An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras
An alternative notion of an existential quantifier on four-valued Łukasiewicz algebras is introduced. The class of four-valued Łukasiewicz algebras endowed with this existential quantifier determines a variety which is denoted by M 2 3 L 4 . It is shown that the alternative existential quantifier is...
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| Veröffentlicht in: | Logica universalis 2017-12, Vol.11 (4), p.439-463 |
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| container_title | Logica universalis |
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| creator | González, L. J. Lattanzi, M. B. Petrovich, A. G. |
| description | An alternative notion of an existential quantifier on four-valued Łukasiewicz algebras is introduced. The class of four-valued Łukasiewicz algebras endowed with this existential quantifier determines a variety which is denoted by
M
2
3
L
4
. It is shown that the alternative existential quantifier is interdefinable with the standard existential quantifier on a four-valued Łukasiewicz algebra. Some connections between the new existential quantifier and the existential quantifiers defined on bounded distributive lattices and Boolean algebras are given. Finally, a completeness theorem for the monadic four-valued Łukasiewicz predicate calculus corresponding to the dual of the alternative existential quantifier is proven. |
| doi_str_mv | 10.1007/s11787-017-0181-4 |
| format | Article |
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M
2
3
L
4
. It is shown that the alternative existential quantifier is interdefinable with the standard existential quantifier on a four-valued Łukasiewicz algebra. Some connections between the new existential quantifier and the existential quantifiers defined on bounded distributive lattices and Boolean algebras are given. Finally, a completeness theorem for the monadic four-valued Łukasiewicz predicate calculus corresponding to the dual of the alternative existential quantifier is proven.</description><identifier>ISSN: 1661-8297</identifier><identifier>EISSN: 1661-8300</identifier><identifier>DOI: 10.1007/s11787-017-0181-4</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Algebra ; Boolean algebra ; Calculus ; Computer Science ; Lattices (mathematics) ; Logic ; Mathematics ; Mathematics and Statistics ; Predicate calculus</subject><ispartof>Logica universalis, 2017-12, Vol.11 (4), p.439-463</ispartof><rights>Springer International Publishing AG, part of Springer Nature 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-2fcfe7bb2ca400191f0f6f2e83eee5c591f940353be876495d07a638ebd505643</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/s11787-017-0181-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11787-017-0181-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>González, L. J.</creatorcontrib><creatorcontrib>Lattanzi, M. B.</creatorcontrib><creatorcontrib>Petrovich, A. G.</creatorcontrib><title>An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras</title><title>Logica universalis</title><addtitle>Log. Univers</addtitle><description>An alternative notion of an existential quantifier on four-valued Łukasiewicz algebras is introduced. The class of four-valued Łukasiewicz algebras endowed with this existential quantifier determines a variety which is denoted by
M
2
3
L
4
. It is shown that the alternative existential quantifier is interdefinable with the standard existential quantifier on a four-valued Łukasiewicz algebra. Some connections between the new existential quantifier and the existential quantifiers defined on bounded distributive lattices and Boolean algebras are given. Finally, a completeness theorem for the monadic four-valued Łukasiewicz predicate calculus corresponding to the dual of the alternative existential quantifier is proven.</description><subject>Algebra</subject><subject>Boolean algebra</subject><subject>Calculus</subject><subject>Computer Science</subject><subject>Lattices (mathematics)</subject><subject>Logic</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Predicate calculus</subject><issn>1661-8297</issn><issn>1661-8300</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kMFKxDAQhoMouK4-gLeC5-pM0qbpcVldFVZEUK8h7U6WrGu7Jq2iNx_O9zJlFbx4GGb4-eef4WPsGOEUAYqzgFioIgUcSmGa7bARSompEgC7vzMvi312EMIKQIICMWI3kyaZrDvyjencKyXnZF3jOtc2SWuTu940nbOOfEiiMmt7nz6adU-L5OuzfzLB0ZurP2LCkipvwiHbs2Yd6Oinj9nD7OJ-epXOby-vp5N5WnOpupTb2lJRVbw2GQCWaMFKy0kJIsrrPAplBiIXFalCZmW-gMJIoaha5JDLTIzZyTZ349uXnkKnV_G1Jp7UWEouBReI0YVbV-3bEDxZvfHu2fh3jaAHanpLTUdqeqCmh2S-3QnR2yzJ_0n-d-kb0HhvpA</recordid><startdate>20171201</startdate><enddate>20171201</enddate><creator>González, L. J.</creator><creator>Lattanzi, M. B.</creator><creator>Petrovich, A. G.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20171201</creationdate><title>An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras</title><author>González, L. J. ; Lattanzi, M. B. ; Petrovich, A. G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-2fcfe7bb2ca400191f0f6f2e83eee5c591f940353be876495d07a638ebd505643</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algebra</topic><topic>Boolean algebra</topic><topic>Calculus</topic><topic>Computer Science</topic><topic>Lattices (mathematics)</topic><topic>Logic</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Predicate calculus</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>González, L. J.</creatorcontrib><creatorcontrib>Lattanzi, M. B.</creatorcontrib><creatorcontrib>Petrovich, A. G.</creatorcontrib><collection>CrossRef</collection><jtitle>Logica universalis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>González, L. J.</au><au>Lattanzi, M. B.</au><au>Petrovich, A. G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras</atitle><jtitle>Logica universalis</jtitle><stitle>Log. Univers</stitle><date>2017-12-01</date><risdate>2017</risdate><volume>11</volume><issue>4</issue><spage>439</spage><epage>463</epage><pages>439-463</pages><issn>1661-8297</issn><eissn>1661-8300</eissn><abstract>An alternative notion of an existential quantifier on four-valued Łukasiewicz algebras is introduced. The class of four-valued Łukasiewicz algebras endowed with this existential quantifier determines a variety which is denoted by
M
2
3
L
4
. It is shown that the alternative existential quantifier is interdefinable with the standard existential quantifier on a four-valued Łukasiewicz algebra. Some connections between the new existential quantifier and the existential quantifiers defined on bounded distributive lattices and Boolean algebras are given. Finally, a completeness theorem for the monadic four-valued Łukasiewicz predicate calculus corresponding to the dual of the alternative existential quantifier is proven.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s11787-017-0181-4</doi><tpages>25</tpages></addata></record> |
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| subjects | Algebra Boolean algebra Calculus Computer Science Lattices (mathematics) Logic Mathematics Mathematics and Statistics Predicate calculus |
| title | An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras |
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