Model Theory and Proof Theory of Coalgebraic Predicate Logic

Journal article
(Original article)


Publication Details

Author(s): Litak TM, Pattinson D, Sano K, Schröder L
Journal: Logical Methods in Computer Science
Publisher: LOGICAL METHODS COMPUTER SCIENCE E V
Publication year: 2018
Volume: 14
Journal issue: 1
ISSN: 1860-5974
Language: English


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 Authors / FAU Editors

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


External institutions with authors

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


How to cite

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: 

Last updated on 2019-16-01 at 09:47