Causal Unfoldings and Disjunctive Causes
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 ma...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2023-04-01
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| Series: | Logical Methods in Computer Science |
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| Online Access: | https://lmcs.episciences.org/6202/pdf |
| _version_ | 1827174302154227712 |
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| author | Marc de Visme Glynn Winskel |
| author_facet | Marc de Visme Glynn Winskel |
| author_sort | Marc de Visme |
| collection | DOAJ |
| description | 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. Finally, we explore
subcategories which support parallel causes as well the key operations needed
in developing probabilistic distributed strategies with parallel causes. |
| first_indexed | 2024-04-25T01:32:42Z |
| format | Article |
| id | doaj.art-bd2210f601d049049c64d0900ec26520 |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2025-03-21T03:53:23Z |
| publishDate | 2023-04-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-bd2210f601d049049c64d0900ec265202024-07-30T09:03:12ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742023-04-01Volume 19, Issue 210.46298/lmcs-19(2:4)20236202Causal Unfoldings and Disjunctive CausesMarc de VismeGlynn WinskelIn 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. Finally, we explore subcategories which support parallel causes as well the key operations needed in developing probabilistic distributed strategies with parallel causes.https://lmcs.episciences.org/6202/pdfcomputer science - logic in computer science |
| spellingShingle | Marc de Visme Glynn Winskel Causal Unfoldings and Disjunctive Causes Logical Methods in Computer Science computer science - logic in computer science |
| title | Causal Unfoldings and Disjunctive Causes |
| title_full | Causal Unfoldings and Disjunctive Causes |
| title_fullStr | Causal Unfoldings and Disjunctive Causes |
| title_full_unstemmed | Causal Unfoldings and Disjunctive Causes |
| title_short | Causal Unfoldings and Disjunctive Causes |
| title_sort | causal unfoldings and disjunctive causes |
| topic | computer science - logic in computer science |
| url | https://lmcs.episciences.org/6202/pdf |
| work_keys_str_mv | AT marcdevisme causalunfoldingsanddisjunctivecauses AT glynnwinskel causalunfoldingsanddisjunctivecauses |