[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122597-en":3,"doc-seo-122597-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},122597,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Logic-Based Explainability in Machine Learning","Machine Learning successes increasingly permeate real-world applications, including safety-critical domains that directly affect people, yet many leading models function as inscrutable black boxes for human decision makers. To address this trust gap, explainable AI research has progressed beyond non-formal, model-agnostic explanations that lack rigor and may yield explanations compatible with multiple predictions. This work surveys ongoing research on rigorous model-based, formal explanations via logical definitions, complexity characterizations, logical encodings for reasoning, and methods to make explanations interpretable.","arXiv :2211 .0054 1v 1 [ cs .AI] 24 Oct 2022  \nLogic-Based Explainability in Machine Learning  \nJoao Marques-Silva [0000−0002−6632−3086]  \nIRIT, CNRS, Toulouse, France  \n[joao.marques-silva@irit.fr](joao.marques-silva@irit.fr)  \nAbstract. The last decade witnessed an ever-increasing stream of successes in Machine Learning (ML) . These successes o􀀛er clear evidence that ML is bound to become pervasive in a wide range of practical uses, including many that directly a􀀛ect humans. Unfortunately, the operation of the most successful ML models is incomprehensible for human decision makers. As a result, the use of ML models, especially in highrisk and safety-critical settings is not without concern. In recent years, there have been e􀀛orts on devising approaches for explaining ML models. Most of these e􀀛orts have focused on so-called model-agnostic approaches. However, all model-agnostic and related approaches o􀀛er no guarantees of rigor, hence being referred to as non-formal. For example, such non-formal explanations can be consistent with di􀀛erent predictions, which renders them useless in practice. This paper overviews the ongoing research e􀀛orts on computing rigorous model-based explanations of ML models; these being referred to as formal explanations. These efforts encompass a variety of topics, that include the actual de􀀜nitions of explanations, the characterization of the complexity of computing explanations, the currently best logical encodings for reasoning about di􀀛erent ML models, and also how to make explanations interpretable for human decision makers, among others.  \nKeywords: Explainable AI · Formal explanations · Automated reasoning  \nTable of Contents  \n1 Introduction . . . . . . . . . . . . . . . . . . . . . . 4  \n2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . 7  \n2.1 Logic Foundations . . . . . . . . . . . . . . . . . . . . 8  \n2.1.1 Propositional Logic & Boolean Satis􀀜ability.............. 8  \n2.1.2 First Order Logic..................................... 12  \n2.1.3 Encodings & Interfacing Reasoners..................... 13  \n2.2 Classi􀀜cation Problems . . . . . . . . . . . . . . . . . . 13  \n2.2.1 Examples of Classi􀀜ers................................ 14  \n2.2.2 Running Examples................................... 16  \n2.3 Non-Formal Explanations . . . . . . . . . . . . . . . . . 21  \n3 Formal Explainability . . . . . . . . . . . . . . . . . . 22  \n3.1 Abductive Explanations . . . . . . . . . . . . . . . . . . 23  \n3.2 Contrastive Explanations . . . . . . . . . . . . . . . . . 24  \n3.3 Global Abductive Explanations & Counterexamples . . . . . . . . 26  \n3.4 Duality Results . . . . . . . . . . . . . . . . . . . . . 27  \n3.5 Additional Notes . . . . . . . . . . . . . . . . . . . . 28  \n3.6 A Timeline for Formal Explainability . . . . . . . . . . . . . 29  \n4 Computing Explanations . . . . . . . . . . . . . . . . . 29  \n4.1 Progress in Computing Explanations . . . . . . . . . . . . . 30  \n4.2 General Oracle-Based Approach . . . . . . . . . . . . . . . 30  \n4.3 Explaining Decision Lists . . . . . . . . . . . . . . . . . 34  \n4.4 From DLs to DTs & DSs. . . . . . . . . . . . . . . . . . 36  \n4.5 Explaining Neural Networks . . . . . . . . . . . . . . . . 38  \n4.6 Other Families of Classi􀀜ers . . . . . . . . . . . . . . . . 39  \n4.7 An Alternative 􀀕 Compilation-Based Approaches . . . . . . . . . 