Implicational (Semilinear) Logics I: A New Hierarchy

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F10%3A00342136" target="_blank" >RIV/67985807:_____/10:00342136 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Implicational (Semilinear) Logics I: A New Hierarchy

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Implicational (Semilinear) Logics I: A New Hierarchy

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GEICC%2F08%2FE018" target="_blank" >GEICC/08/E018: Logické modely usuzovaní s vagními informacemi</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2010

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Archive for Mathematical Logic

ISSN

1432-0665

e-ISSN

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Svazek periodika

49

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

30

Strana od-do

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Kód UT WoS článku

000277246000001

EID výsledku v databázi Scopus

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