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COMPLETE LOGICS FOR ELEMENTARY TEAM PROPERTIES

Part of: General logic

Published online by Cambridge University Press:  01 December 2022

JUHA KONTINEN Open the ORCID record for JUHA KONTINEN [Opens in a new window]  and
FAN YANG Open the ORCID record for FAN YANG [Opens in a new window]
JUHA KONTINEN
Affiliation:
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF HELSINKI PL 68 (PIETARI KALMIN KATU 5) 00014, HELSINKI FINLAND E-mail: juha.kontinen@helsinki.fi
FAN YANG*
Affiliation:
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF HELSINKI PL 68 (PIETARI KALMIN KATU 5) 00014, HELSINKI FINLAND E-mail: juha.kontinen@helsinki.fi
*
E-mail: fan.yang.c@gmail.com
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Abstract

In this paper, we introduce a logic based on team semantics, called $\mathbf {FOT} $, whose expressive power is elementary, i.e., coincides with first-order logic both on the level of sentences and (possibly open) formulas, and we also show that a sublogic of $\mathbf {FOT} $, called $\mathbf {FOT}^{\downarrow } $, captures exactly downward closed elementary (or first-order) team properties. We axiomatize completely the logic $\mathbf {FOT} $, and also extend the known partial axiomatization of dependence logic to dependence logic enriched with the logical constants in $\mathbf {FOT}^{\downarrow } $.

Keywords

dependence logicteam semanticsfirst-order logicaxiomatization

MSC classification

Primary: 03B60: Other nonclassical logic

Information

Type
Article
Information
The Journal of Symbolic Logic , Volume 88 , Issue 2 , June 2023 , pp. 579 - 619
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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