypersequent calculi
modal logic
proof theory
Semantics
Syntactics
Title From Frame Properties to Hypersequent Rules in Modal Logics
URI https://ieeexplore.ieee.org/document/6571573
WOSCitedRecordID wos000326815000046&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/eLvHCXMwlV07a8MwEBZJ6NApbZPSNxo6Von8kmw6hpoU2hD6gGxBlk4QSOPgOP39PdlOAqVLN0sYYWTuvjvpu_sIuTc88SWPLVOR1iwUmUGbCxPGDaKP0GhRmldiE3IyiWezZNoiD_taGACoyGcwcI_VXb7J9dYdlQ1FJL1IBm3SllLUtVqH8xR3JRYcvDACfdOJIGACs4KqqEui70Wvnex6PTVjsWfEJ8OX59G7Y3wFg1-KKxXgpN3_feoJ6R8q9-h0j0mnpAWrM9LdSTfQxpJ75DEt8i-aOmaWe3_t2NWwoWVOx5iYFjXBuqRv2yXOLlb0NTdqSZ0ws970yWf69DEas0ZHgSnE55JpT2gZKR8wNMqsyLgOrVJSKPAEtwr8RBhPABdGGoz-0O0AcNfoDaMTa1QcnJPOKl_BBaGhlbEIFVcZplnG2MxCjIvJCO0YMHq7JD23F_N13Spj3mzD1d_T1-TYr9UlGPduSKcstnBLjvR3udgUd9X__QGRLJ7-
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1bS8MwFA5zCvo0dRPv5sFHs6W3pMXHYdlwG0Mn7G2kucBgtqPr_P2etHUD8cW3JpRQUs75zkm-cz6EHhWNXE5DQ0QgJfFZosDm_IhQBejDJFiUpKXYBJ9Mwvk8mjbQ064WRmtdks901z6Wd_kqk1t7VNZjAXcC7h2gw8D3XVpVa-1PVOylmLf3wwD1dS8CjzDIC8qyLg7eF_x29NPtqR6zHSc-6o2G_XfL-fK6vzRXSsiJW__72FPU2dfu4ekOlc5QQ6fnqPUj3oBrW26j5zjPPnFsuVn2_bXlV-sNLjI8gNQ0ryjWBX7brmB2meJxpsQKW2lmuemgj_hl1h-QWkmBCEDogkiHSR4IV0NwlBiWUOkbITgT2mHUCO1GTDlMU6a4gvgPHI_W1LZ6g_jEKBF6F6iZZqm-RNg3PGS-oCKBREspkxgdwmI8AEvWEL9dobbdi8W6apaxqLfh-u_pB3Q8mI1Hi9Fw8nqDTtxKa4JQ5xY1i3yr79CR_CqWm_y-_NffDpuiRQ
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=From+Frame+Properties+to+Hypersequent+Rules+in+Modal+Logics&rft.au=Lahav%2C+Ori&rft.date=2013-06-01&rft.pub=IEEE&rft.isbn=9781479904136&rft.issn=1043-6871&rft.spage=408&rft.epage=417&rft_id=info:doi/10.1109%2FLICS.2013.47&rft.externalDocID=6571573
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