Default Logic and Bounded Treewidth

Default Logic and Bounded Treewidth

In this paper, we study Reiter's propositional default logic when the treewidth of a certain graph representation (semi-primal graph) of the input theory is bounded. We establish a dynamic programming algorithm on tree decompositions that decides whether a theory has a consistent stable extensi...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2017-12
Hauptverfasser: Fichte, Johannes K, Hecher, Markus, Schindler, Irina
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Dynamic programming
Graph representations
Graphical representations
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Fichte, Johannes K
Hecher, Markus
Schindler, Irina
description In this paper, we study Reiter's propositional default logic when the treewidth of a certain graph representation (semi-primal graph) of the input theory is bounded. We establish a dynamic programming algorithm on tree decompositions that decides whether a theory has a consistent stable extension (Ext). Our algorithm can even be used to enumerate all generating defaults (ExtEnum) that lead to stable extensions. We show that our algorithm decides Ext in linear time in the input theory and triple exponential time in the treewidth (so-called fixed-parameter linear algorithm). Further, our algorithm solves ExtEnum with a pre-computation step that is linear in the input theory and triple exponential in the treewidth followed by a linear delay to output solutions.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2068916881</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2068916881</sourcerecordid><originalsourceid>FETCH-proquest_journals_20689168813</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mRQdklNSyzNKVHwyU_PTFZIzEtRcMovzUtJTVEIKUpNLc9MKcngYWBNS8wpTuWF0twMym6uIc4eugVF-YWlqcUl8Vn5pUV5QKl4IwMzC0tDMwsLQ2PiVAEAZogt4Q</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2068916881</pqid></control><display><type>article</type><title>Default Logic and Bounded Treewidth</title><source>Free E- Journals</source><creator>Fichte, Johannes K ; Hecher, Markus ; Schindler, Irina</creator><creatorcontrib>Fichte, Johannes K ; Hecher, Markus ; Schindler, Irina</creatorcontrib><description>In this paper, we study Reiter's propositional default logic when the treewidth of a certain graph representation (semi-primal graph) of the input theory is bounded. We establish a dynamic programming algorithm on tree decompositions that decides whether a theory has a consistent stable extension (Ext). Our algorithm can even be used to enumerate all generating defaults (ExtEnum) that lead to stable extensions. We show that our algorithm decides Ext in linear time in the input theory and triple exponential time in the treewidth (so-called fixed-parameter linear algorithm). Further, our algorithm solves ExtEnum with a pre-computation step that is linear in the input theory and triple exponential in the treewidth followed by a linear delay to output solutions.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algorithms ; Dynamic programming ; Graph representations ; Graphical representations</subject><ispartof>arXiv.org, 2017-12</ispartof><rights>2017. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784</link.rule.ids></links><search><creatorcontrib>Fichte, Johannes K</creatorcontrib><creatorcontrib>Hecher, Markus</creatorcontrib><creatorcontrib>Schindler, Irina</creatorcontrib><title>Default Logic and Bounded Treewidth</title><title>arXiv.org</title><description>In this paper, we study Reiter's propositional default logic when the treewidth of a certain graph representation (semi-primal graph) of the input theory is bounded. We establish a dynamic programming algorithm on tree decompositions that decides whether a theory has a consistent stable extension (Ext). Our algorithm can even be used to enumerate all generating defaults (ExtEnum) that lead to stable extensions. We show that our algorithm decides Ext in linear time in the input theory and triple exponential time in the treewidth (so-called fixed-parameter linear algorithm). Further, our algorithm solves ExtEnum with a pre-computation step that is linear in the input theory and triple exponential in the treewidth followed by a linear delay to output solutions.</description><subject>Algorithms</subject><subject>Dynamic programming</subject><subject>Graph representations</subject><subject>Graphical representations</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mRQdklNSyzNKVHwyU_PTFZIzEtRcMovzUtJTVEIKUpNLc9MKcngYWBNS8wpTuWF0twMym6uIc4eugVF-YWlqcUl8Vn5pUV5QKl4IwMzC0tDMwsLQ2PiVAEAZogt4Q</recordid><startdate>20171230</startdate><enddate>20171230</enddate><creator>Fichte, Johannes K</creator><creator>Hecher, Markus</creator><creator>Schindler, Irina</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20171230</creationdate><title>Default Logic and Bounded Treewidth</title><author>Fichte, Johannes K ; Hecher, Markus ; Schindler, Irina</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20689168813</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algorithms</topic><topic>Dynamic programming</topic><topic>Graph representations</topic><topic>Graphical representations</topic><toplevel>online_resources</toplevel><creatorcontrib>Fichte, Johannes K</creatorcontrib><creatorcontrib>Hecher, Markus</creatorcontrib><creatorcontrib>Schindler, Irina</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fichte, Johannes K</au><au>Hecher, Markus</au><au>Schindler, Irina</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Default Logic and Bounded Treewidth</atitle><jtitle>arXiv.org</jtitle><date>2017-12-30</date><risdate>2017</risdate><eissn>2331-8422</eissn><abstract>In this paper, we study Reiter's propositional default logic when the treewidth of a certain graph representation (semi-primal graph) of the input theory is bounded. We establish a dynamic programming algorithm on tree decompositions that decides whether a theory has a consistent stable extension (Ext). Our algorithm can even be used to enumerate all generating defaults (ExtEnum) that lead to stable extensions. We show that our algorithm decides Ext in linear time in the input theory and triple exponential time in the treewidth (so-called fixed-parameter linear algorithm). Further, our algorithm solves ExtEnum with a pre-computation step that is linear in the input theory and triple exponential in the treewidth followed by a linear delay to output solutions.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2017-12
issn 2331-8422
language eng
recordid cdi_proquest_journals_2068916881
source Free E- Journals
subjects Algorithms
Dynamic programming
Graph representations
Graphical representations
title Default Logic and Bounded Treewidth
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-02T11%3A33%3A10IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Default%20Logic%20and%20Bounded%20Treewidth&rft.jtitle=arXiv.org&rft.au=Fichte,%20Johannes%20K&rft.date=2017-12-30&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2068916881%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2068916881&rft_id=info:pmid/&rfr_iscdi=true