[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-327364-105":59,"doc-detail-327364-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","actual-causality-in-fault-trees","Actual causality in fault trees","","Fault trees are widely used risk models for complex systems, traditionally addressing what can go wrong through minimal cut set analysis. This work studies fault trees using Halpern & Pearl’s theory of actual causality to explain why failures occur after the fact, supporting failure diagnostics. It provides a complete classification of actual causality notions based on fault-tree graph and logical structure and shows how minimal cut sets correspond to actual causes. The study also examines computational complexity and introduces algorithms for causality computation in fault trees.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/actual-causality-in-fault-trees/327364/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/actual-causality-in-fault-trees/327364.png","ImageObject",300,407,{"name":92,"@type":93},"Aurora","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-05","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does minimal cut set analysis tell us in a fault tree?","Question",{"text":112,"@type":113},"Minimal cut sets identify the combinations of basic failure events that must occur together for the system to fail, supporting reliability assessment and risk analysis.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does actual causality differ from fault-tree risk analysis?",{"text":117,"@type":113},"Risk analysis focuses on what can go wrong, while actual causality asks why the failure has occurred in a given context after the fact.",{"name":119,"@type":110,"acceptedAnswer":120},"What contribution does the paper make by combining actual causality with fault trees?",{"text":121,"@type":113},"It applies Halpern-Pearl actual causality to static, coherent fault trees, giving concise classifications of actual causes for multiple causality definitions and relating minimal cut sets to actual causes.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},327364,1790501855,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":36,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144,"preview_page_count":4},4810365810221,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","arXiv :2607 .0 1840v 1 [ cs .AI] 2 Jul 2026  \nActual causality in fault trees  \nGeorgiana Caltais 1 [0000-0002-8653-2299] Milan Lopuhaä-Zwakenberg 1 [0000-0001-5687-854X]  \nMariëlle Stoelinga 1 ,2 [0000-0001-6793-8165]  \n1 University of Twente, The Netherlands  \n2 Radboud University, The Netherlands  \n{g.g.c.caltais,m.a.lopuhaa,[m.i.a.stoelinga}@utwente.nl](m.i.a.stoelinga}@utwente.nl)  \nAbstract. Fault trees are a widely used as effective risk models for complex systems, answering the question what can go wrong?, especially through minimal cut set analysis. We study fault trees from the perspective of Halpern & Pearl’s theory of actual causality. This allows us to use fault trees to answer the question why has it gone wrong?, which is fundamental to failure diagnostics. We give a complete classification of each of the different notions of actual causality in terms of the fault tree’s graph structure and logical structure, and show how minimal cut sets give rise to actual causes. Furthermore, we discuss the complexity of computing causality in fault trees, and develop algorithms to do so.  \nKeywords: System Failures · Fault Trees · Actual Causality.  \n1 Introduction  \nThe visdeurbel (“fish doorbell”) is a citizen-science initiative designed to support migrating fish as they pass through the waterways of Utrecht, a major Dutch city [30, 32] . An underwater camera provides a live stream of fish in front of the lock. The lock operator can be alerted in two ways. Public observers may ring the virtual doorbell when they see fish, or the operator can watch the camera feed directly. The system aids fish migration and raises public awareness of ecology. This example illustrates how different components and failures (electric, public and operator failures) contribute to a system-level failure (the lock failing to open) .  \nlock fails  \nFig. 1: FT modeling a visdeurbel, a system supporting migrating fish in the waterways of Utrecht: public observers and operators can both ring a door bell to open the lock when they see a fish on an underwater camera. The lock fails to open (OR-gate) if either electricity fails (basic event, BE) or if the alert fails (AND-gate), which happens if both the public and the operator fail to act.  \nFault trees (FTs) are a structured, hierarchical model to analyse failure propagation in complex systems [37, 38] . FTs enable a top-down, deductive approach to failure analysis, breaking down system failures into combinations of component failures using logical gates (e.g., AND, OR) . In FT-terminology, the inputs of such a gate are often called the immediate causes of the higher-level cause labeled by the gate [39] . Widely used in safety-critical industries such as aerospace [7], nuclear energy [16], and cybersecurity [31], FTs enable structured reasoning about system reliability, risk assessment, and failure propagation. They serve as a powerful design tool, helping engineers identify weak points and prioritise mitigation strategies. An FT for the “fish doorbell” is given in Fig. 1.  \nAs a risk model, FTs are primarily used to analyze potential failures: what can go wrong? This is done via minimal cut set (MCS) analysis: an MCS is a set of basic failure events that need to happen simultaneously in order for the system to fail. After finding a FT’s MCSs, these are then analyzed in terms of size, likelihood, and common causes to determine the system’s overall reliability. Actual causality in the Halpern-Pearl framework. Causality, on the other hand, asks the question why has it gone wrong? after the fact. In computer science, the framework of actual causality (AC) by Halpern and Pearl [19] has been especially popular. In AC, a system is modeled as a causal model: a directed acyclic graph of variables, with functions describing each variable in terms of its input. The system’s context is given by values of the initial variables. Within such a system one can perform interventions using do-calculus [34] to forcibly s","cbCaiu1s1bPo2YWp","https://ap.wps.com/l/cbCaiu1s1bPo2YWp","pdf",1950981,"English","# Introduction\n## Fault trees as risk models\n## Actual causality in Halpern-Pearl framework\n## Incident analysis and diagnostics with fault trees\n## Contributions","[{\"question\":\"What does minimal cut set analysis tell us in a fault tree?\",\"answer\":\"Minimal cut sets identify the combinations of basic failure events that must occur together for the system to fail, supporting reliability assessment and risk analysis.\"},{\"question\":\"How does actual causality differ from fault-tree risk analysis?\",\"answer\":\"Risk analysis focuses on what can go wrong, while actual causality asks why the failure has occurred in a given context after the fact.\"},{\"question\":\"What contribution does the paper make by combining actual causality with fault trees?\",\"answer\":\"It applies Halpern-Pearl actual causality to static, coherent fault trees, giving concise classifications of actual causes for multiple causality definitions and relating minimal cut sets to actual causes.\"}]","Actual causality in fault trees | PDF",1789977069,101]