[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82894-en":3,"doc-seo-82894-105":29,"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":20,"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":13,"seo_description":14,"update_tm":27,"read_time":28},82894,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Tempus fugit: Anyone can understand temporal logic if they have to save the realm","Tempus fugit is a small single-player browser game that teaches linear temporal logic with past (PLTL) through deck-building magic combat. Players defeat enemies by casting spells whose applicability conditions—and enemy abilities—are specified as PLTL formulas evaluated over finite traces the player builds over time. The paper explains how game mechanics map to PLTL semantics, how players learn to manipulate valuations of atomic propositions, and how such a game can make formal logic approachable for non-experts.","Tempus fugit: Anyone can understand temporal logic if they have to save the realm  \nBenjamin Bisping \\# Ñ  \nTélécom SudParis, Institut Polytechnique de Paris, France Tobias Loch \\#  \nTechnische Universität Berlin, Germany Mustafa Mohsen \\# Technische Universität Berlin, Germany Alessio Nicolo Perna \\# Technische Universität Berlin, Germany Maximilian Lukas Stamm  \nTechnische Universität Berlin, Germany  \n~~ Abstract ~~  \nOften, the easiest way to learn something is to have to use it for a purpose. This purpose can be playful: In Tempus fugit, the player takes on the role of a magician who has to defeat enemies by casting spells. The applicability of spells and enemy attacks depends on the truth of formulas in linear temporal logic with past with respect to a trace that the player gradually builds. So, whoever wants to save the realm from monsters has to learn to read logic formulas.  \nThis paper describes the small browser game and explains our design choices. We expose how game mechanics connect to linear temporal logic with past over finite traces, and how this can help players approach a daunting topic like formal logic.  \n2012 ACM Subject Classification Applied computing → Education; Theory of computation → Logic  \nKeywords and phrases Linear temporal logic, Temporal logic, Game-based learning, Computer game  \nFunding Benjamin Bisping is partially funded by the Orange and Télécom SudParis CRE Project“Formal validation of the singularization principle.”  \nAcknowledgements Apart from the paper authors, Florian Eyert and Kejni Dema contributed to the development of Tempus fugit. We thank Philipp Schlehuber-Caissier and Arno Wilhelm-Weidner for feedback on a draft version of the paper.  \n 1  Introduction  \nSadly, most people never learn to read formal logics, let alone temporal and modal ones. Despite persistent preaching on the merits of such logics, for instance by Lamport [8], and its inclusion in many curricula, the majority of the programmer population lives under the assumption that temporal logics are an arcane art, something to be discarded as too complicated. But the core concepts are easy to grasp—even in the context of a science communication event or a chat at a family gathering. How do we help people take the first step beyond the initial barriers of notation and limiting beliefs?  \nTempus fugit is a small browser game in which one plays a magician. Which spells one can cast depends on atomic propositions that players set over time. The twist: Spell cards express their applicability conditions in linear temporal logic with past (PLTL), as do enemy abilities. In order to play effectively, players must thus learn to read formulas of PLTL.  \nBy framing the challenge in terms of magic in a computer game, we “trick” players into engaging with temporal logic. Implicitly, strange logical notation becomes part of the fun.  \n2 Tempus fugit: Anyone can understand temporal logic  \nLimiting beliefs like “Formal logic is made for people who are more mathematical than me”are overwritten by “This game is made to be played by people like me.”  \nContribution In this paper, we present Tempus fugit, a computer game that can be employed to convey the basics of temporal logic to everyday people, for instance, in science communication contexts or at the beginning of a logic course.  \nPlayers of the game implicitly learn how to manipulate valuations of atomic propositionsin order to make propositional and temporal formulas true or false. This seeds the concepts of atomic propositions, valuations, and traces, as well as operators, formulas, and truth-value semantics.  \nStructure This paper recalls definitions of temporal logic PLTL (Section 2), describes the game mechanics and how they relate to PLTL (Section 3) and discusses the choices we have made in design and implementation (Section 4) . Section 5 closes with some remarks on limits and opportunities in the context of “games as learning machines.”  \nAvailability Tempus fugit can be p","cbCaiabbxtU13LKj","https://ap.wps.com/l/cbCaiabbxtU13LKj","pdf",806530,1,10,"English","en",105,"# Introduction\n# Background: Linear temporal logic\n# Tempus fugit\n## Mechanics and gameplay\n## Relation to PLTL\n## Game narrative\n# Design and implementation choices","[{\"question\":\"What role do PLTL formulas play in Tempus fugit?\",\"answer\":\"Spells and enemy abilities are governed by applicability conditions written in linear temporal logic with past (PLTL). These formulas are evaluated over finite traces that evolve based on the player’s actions over time.\"},{\"question\":\"How does the game help players learn temporal logic?\",\"answer\":\"Players repeatedly manipulate valuations of atomic propositions (“runes”) across time to make propositional and temporal formulas true or false. This naturally introduces concepts like traces, operators, and truth-value semantics.\"},{\"question\":\"Where can Tempus fugit be played and demonstrated?\",\"answer\":\"The game can be played directly in a browser, with TypeScript source code available on GitHub. A demo is planned for the TEAL 2026 workshop during FLoC 2026 in Lisbon, and the authors can repeat it elsewhere.\"}]",1784183760,25,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"tempus-fugit-anyone-can-understand-temporal-logic-if-they-have-to-save-the-realm","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/tempus-fugit-anyone-can-understand-temporal-logic-if-they-have-to-save-the-realm/82894/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What role do PLTL formulas play in Tempus fugit?","Question",{"text":75,"@type":76},"Spells and enemy abilities are governed by applicability conditions written in linear temporal logic with past (PLTL). These formulas are evaluated over finite traces that evolve based on the player’s actions over time.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the game help players learn temporal logic?",{"text":80,"@type":76},"Players repeatedly manipulate valuations of atomic propositions (“runes”) across time to make propositional and temporal formulas true or false. This naturally introduces concepts like traces, operators, and truth-value semantics.",{"name":82,"@type":73,"acceptedAnswer":83},"Where can Tempus fugit be played and demonstrated?",{"text":84,"@type":76},"The game can be played directly in a browser, with TypeScript source code available on GitHub. 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