[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86073-en":3,"doc-seo-86073-105":28,"detail-sidebar-cat-0-en-105":90},{"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":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":13,"seo_description":14,"update_tm":26,"read_time":27},86073,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Learning Linear Temporal Specifications from Demonstrations with Uncertainty","Learning temporal logic specifications from system demonstrations is key for formal verification and controller synthesis, especially in safety-critical domains. Existing methods often assume demonstrations are correct or only affected by misclassification errors, while real traces are frequently uncertain or incomplete because of sensor faults, measurement inaccuracies, or data loss. The framework learns minimal Linear Temporal Logic (LTL) formulas from uncertain demonstrations by modeling uncertainty via Hamming distance, grouping trace estimates with consistency constraints, and reducing the task to Pseudo-Boolean Optimization.","Learning Linear Temporal Specifications from Demonstrations with Uncertainty  \nParastou Fahim 1 , Constantino Lagoa 1 , and Rômulo Meira-Góes 1  \narXiv :2607 . 109 18v 1 [ cs .AI] 12 Jul 2026  \nAbstract—Learning temporal logic specifications from system demonstrations is essential for tasks such as formal verification and controller synthesis, especially in safetycritical domains. Existing approaches typically assume demonstrations are correct or only affected by misclassification errors. In practice, however, system traces are often uncertain or incomplete due to sensor faults, measurement errors, or data loss. We present a framework for learning minimal Linear Temporal Logic (LTL) formulas from demonstrations with uncertainty. Our approach models uncertainty via Hamming distance to generate possible estimates around each observed trace, which are grouped with constraints requiring that at least one trace per group is consistent with the learned formula. Our problem is then reduced to an equivalent Pseudo-Boolean Optimization. We evaluate our method against state-of-the-art LTL learning approaches and show that it recovers specifications that more closely align with ground-truth formulas under uncertainty.  \nI. INTRODUCTION  \nThe challenge of inferring temporal logic specifications from system observations has gained increasing attention in recent years, particularly in areas such as robotics, control systems, and cyber-physical security [1],[2],[3] . Learning an interpretable specification from system behavior is essential for facilitating formal verification and controller synthesis [4] . This need is heightened in safety-critical applications, such as autonomous vehicles, unmanned aerial systems, and medical devices, where incorrect or unforeseen behaviors can result in catastrophic outcomes [5] . As system complexity grows, manually specifying temporal behaviors becomes challenging and error-prone. Automatically inferring temporal logic specifications from system executions provides a scalable alternative. This enables constructing human-interpretable models of system behaviors, the identification of deviations or faults, and the formal verification of system correctness [6], [7] . Linear temporal logic (LTL) has emerged as a specification formalism for capturing system behaviors over time. Recent studies have demonstrated that LTL properties can be automatically learned from observed executions, typically using both positive and negative examples [6], [8], [9] . Two common frameworks for the learning task are automata-based learning and SAT-based learning. Automata-based methods operate by translating LTL formulas into automata whose accepted languages  \n*This research was supported by Rising Researcher award ICDS:RR25-SCR025154 from Penn State’s Institute for Computational & Data Sciences.  \n1 PF, CL, and RMG are with the School of Electrical Engineering and Computer Science at The Pennsylvania State University, State College, USA {pbf5107,cml18,[romulo}@psu.edu](romulo}@psu.edu)  \ncorrespond to the set of traces that satisfy the given specifications. Depending on the complexity of the temporal behaviors to be captured, different types of automata maybe employed, such as finite state automata (FSA) [10], Büchi automata [11], or Rabin automata [12], each defined by distinct acceptance conditions tailored to varying levels of expressivity [4] . In this paper, we will focus on SAT-based learning methods since they usually offer amore direct and scalable approach to learn LTL formulas. SAT-based learning methods encode the task of learning an LTL formula as a satisfiability problem (SAT)  \n[6]. Many recent studies have adopted SAT-based learning methods because they provide a practical balance between computational performance and model explainability, particularly in large-scale scenarios [13] . For example, the study by Camacho and McIlraith [14] proposes a SATbased framework for both passive and active learning of minima","cbCailaaz6sLwsE9","https://ap.wps.com/l/cbCailaaz6sLwsE9","pdf",552398,1,"English","en",105,"# Introduction\n## Temporal logic specification learning from demonstrations\n## Learning frameworks: automata-based and SAT-based\n## Motivation for uncertainty-aware learning\n## Related work on robustness and optimization-based approaches","[{\"question\":\"Why is learning temporal logic specifications from demonstrations important?\",\"answer\":\"It enables formal verification and controller synthesis by producing interpretable specifications from observed system behavior, which helps identify deviations or faults. In safety-critical systems, incorrect temporal behavior can have catastrophic consequences.\"},{\"question\":\"What limitation do existing LTL learning approaches often have regarding demonstrations?\",\"answer\":\"They typically assume demonstrations are correct or only affected by misclassification errors. The document highlights that in practice traces can be uncertain or incomplete due to sensor faults, measurement errors, or data loss.\"},{\"question\":\"How does the proposed method model uncertainty and formulate the learning problem?\",\"answer\":\"It models uncertainty using Hamming distance to generate possible estimates around each observed trace, then groups traces with constraints requiring at least one trace per group to be consistent with the learned LTL formula. The learning task is reduced to an equivalent Pseudo-Boolean Optimization problem.\"}]",1784208350,20,{"code":4,"msg":29,"data":30},"ok",{"site_id":23,"language":22,"slug":31,"title":13,"keywords":32,"description":14,"schema_data":33,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":26},"learning-linear-temporal-specifications-from-demonstrations-with-uncertainty","",{"@graph":34,"@context":84},[35,52,67],{"@type":36,"itemListElement":37},"BreadcrumbList",[38,42,46,49],{"item":39,"name":40,"@type":41,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":43,"name":44,"@type":41,"position":45},"https://docshare.wps.com/document/","Document",2,{"item":47,"name":12,"@type":41,"position":48},"https://docshare.wps.com/document/research-report/",3,{"item":50,"name":13,"@type":41,"position":51},"https://docshare.wps.com/document/learning-linear-temporal-specifications-from-demonstrations-with-uncertainty/86073/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":22,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":39,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"Why is learning temporal logic specifications from demonstrations important?","Question",{"text":74,"@type":75},"It enables formal verification and controller synthesis by producing interpretable specifications from observed system behavior, which helps identify deviations or faults. In safety-critical systems, incorrect temporal behavior can have catastrophic consequences.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What limitation do existing LTL learning approaches often have regarding demonstrations?",{"text":79,"@type":75},"They typically assume demonstrations are correct or only affected by misclassification errors. The document highlights that in practice traces can be uncertain or incomplete due to sensor faults, measurement errors, or data loss.",{"name":81,"@type":72,"acceptedAnswer":82},"How does the proposed method model uncertainty and formulate the learning problem?",{"text":83,"@type":75},"It models uncertainty using Hamming distance to generate possible estimates around each observed trace, then groups traces with constraints requiring at least one trace per group to be consistent with the learned LTL formula. 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