Monotonic and nonmonotonic gentzen deduction systems for L3-valued propositional logic
A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In L 3 -valued propositional logic, a multisequent is a triple Δ|Θ|Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in...
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| Veröffentlicht in: | Frontiers of Computer Science 2021-06, Vol.15 (3), p.153401, Article 153401 |
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| creator | Cao, Cungen Hu, Lanxi Sui, Yuefei |
| description | A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In
L
3
-valued propositional logic, a multisequent is a triple Δ|Θ|Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in Θ has truth-value m, or some formula in Γ has truth-value f. Correspondingly there is a sound and complete Gentzen deduction system
G
for multisequents which is monotonic. Dually, a co-multisequent is a triple Δ: Θ: Γ, which is valid if there is an assignment
v
in which each formula in Δ has truth-value ≠ t, each formula in Θ has truth-value ≠ m, and each formula in Γ has truth-value ≠ f. Correspondingly there is a sound and complete Gentzen deduction system
G
−
for co-multisequents which is nonmonotonic. |
| doi_str_mv | 10.1007/s11704-020-9076-2 |
| format | Article |
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L
3
-valued propositional logic, a multisequent is a triple Δ|Θ|Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in Θ has truth-value m, or some formula in Γ has truth-value f. Correspondingly there is a sound and complete Gentzen deduction system
G
for multisequents which is monotonic. Dually, a co-multisequent is a triple Δ: Θ: Γ, which is valid if there is an assignment
v
in which each formula in Δ has truth-value ≠ t, each formula in Θ has truth-value ≠ m, and each formula in Γ has truth-value ≠ f. Correspondingly there is a sound and complete Gentzen deduction system
G
−
for co-multisequents which is nonmonotonic.</description><identifier>ISSN: 2095-2228</identifier><identifier>EISSN: 2095-2236</identifier><identifier>DOI: 10.1007/s11704-020-9076-2</identifier><language>eng</language><publisher>Beijing: Higher Education Press</publisher><subject>Computer Science ; Logic ; Research Article ; Semantics ; Variables</subject><ispartof>Frontiers of Computer Science, 2021-06, Vol.15 (3), p.153401, Article 153401</ispartof><rights>Higher Education Press 2020</rights><rights>Higher Education Press 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c1832-f2946eb1d935bfbeea2c73ed7adaf0f290af2b08063465bfb08dd6cf3835c03c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11704-020-9076-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918721637?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,776,780,21367,27901,27902,33721,41464,42533,43781,51294</link.rule.ids></links><search><creatorcontrib>Cao, Cungen</creatorcontrib><creatorcontrib>Hu, Lanxi</creatorcontrib><creatorcontrib>Sui, Yuefei</creatorcontrib><title>Monotonic and nonmonotonic gentzen deduction systems for L3-valued propositional logic</title><title>Frontiers of Computer Science</title><addtitle>Front. Comput. Sci</addtitle><description>A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In
L
3
-valued propositional logic, a multisequent is a triple Δ|Θ|Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in Θ has truth-value m, or some formula in Γ has truth-value f. Correspondingly there is a sound and complete Gentzen deduction system
G
for multisequents which is monotonic. Dually, a co-multisequent is a triple Δ: Θ: Γ, which is valid if there is an assignment
v
in which each formula in Δ has truth-value ≠ t, each formula in Θ has truth-value ≠ m, and each formula in Γ has truth-value ≠ f. Correspondingly there is a sound and complete Gentzen deduction system
G
−
for co-multisequents which is nonmonotonic.</description><subject>Computer Science</subject><subject>Logic</subject><subject>Research Article</subject><subject>Semantics</subject><subject>Variables</subject><issn>2095-2228</issn><issn>2095-2236</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp1kEtLAzEUhYMoWLQ_wF3AdfTmpvNaSvEFFTfqNmTyKFOmSU1mhPrrTRmpK1f3cu93DodDyBWHGw5Q3SbOK1gwQGANVCXDEzJDaAqGKMrT4471OZmntAHIJBYF4ox8vAQfhuA7TZU31Ae_PR7W1g_f1lNjzaiHLnia9mmw20RdiHQl2JfqR2voLoZdSN2BUD3tw7rTl-TMqT7Z-e-8IO8P92_LJ7Z6fXxe3q2Y5rVA5rBZlLblphFF61prFepKWFMpoxzkLyiHLdRQikV5IKA2ptRO1KLQILS4INeTb87wOdo0yE0YY46RJDa8rpCXosoUnygdQ0rROrmL3VbFveQgDw3KqUGZe5GHBiVmDU6alFm_tvHP-X_RD38MdMQ</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>Cao, Cungen</creator><creator>Hu, Lanxi</creator><creator>Sui, Yuefei</creator><general>Higher Education Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope></search><sort><creationdate>20210601</creationdate><title>Monotonic and nonmonotonic gentzen deduction systems for L3-valued propositional logic</title><author>Cao, Cungen ; Hu, Lanxi ; Sui, Yuefei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1832-f2946eb1d935bfbeea2c73ed7adaf0f290af2b08063465bfb08dd6cf3835c03c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Computer Science</topic><topic>Logic</topic><topic>Research Article</topic><topic>Semantics</topic><topic>Variables</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cao, Cungen</creatorcontrib><creatorcontrib>Hu, Lanxi</creatorcontrib><creatorcontrib>Sui, Yuefei</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection (ProQuest)</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>Frontiers of Computer Science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cao, Cungen</au><au>Hu, Lanxi</au><au>Sui, Yuefei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Monotonic and nonmonotonic gentzen deduction systems for L3-valued propositional logic</atitle><jtitle>Frontiers of Computer Science</jtitle><stitle>Front. Comput. Sci</stitle><date>2021-06-01</date><risdate>2021</risdate><volume>15</volume><issue>3</issue><spage>153401</spage><pages>153401-</pages><artnum>153401</artnum><issn>2095-2228</issn><eissn>2095-2236</eissn><abstract>A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In
L
3
-valued propositional logic, a multisequent is a triple Δ|Θ|Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in Θ has truth-value m, or some formula in Γ has truth-value f. Correspondingly there is a sound and complete Gentzen deduction system
G
for multisequents which is monotonic. Dually, a co-multisequent is a triple Δ: Θ: Γ, which is valid if there is an assignment
v
in which each formula in Δ has truth-value ≠ t, each formula in Θ has truth-value ≠ m, and each formula in Γ has truth-value ≠ f. Correspondingly there is a sound and complete Gentzen deduction system
G
−
for co-multisequents which is nonmonotonic.</abstract><cop>Beijing</cop><pub>Higher Education Press</pub><doi>10.1007/s11704-020-9076-2</doi></addata></record> |
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| language | eng |
| recordid | cdi_proquest_journals_2918721637 |
| source | SpringerLink Journals - AutoHoldings; ProQuest Central |
| subjects | Computer Science Logic Research Article Semantics Variables |
| title | Monotonic and nonmonotonic gentzen deduction systems for L3-valued propositional logic |
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