bibtype	C - Conference Paper (international conference)
ARLID	0491981
utime	20250112195927.8
mtime	20180806235959.9
SCOPUS	85049630574
WOS	000478664000007
DOI	10.1007/978-3-662-57669-4_7
title (primary) (eng)	Lindenbaum and Pair Extension Lemma in Infinitary Logics
specification	page_count 15 s. media_type P
serial	ARLID cav_un_epca*0491980 ISBN 978-3-662-57668-7 ISSN 0302-9743 title Logic, Language, Information and Computation page_num 130-144 publisher place Berlin name Springer year 2018 editor name1 Moss name2 L. S. editor name1 de Queiroz name2 R. editor name1 Martinez name2 M.
keyword	Lindenbaum lemma
keyword	Pair extension lemma
keyword	Infinitary logic
keyword	Infinitary deduction rule
keyword	Strong disjunction
keyword	Prime theory
author (primary)	ARLID cav_un_auth*0218529 name1 Bílková name2 Marta 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*0100737 name1 Cintula name2 Petr institution UIVT-O full_dept (cz) Oddělení teoretické informatiky full_dept Department of Theoretical Computer Science full_dept Department of Theoretical Computer Science garant K fullinstit Ústav informatiky AV ČR, v. v. i.
author	ARLID cav_un_auth*0341114 name1 Lávička name2 Tomáš 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 country CZ fullinstit Ústav teorie informace a automatizace AV ČR, v. v. i.
cas_special	project ARLID cav_un_auth*0349495 project_id GA17-04630S agency GA ČR project ARLID cav_un_auth*0348385 project_id GC16-07954J agency GA ČR country CZ project ARLID cav_un_auth*0348811 project_id JSPS-16-08 agency AV ČR country CZ country JP abstract (eng) The abstract Lindenbaum lemma is a crucial result in algebraic logic saying that the prime theories form a basis of the closure systems of all theories of an arbitrary given logic. Its usual formulation is however limited to finitary logics, i.e., logics with Hilbert-style axiomatization using finitary rules only. In this contribution, we extend its scope to all logics with a countable axiomatization and a well-behaved disjunction connective. We also relate Lindenbaum lemma to the Pair extension lemma, other well-known result with many applications mainly in the theory of non-classical modal logics. While a restricted form of this lemma (to pairs with finite right-hand side) is, in our context, equivalent to Lindenbaum lemma, we show a perhaps surprising result that in full strength it holds for finitary logics only. Finally we provide examples demonstrating both limitations and applications of our results. action ARLID cav_un_auth*0362872 name WoLLIC 2018. International Workshop on Logic, Language, Information and Computation /25./ dates 20180724 place Bogotá country CO mrcbC20-s 20180727 RIV BA FORD0 10000 FORD1 10200 FORD2 10201 reportyear 2019 mrcbC47 UTIA-B 10000 10100 10101 mrcbC52 4 E R 4e 4r a 20231122143320.7 A 20250112195927.7 mrcbC55 UTIA-B BA inst_support RVO:67985807 inst_support RVO:67985556 permalink http://hdl.handle.net/11104/0285566 confidential S mrcbC86 3+4 Proceedings Paper Computer Science Artificial Intelligence|Computer Science Theory Methods mrcbT16-s 0.339 mrcbT16-4 Q2 mrcbT16-E Q2 arlyear 2018 mrcbTft \nSoubory v repozitáři: dodatecne_citace_k_0554811.pdf, a0491981prep.pdf, a0491981.pdf mrcbU14 85049630574 SCOPUS mrcbU24 PUBMED mrcbU34 000478664000007 WOS mrcbU63 cav_un_epca*0491980 Logic, Language, Information and Computation Springer 2018 Berlin 130 144 978-3-662-57668-7 Lecture Notes on Computer Science 10944 0302-9743 mrcbU67 340 Moss L. S. mrcbU67 340 de Queiroz R. mrcbU67 340 Martinez M.