Assertional logics, truth-equational logics, and the hierarchies of abstract algebraic logic

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F18%3A00488936" target="_blank" >RIV/67985807:_____/18:00488936 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/book/10.1007/978-3-319-74772-9" target="_blank" >https://link.springer.com/book/10.1007/978-3-319-74772-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-74772-9_2" target="_blank" >10.1007/978-3-319-74772-9_2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Assertional logics, truth-equational logics, and the hierarchies of abstract algebraic logic

Popis výsledku v původním jazyce

We establish some relations between the class of truth-equational logics, the class of assertional logics, other classes in the Leibniz hierarchy, and the classes in the Frege hierarchy. We argue that the class of assertional logics belongs properly in the Leibniz hierarchy. We give two new characterizations of truth-equational logics in terms of their full generalized models, and use them to obtain further results on the internal structure of the Frege hierarchy and on the relations between the two hierarchies. Some of these results and several counter examples contribute to answer a few open problems in abstract algebraic logic, and open a new one.

Název v anglickém jazyce

Assertional logics, truth-equational logics, and the hierarchies of abstract algebraic logic

Popis výsledku anglicky

We establish some relations between the class of truth-equational logics, the class of assertional logics, other classes in the Leibniz hierarchy, and the classes in the Frege hierarchy. We argue that the class of assertional logics belongs properly in the Leibniz hierarchy. We give two new characterizations of truth-equational logics in terms of their full generalized models, and use them to obtain further results on the internal structure of the Frege hierarchy and on the relations between the two hierarchies. Some of these results and several counter examples contribute to answer a few open problems in abstract algebraic logic, and open a new one.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název knihy nebo sborníku

Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science

ISBN

978-3-319-74771-2

Počet stran výsledku

27

Strana od-do

53-79

Počet stran knihy

454

Název nakladatele

Springer

Místo vydání

Cham

Kód UT WoS kapitoly

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