Coalgebraic Predicate Logic: Equipollence Results and Proof Theory

Litak T, Pattinson D, Sano K (2013)

Publication Type: Conference contribution

Publication year: 2013

Journal

Lecture Notes in Computer Science Springer Verlag

Publisher: Springer-verlag

Edited Volumes: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Series: Logic, Language, and Computation. Revised Selected Papers of TbiLLC 2011

City/Town: Berlin/Heidelberg

Book Volume: 7758

Pages Range: 257-276

Conference Proceedings Title: Chapter in Logic, Language, and Computation. Revised Selected Papers of TbiLLC 2011

Event location: Kutaisi

ISBN: 978-3-642-36975-9

DOI: 10.1007/978-3-642-36976-6_16

Abstract

The recently introduced Coalgebraic Predicate Logic (CPL) provides a general first-order syntax together with extra modal-like operators that are interpreted in a coalgebraic setting. The universality of the coalgebraic approach allows us to instantiate the framework to a wide variety of situations, including probabilistic logic, coalition logic or the logic of neighbourhood frames. The last case generalises a logical setup proposed by C.C. Chang in early 1970's. We provide further evidence of the naturality of this framework. We identify syntactically the fragments of CPL corresponding to extended modal formalisms and show that the full CPL is equipollent with coalgebraic hybrid logic with the downarrow binder and the universal modality. Furthermore, we initiate the study of structural proof theory for CPL by providing a sequent calculus and a cut-elimination result. © 2013 Springer-Verlag.

Authors with CRIS profile

Tadeusz Litak Lehrstuhl für Informatik 8 (Theoretische Informatik)

Involved external institutions

Australian National University (ANU) AU Australia (AU) Hokkaido University (Hokudai) / 北海道大学 JP Japan (JP)

How to cite

APA:

Litak, T., Pattinson, D., & Sano, K. (2013). Coalgebraic Predicate Logic: Equipollence Results and Proof Theory. In Chapter in Logic, Language, and Computation. Revised Selected Papers of TbiLLC 2011 (pp. 257-276). Kutaisi: Berlin/Heidelberg: Springer-verlag.

MLA:

Litak, Tadeusz, Dirk Pattinson, and Katsuhiko Sano. "Coalgebraic Predicate Logic: Equipollence Results and Proof Theory." Proceedings of the 9th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2011, Kutaisi Berlin/Heidelberg: Springer-verlag, 2013. 257-276.

BibTeX: Download