A Henkin-Style Proof of Completeness for First-Order Algebraizable Logics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00428704" target="_blank" >RIV/67985807:_____/15:00428704 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985556:_____/15:00428704

Výsledek na webu

<a href="http://dx.doi.org/10.1017/jsl.2014.19" target="_blank" >http://dx.doi.org/10.1017/jsl.2014.19</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/jsl.2014.19" target="_blank" >10.1017/jsl.2014.19</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Henkin-Style Proof of Completeness for First-Order Algebraizable Logics

Popis výsledku v původním jazyce

This paper considers Henkin?s proof of completeness of classical first-order logic and extends its scope to the realm of algebraizable logics in the sense of Blok and Pigozzi. Given a propositional logic (for which we only need to assume that it has an algebraic semantics and a suitable disjunction) we axiomatize two natural first-order extensions and prove that one is complete with respect to all models over its algebras, while the other one is complete with respect to all models over relatively finitely subdirectly irreducible ones. While the first completeness result is relatively straightforward, the second requires non-trivial modifications of Henkin?s proof by making use of the disjunction connective. As a byproduct, we also obtain a form of Skolemization provided that the algebraic semantics admits regular completions. The relatively modest assumptions on the propositional side allow for a wide generalization of previous approaches by Rasiowa, Sikorski, Hájek, Horn, and others a

Název v anglickém jazyce

A Henkin-Style Proof of Completeness for First-Order Algebraizable Logics

Popis výsledku anglicky

This paper considers Henkin?s proof of completeness of classical first-order logic and extends its scope to the realm of algebraizable logics in the sense of Blok and Pigozzi. Given a propositional logic (for which we only need to assume that it has an algebraic semantics and a suitable disjunction) we axiomatize two natural first-order extensions and prove that one is complete with respect to all models over its algebras, while the other one is complete with respect to all models over relatively finitely subdirectly irreducible ones. While the first completeness result is relatively straightforward, the second requires non-trivial modifications of Henkin?s proof by making use of the disjunction connective. As a byproduct, we also obtain a form of Skolemization provided that the algebraic semantics admits regular completions. The relatively modest assumptions on the propositional side allow for a wide generalization of previous approaches by Rasiowa, Sikorski, Hájek, Horn, and others a

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/GA13-14654S" target="_blank" >GA13-14654S: Neklasické výrokové a predikátové logiky: přístup založený na uspořádání</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Journal of Symbolic Logic

ISSN

0022-4812

e-ISSN

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Svazek periodika

80

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

18

Strana od-do

341-358

Kód UT WoS článku

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EID výsledku v databázi Scopus

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