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Implicational (semilinear) logics III: completeness properties

SYSNO ASEP	0477040
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Implicational (semilinear) logics III: completeness properties
Author(s)	Cintula, Petr (UIVT-O)_{RID, ORCID, SAI} Noguera, Carles (UTIA-B)_{RID, ORCID}
Source Title	Archive for Mathematical Logic. - : Springer - ISSN 0933-5846 Roč. 57, 3-4 (2018), s. 391-420
Number of pages	30 s.
Language	eng - English
Country	DE - Germany
Keywords	abstract algebraic logic ; protoalgebraic logics ; implicational logics ; disjunctional logics ; semilinear logics ; non-classical logics ; completeness theorems ; rational completeness
Subject RIV	BA - General Mathematics
OECD category	Pure mathematics
Subject RIV - cooperation	Institute of Information Theory and Automation - General Mathematics
R&D Projects	GA13-14654S GA ČR - Czech Science Foundation (CSF)
Institutional support	UIVT-O - RVO:67985807 ; UTIA-B - RVO:67985556
UT WOS	000428317500011
EID SCOPUS	85026497280
DOI	10.1007/s00153-017-0577-0
Annotation	This paper presents an abstract study of completeness properties of non-classical logics with respect to matricial semantics. Given a class of reduced matrix models we define three completeness properties of increasing strength and characterize them in several useful ways. Some of these characterizations hold in absolute generality and others are for logics with generalized implication or disjunction connectives, as considered in the previous papers. Finally, we consider completeness with respect to matrices with a linear dense order and characterize it in terms of an extension property and a syntactical metarule. This is the final part of the investigation started and developed in the papers (Cintula and Noguera in Arch Math Logic 49(4):417–446, 2010 and Arch Math Logic 53(3):353–372, 2016).
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2019

Number of the records: 1