Document

# Causal Unfoldings

## File

LIPIcs.CALCO.2019.9.pdf
• Filesize: 496 kB
• 18 pages

## Acknowledgements

Thanks to the anonymous referees. Thanks to Simon Castellan, Pierre Clairambault, Ioana Cristescu, Mai Gehrke, Jonathan Hayman, Tamas Kispeter, Jean Krivine, Martin Hyland and Daniele Varacca for discussions, advice and encouragement; to ENS Paris for supporting Marc de Visme’s internship; and to the ERC for Advanced Grant ECSYM.

## Cite As

Marc de Visme and Glynn Winskel. Causal Unfoldings. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.CALCO.2019.9

## Abstract

In the simplest form of event structure, a prime event structure, an event is associated with a unique causal history, its prime cause. However, it is quite common for an event to have disjunctive causes in that it can be enabled by any one of multiple sets of causes. Sometimes the sets of causes may be mutually exclusive, inconsistent one with another, and sometimes not, in which case they coexist consistently and constitute parallel causes of the event. The established model of general event structures can model parallel causes. On occasion however such a model abstracts too far away from the precise causal histories of events to be directly useful. For example, sometimes one needs to associate probabilities with different, possibly coexisting, causal histories of a common event. Ideally, the causal histories of a general event structure would correspond to the configurations of its causal unfolding to a prime event structure; and the causal unfolding would arise as a right adjoint to the embedding of prime in general event structures. But there is no such adjunction. However, a slight extension of prime event structures remedies this defect and provides a causal unfolding as a universal construction. Prime event structures are extended with an equivalence relation in order to dissociate the two roles, that of an event and its enabling; in effect, prime causes are labelled by a disjunctive event, an equivalence class of its prime causes. With this enrichment a suitable causal unfolding appears as a pseudo right adjoint. The adjunction relies critically on the central and subtle notion of extremal causal realisation as an embodiment of causal history.

## Subject Classification

##### ACM Subject Classification
• Theory of computation → Concurrency
##### Keywords
• Event Structures
• Parallel Causes
• Causal Unfolding
• Probability

## Metrics

• Access Statistics
• Total Accesses (updated on a weekly basis)
0

## References

1. Simon Castellan, Pierre Clairambault, and Glynn Winskel. Symmetry in concurrent games. In Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS '14, Vienna, Austria, July 14 - 18, 2014. ACM, 2014.
2. Pierre Clairambault, Julian Gutierrez, and Glynn Winskel. The Winning Ways of Concurrent Games. In Proceedings of the 27th Annual IEEE Symposium on Logic in Computer Science, LICS 2012, Dubrovnik, Croatia, June 25-28, 2012. IEEE Computer Society, 2012.
3. Ioana Cristescu. Operational and denotational semantics for the reversible pi-calculus. PhD thesis, PPS, Université Paris Diderot, 2015.
4. Ioana Cristescu, Jean Krivine, and Daniele Varacca. Rigid families for CCS and the pi-Calculus. In International Colloquium on Theoretical Aspects of Computing ICTAC, 12th ed. Cali, Colombia, 2015.
5. Vincent Danos, Jerome Feret, Walter Fontana, Russell Harmer, Jonathan Hayman, Jean Krivine, Chris Thompson-Walsh, and Glynn Winskel. Graphs, Rewriting and Pathway Reconstruction for Rule-Based Models. In FSTTCS 2012, volume 18 of LIPIcs, pages 276-288. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2012.
6. Marc de Visme. Cambridge Internship Report, ENS Paris. Available from Glynn Winskel's homepage http://www.cl.cam.ac.uk/∼gw104/mdv-report.pdf, 2015.
7. Marc de Visme and Glynn Winskel. Strategies with Parallel Causes. In CSL 2017, volume 82 of LIPIcs. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2017.
8. G. M. Kelly. Basic concepts of enriched category theory. LNM 64. CUP, 1982.
9. Y. Kinoshita and J. Power. Category theoretic structure of setoids. TCS, 546, 2014.
10. Mogens Nielsen, Gordon Plotkin, and Glynn Winskel. Petri Nets, Event Structures and Domains. TCS, 13:85-108, 1981.
11. Judea Pearl. Causality. CUP, 2013.
12. John Power. 2-Categories. BRICS Notes Series NS-98-7, 1998.
13. Glynn Winskel. Events in computation. Edinburgh University, 1980. PhD thesis, Edinburgh.
14. Glynn Winskel. Event Structures. In Advances in Petri Nets, LNCS 255, 1986.
15. Glynn Winskel and Mogens Nielsen. Models for concurrency. In Samson Abramsky and Dov Gabbay, editors, Semantics and Logics of Computation. OUP, 1995.