[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83838-en":3,"doc-seo-83838-105":30,"detail-sidebar-cat-0-en-105":92},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83838,2336464648322,"Aria","https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488",8,"Research & Report","Classification of σ-validity","Classification of σ-validity in dynamic epistemic logic for public and iterated announcements. Building on a 2018 framework that extends success, self-refutation, true lies, and impossible lies to arbitrary 0–1 sequences σ, the work disproves a stated conjecture. Corrected classifications are provided for multi-agent K45, single-agent KD45, and multi-agent S5, while the multi-agent KD45 case with multiple agents remains open. The results reveal an asymmetry: truthful announcements stabilize truth, whereas false announcements are unstable.","arXiv :2607 .04685v 1 [ cs .LO] 6 Jul 2026  \nClassification of σ-validity  \nEiji Yamada 1*  \n1* Department of Mathematical and Computing Science, Institute of  \nScience Tokyo, Tokyo, Japan.  \nCorresponding author(s). E-mail(s): [yamada.e.112d@m.isct.ac.jp](yamada.e.112d@m.isct.ac.jp) ;  \nAbstract  \nIn their 2018 paper, ˚Agotnes, van Ditmarsch, and Wang extended the notions of success and self-refutation in public announcements to true lies, impossible lies, and σ-validity in general, where σ is a finite or infinite sequence of 0s and 1s. For example, successful formulas and self-refuting formulas are 11-valid and 10-valid, respectively. They then posed a conjecture on the classification of such sequencesin terms of σ-validity. In this paper, we disprove the conjecture and give corrected classifications for multi-agent K45, single-agent KD45, and multi-agent S5 after reformulating the statement more explicitly. We leave the multi-agent KD45 case with more than one agent open. The results indicate that there is anasymmetry between truthful announcements and false announcements: the former are stable while the latter are unstable. In particular, successful formulas remain true forever while impossible lies can be true at some point when repeatedly announced. Also, although self-refuting formulas can become true again after following the truth pattern 10 , 100-valid formulas are destructive in the sense that they remain false forever once they become false. On the other hand, true lies are fragile in the sense that truths created by lying can become false again.  \nKeywords: dynamic epistemic logic, public announcements, iterated announcements,σ-validity  \n1 Introduction  \nDynamic epistemic logic is the study of information flow, knowledge acquisition, and belief revision. Public announcements are one of the main topics in the field. A public announcement of a proposition φ means to announce that φ holds to a group of agents. Public announcement logic (PAL) was proposed (Plaza, 2007) to express  \n1  \npublic announcements, which deletes all the states where φ is false after a public announcement of φ .  \nHowever, in public announcement logic, we can no longer consider the truth of formulas at states that have already been eliminated. That is, when we consider the truth of a formula φ at the pointed model M, w, we can no longer consider the truth at w in the updated model Mφ whenever M, w |= ¬φ, simply because w  Mφ .  \nOn the other hand, Gerbrandy and Groeneveld (1997) proposed the logic of conscious updates also known as believed public announcement logic (BPAL), which deletes all arrows that go to states where φ is false. That is, in believed public announcement logic, we define the accessibility relation R|φ of the updated model M|φ as w(R|φ)v iff wRv and M, v |= φ where M = (W, R, V ) is a (initial) model. This allows us to consider not only truthful announcements but also false announcements. In particular, we can keep track of the truth of a formula φ at M, w that becomes false at some stage when φ is announced repeatedly (iterated announcements of φ) .  \nOne of the major topics in public announcements is the discussion of successful formulas. We say that a formula φ is successful iff whenever φ is true, it remains true after a public announcement of φ . Formally, φ is successful iff the formula φ → [↑ φ]φ is valid, where [↑ φ]ψ means in BPAL that after a public announcement of φ , ψ holds. This notion matters since “successful” guarantees that true information is shared with others without changing its truth, which is oftentimes the purpose of announcements.  \nIn contrast, there are formulas that change their truth after an announcement. We say that φ is self-refuting iff whenever φ is true, it becomes false after an announcement (Holliday & Icard, 2010), with the Moore sentence φ := p ∧ ¬□p being the most typical example (Hintikka, 1962; Moore, 1952) . ˚Agotnes, van Ditmarsch, and Wang (2018) proposed true lies and impossibl","cbCaiuD60VGLFEZJ","https://ap.wps.com/l/cbCaiuD60VGLFEZJ","pdf",574560,6,1,21,"English","en",105,"# Introduction\n## Dynamic epistemic logic and public announcements\n## Successful, self-refuting, true lies, and impossible lies\n## σ-validity and σ-satisfiability\n## Prior conjecture and completion equivalence","[{\"question\":\"What is σ-validity in the context of iterated public announcements?\",\"answer\":\"A formula is σ-valid if, under iterated announcements, its truth values along the pointed model follow the 0–1 pattern specified by σ whenever the initial truth value matches the first digit of σ.\"},{\"question\":\"Which agent-system cases does the paper successfully classify, and which remains open?\",\"answer\":\"The paper gives corrected classifications for multi-agent K45, single-agent KD45, and multi-agent S5. The multi-agent KD45 case with more than one agent is left open.\"},{\"question\":\"What key asymmetry does the paper identify between truthful and false announcements?\",\"answer\":\"Truthful announcements yield stable truths: successful formulas remain true forever. False announcements are unstable: impossible lies can become true at some later point under repeated announcements.\"}]",1784190897,53,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"classification-of-validity","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"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/classification-of-validity/83838/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What is σ-validity in the context of iterated public announcements?","Question",{"text":76,"@type":77},"A formula is σ-valid if, under iterated announcements, its truth values along the pointed model follow the 0–1 pattern specified by σ whenever the initial truth value matches the first digit of σ.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Which agent-system cases does the paper successfully classify, and which remains open?",{"text":81,"@type":77},"The paper gives corrected classifications for multi-agent K45, single-agent KD45, and multi-agent S5. The multi-agent KD45 case with more than one agent is left open.",{"name":83,"@type":74,"acceptedAnswer":84},"What key asymmetry does the paper identify between truthful and false announcements?",{"text":85,"@type":77},"Truthful announcements yield stable truths: successful formulas remain true forever. 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