40  \n5 Tractable Explanations. . . . . . . . . . . . . . . . . . 40  \n5.1 Decision Trees . . . . . . . . . . . . . . . . . . . . . 40  \n5.2 Monotonic Classi􀀜ers . . . . . . . . . . . . . . . . . . . 43  \n5.3 Other Families of Classi􀀜ers . . . . . . . . . . . . . . . . 45  \n6 Explainability Queries . . . . . . . . . . . . . . . . . . 46  \n6.1 Enumeration of Explanations . . . . . . . . . . . . . . . . 46  \n6.2 Explanation Membership . . . . . . . . . . . . . . . . . 48  \n6.3 Additional Explainability Queries . . . . . . . . . . . . . . 50  \n7 Probabilistic Explanations . . . . . . . . . . . . . . . . 50  \n7.1 Problem Formu","cbCaiviqMOQeoUaN","https://ap.wps.com/l/cbCaiviqMOQeoUaN","pdf",937753,1,73,"English","en",105,"# Introduction\n# Preliminaries\n## Logic Foundations\n## Classification Problems\n## Non-Formal Explanations\n# Formal Explainability\n## Abductive Explanations\n## Contrastive Explanations\n## Global Abductive Explanations & Counterexamples\n## Duality Results\n## Additional Notes\n## A Timeline for Formal Explainability\n# Computing Explanations\n## Progress in Computing Explanations\n## General Oracle-Based Approach\n## Explaining Decision Lists\n## From DLs to DTs & DSs\n## Explaining Neural Networks\n## Other Families of Classifiers\n## An Alternative Compilation-Based Approaches\n# Tractable Explanations\n## Decision Trees\n## Monotonic Classifiers\n## Other Families of Classifiers\n# Explainability Queries\n## Enumeration of Explanations\n## Explanation Membership\n## Additional Explainability Queries\n# Probabilistic Explanations\n## Problem Formulation\n## Probabilistic Explanations for Decision Trees\n## Additional Topics\n# Input Constraints & Distributions\n# Formal Explanations with Surrogate Models\n# Additional Topics & Extensions\n# Future Research & Conclusions","[{\"question\":\"Why are explainable AI methods needed for machine learning models?\",\"answer\":\"Many high-performing ML models are difficult to understand, creating distrust for human decision makers. This is especially problematic in settings where incorrect or unfair behavior can have serious consequences.\"},{\"question\":\"What distinguishes formal, logic-based explanations from non-formal explanations?\",\"answer\":\"Non-formal, model-agnostic explanations do not provide rigor and can be consistent with different predictions, making them unreliable. Formal explanations target rigorous, model-based justification using logical foundations.\"},{\"question\":\"What kinds of topics does the survey cover in formal explainability?\",\"answer\":\"It covers definitions of explanations, complexity of computing them, logical encodings for reasoning about different ML models, and ways to make explanations interpretable for human decision makers.\"}]","Logic-Based Explainability in Machine Learning | PDF",1785811652,184,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"logic-based-explainability-in-machine-learning","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/logic-based-explainability-in-machine-learning/122597/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why are explainable AI methods needed for machine learning models?","Question",{"text":75,"@type":76},"Many high-performing ML models are difficult to understand, creating distrust for human decision makers. This is especially problematic in settings where incorrect or unfair behavior can have serious consequences.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What distinguishes formal, logic-based explanations from non-formal explanations?",{"text":80,"@type":76},"Non-formal, model-agnostic explanations do not provide rigor and can be consistent with different predictions, making them unreliable. Formal explanations target rigorous, model-based justification using logical foundations.",{"name":82,"@type":73,"acceptedAnswer":83},"What kinds of topics does the survey cover in formal explainability?",{"text":84,"@type":76},"It covers definitions of explanations, complexity of computing them, logical encodings for reasoning about different ML models, and ways to make explanations interpretable for human decision makers.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]