1. bookVolume 22 (2019): Issue 1 (December 2019)
Journal Details
License
Format
Journal
eISSN
1647-659X
First Published
01 Mar 2016
Publication timeframe
3 times per year
Languages
English
access type Open Access

Categorical Interpretation of Modal Structures under Bisimulation

Published Online: 03 Mar 2020
Volume & Issue: Volume 22 (2019) - Issue 1 (December 2019)
Page range: 54 - 71
Journal Details
License
Format
Journal
eISSN
1647-659X
First Published
01 Mar 2016
Publication timeframe
3 times per year
Languages
English
Abstract

In this work we summarise the concept of bisimulation, widely used both in computational sciences and in modal logic, that characterises modal structures with the same behaviour in terms of accessibility relations. Then, we offer a sketch of categorical interpretation of bisimulation between modal structures, which comprise both the structure and the valuation from a propositional language.

Keywords

(1) Alechina, N., Mendler, M., De Paiva, V., & Ritter, E. (2001, September). Categorical and Kripke semantics for constructive S4 modal logic. En International Workshop on Computer Science Logic (pp. 292–307). Springer Berlin Heidelberg.10.1007/3-540-44802-0_21Search in Google Scholar

(2) Van Benthem, J. (1976). Modal correspondence theory [Ph.D. Thesis]. University of Amsterdam, Netherlands.Search in Google Scholar

(3) Blackburn, P., De Rijke, M., & Venema, Y. (2001). Modal logic, volume 53 of Cambridge tracts in theoretical computer science.10.1017/CBO9781107050884Search in Google Scholar

(4) Van Ditmarsch, H., van Der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic (Vol. 337). Springer Science & Business Media.Search in Google Scholar

(5) Gerbrandy, J.D. (1999). Bisimulations on planet Kripke. ILLC Dissertation Series.Search in Google Scholar

(6) Goranko, V., & Otto, M. (2007). 5 Model theory of modal logic. Studies in Logic and Practical Reasoning, 3, 249–329.10.1016/S1570-2464(07)80008-5Search in Google Scholar

(7) Hennessy, M., & Milner, R. (1980). On observing nondeterminism and concurrency. Automata, Languages and Programming, 299–309.10.1007/3-540-10003-2_79Search in Google Scholar

(8) Keller, R.M. (1976). Formal verification of parallel programs. Communications of the ACM, 19(7), 371–384.10.1145/360248.360251Search in Google Scholar

(9) Park, D. (1981). Concurrency and automata on infinite sequences. In Theoretical computer science (pp. 167–183). Springer Berlin Heidelberg.10.1007/BFb0017309Search in Google Scholar

(10) Sangiorgi, D. (2009). On the origins of bisimulation and coinduction. ACM Transactions on Programming Languages and Systems (TOPLAS), 31(4), 15.10.1145/1516507.1516510Search in Google Scholar

(11) Stirling, C. (2012). Bisimulation and logic. Sangiorgi and Rutten [24, Chapter 4], 173–196.Search in Google Scholar

(12) Venema, Y. (2007). 6 Algebras and coalgebras. Studies in Logic and Practical Reasoning, 3, 331–426.10.1016/S1570-2464(07)80009-7Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo