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

Result code in 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>

Alternative codes found

RIV/67985556:_____/15:00428704

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

<a href="/en/project/GA13-14654S" target="_blank" >GA13-14654S: An Order-Based Approach to Non-Classical Propositional and Predicate Logics</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2015

Confidentiality

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

Name of the periodical

Journal of Symbolic Logic

ISSN

0022-4812

e-ISSN

—

Volume of the periodical

80

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

18

Pages from-to

341-358

UT code for WoS article

—

EID of the result in the Scopus database

—