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Statements

Subject Item
n2:RIV%2F67985807%3A_____%2F10%3A00342136%21RIV11-GA0-67985807
rdf:type
n10:Vysledek skos:Concept
dcterms:description
In abstract algebraic logic, the general study of propositional logics is based on the abstraction of the Lindenbaum-Tarski process, one considers the Leibniz relation of indiscernible formulae. It leads to the Leibniz hierarchy; a classification of logics based on generalized equivalences. We perform an analogous abstract study of non-classical logics based on generalized implications. It yields the hierarchy of implicational logics which expands Leibniz hierarchy. The notion of implicational semilinear logic is then naturally introduced as a property of the implication, namely a logic is an implicational semilinear logic iff it has an implication and is complete w.r.t. the matrices where this implication induces a linear order, a property which is satisfied by majority of fuzzy logics. This hierarchy is then restricted to the semilinear case obtaining a classification that encompasses almost all the known examples of fuzzy logics and suggests new directions for research. In abstract algebraic logic, the general study of propositional logics is based on the abstraction of the Lindenbaum-Tarski process, one considers the Leibniz relation of indiscernible formulae. It leads to the Leibniz hierarchy; a classification of logics based on generalized equivalences. We perform an analogous abstract study of non-classical logics based on generalized implications. It yields the hierarchy of implicational logics which expands Leibniz hierarchy. The notion of implicational semilinear logic is then naturally introduced as a property of the implication, namely a logic is an implicational semilinear logic iff it has an implication and is complete w.r.t. the matrices where this implication induces a linear order, a property which is satisfied by majority of fuzzy logics. This hierarchy is then restricted to the semilinear case obtaining a classification that encompasses almost all the known examples of fuzzy logics and suggests new directions for research.
dcterms:title
Implicational (Semilinear) Logics I: A New Hierarchy Implicational (Semilinear) Logics I: A New Hierarchy
skos:prefLabel
Implicational (Semilinear) Logics I: A New Hierarchy Implicational (Semilinear) Logics I: A New Hierarchy
skos:notation
RIV/67985807:_____/10:00342136!RIV11-GA0-67985807
n3:aktivita
n16:P n16:Z
n3:aktivity
P(GEICC/08/E018), Z(AV0Z10300504)
n3:cisloPeriodika
4
n3:dodaniDat
n14:2011
n3:domaciTvurceVysledku
n6:1922688
n3:druhVysledku
n15:J
n3:duvernostUdaju
n5:S
n3:entitaPredkladatele
n13:predkladatel
n3:idSjednocenehoVysledku
263122
n3:idVysledku
RIV/67985807:_____/10:00342136
n3:jazykVysledku
n11:eng
n3:klicovaSlova
abstract algebraic logic; hierarchy of implicational logics; implicative logics; Leibniz hierarchy; linearly ordered logical matrices; mathematical fuzzy logic; non-classical logics; semilinear logics
n3:klicoveSlovo
n4:semilinear%20logics n4:Leibniz%20hierarchy n4:implicative%20logics n4:mathematical%20fuzzy%20logic n4:abstract%20algebraic%20logic n4:non-classical%20logics n4:linearly%20ordered%20logical%20matrices n4:hierarchy%20of%20implicational%20logics
n3:kodStatuVydavatele
DE - Spolková republika Německo
n3:kontrolniKodProRIV
[7B8C8DF3185E]
n3:nazevZdroje
Archive for Mathematical Logic
n3:obor
n9:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n18:GEICC%2F08%2FE018
n3:rokUplatneniVysledku
n14:2010
n3:svazekPeriodika
49
n3:tvurceVysledku
Noguera, C. Cintula, Petr
n3:wos
000277246000001
n3:zamer
n17:AV0Z10300504
s:issn
1432-0665
s:numberOfPages
30