bibtype	J - Journal Article
ARLID	0428704
utime	20240103204307.6
mtime	20140609235959.9
SCOPUS	84937900561
WOS	000351311600018
DOI	10.1017/jsl.2014.19
title (primary) (eng)	A Henkin-Style Proof of Completeness for First-Order Algebraizable Logics
specification	page_count 18 s.
serial	ARLID cav_un_epca*0257123 ISSN 0022-4812 title Journal of Symbolic Logic volume_id 80 volume 1 (2015) page_num 341-358 publisher name Cambridge University Press
keyword	abstract algebraic logics
keyword	algebraizable logics
keyword	first-order logics
keyword	completeness theorem
keyword	Henkin theories
author (primary)	ARLID cav_un_auth*0100737 name1 Cintula name2 Petr institution UIVT-O full_dept (cz) Oddělení teoretické informatiky full_dept (eng) Department of Theoretical Computer Science full_dept Department of Theoretical Computer Science fullinstit Ústav informatiky AV ČR, v. v. i.
author	ARLID cav_un_auth*0293476 name1 Noguera name2 Carles institution UTIA-B full_dept (cz) Matematická teorie rozhodování full_dept Department of Decision Making Theory department (cz) MTR department MTR full_dept Department of Decision Making Theory fullinstit Ústav teorie informace a automatizace AV ČR, v. v. i.
cas_special	project project_id GA13-14654S agency GA ČR ARLID cav_un_auth*0292719 project project_id 247584 agency EC country XE ARLID cav_un_auth*0323440 abstract (eng) 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 and help to illuminate the “essentially first-order” steps in the classical Henkin’s proof. RIV BA reportyear 2015 mrcbC52 4 O R hod 4o 4rh 20231122140250.4 inst_support RVO:67985807 inst_support RVO:67985556 permalink http://hdl.handle.net/11104/0234002 mrcbC64 1 Department of Theoretical Computer Science UIVT-O 10100 LOGIC mrcbC64 1 Department of Decision Making Theory UTIA-B 10100 LOGIC confidential S mrcbC86 n.a. Article Mathematics|Logic mrcbT16-e LOGIC|MATHEMATICS mrcbT16-j 0.724 mrcbT16-s 1.203 mrcbT16-4 Q1 mrcbT16-B 62.403 mrcbT16-C 34.914 mrcbT16-D Q2 mrcbT16-E Q1 arlyear 2015 mrcbTft \nSoubory v repozitáři: 0428704.pdf, a0428704.pdf mrcbU14 84937900561 SCOPUS mrcbU34 000351311600018 WOS mrcbU63 cav_un_epca*0257123 Journal of Symbolic Logic 0022-4812 1943-5886 Roč. 80 č. 1 2015 341 358 Cambridge University Press