Model Theory and Proof Theory of Coalgebraic Predicate Logic

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Litak TM, Pattinson D, Sano K, Schröder L
Zeitschrift: Logical Methods in Computer Science
Verlag: LOGICAL METHODS COMPUTER SCIENCE E V
Jahr der Veröffentlichung: 2018
Band: 14
Heftnummer: 1
ISSN: 1860-5974
Sprache: Englisch


Abstract

We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and completeness results for several natural classes of such logics. Moreover, we show that an entirely general completeness result is not possible. We study the expressive power of our language, both in comparison with coalgebraic hybrid logics and with existing first-order proposals for special classes of Set-coalgebras (apart from relational structures, also neighbourhood frames and topological spaces). Basic model-theoretic constructions and results, in particular ultraproducts, obtain for the two classes that allow completeness-and in some cases beyond that. Finally, we discuss a basic sequent system, for which we establish a syntactic cut-elimination result.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Litak, Tadeusz Michal PD Dr. habil.
Lehrstuhl für Informatik 8 (Theoretische Informatik)
Schröder, Lutz Prof. Dr.
Lehrstuhl für Informatik 8 (Theoretische Informatik)


Einrichtungen weiterer Autorinnen und Autoren

Australian National University (ANU)
Hokkaido University (Hokudai) / 北海道大学


Zitierweisen

APA:
Litak, T.M., Pattinson, D., Sano, K., & Schröder, L. (2018). Model Theory and Proof Theory of Coalgebraic Predicate Logic. Logical Methods in Computer Science, 14(1). https://dx.doi.org/10.23638/LMCS-14(1:22)2018

MLA:
Litak, Tadeusz Michal, et al. "Model Theory and Proof Theory of Coalgebraic Predicate Logic." Logical Methods in Computer Science 14.1 (2018).

BibTeX: 

Zuletzt aktualisiert 2019-16-01 um 09:47

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