Collabora Online (often abbreviated as COOL) is an open-source online office suite developed by Collabora, based on LibreOffice Online, the web-based edition of the LibreOffice office suite. It enables real-time collaborative editing of documents, spreadsheets, presentations, and vector graphics in a web browser. Optional applications are available for offline use on Android, ChromeOS, iOS, iPadOS, Linux distributions, macOS, and Windows. It supports the OpenDocument format and is compatible with other major formats, including those used by Microsoft Office. The Document Foundation (TDF), the nonprofit organization behind LibreOffice, states that a majority of the LibreOffice software development is done by its partners like Collabora. Collabora Online is an open-source alternative to proprietary cloud office platforms such as Google Workspace and Microsoft 365. Unlike these services, it can be self-hosted or hosted by third-party providers. The platform is marketed particularly toward enterprises and public institutions seeking greater digital sovereignty and independence from U.S.-based "big tech" companies. Collabora also develops Collabora Office, a standalone desktop and mobile app suite based on LibreOffice. Although Collabora Online has increasingly taken on a central role, both products may be used in parallel, similar to Microsoft Office and Microsoft 365. In November 2025, Collabora released Collabora Office Desktop and renamed the previous product Collabora Office Classic. The new product shares code with Collabora Online and brings the same user interface to the desktop on Linux, Windows and MacOS. A separate version, the Collabora Online Development Edition (CODE), is offered free of charge and is recommended for individuals, small teams, and developers. CODE provides early access to new features and serves as a testing and development platform for open-source community contributors. As TDF does not offer a free version of LibreOffice Online, CODE represents the primary freely available option for organizations and individuals interested in deploying LibreOffice in a web-based, collaborative setting. == Applications == Collabora Online includes several applications for document editing, available through the web-based interface and optional desktop and mobile apps: Collabora Writer – A word processor based on LibreOffice Writer, comparable to Microsoft Word and Google Docs. It supports WYSIWYG editing, styles, formatting tools, comment threads, and change tracking. Collabora Calc – A spreadsheet editor based on LibreOffice Calc, similar to Microsoft Excel and Google Sheets. Features include pivot tables, formulas, data validation, conditional formatting, advanced sorting and filtering, charts, and support for up to 16,000 columns. Compatible with some macros written in VBA. Collabora Impress – A presentation program based on LibreOffice Impress, comparable to Microsoft PowerPoint and Google Slides. It supports master slides, transitions, speaker notes, and multimedia elements. Collabora Draw is not a separate application, most of the functionality of the Draw application is now integrated in Writer and Impress – vector graphics editor based on LibreOffice Draw, comparable to Microsoft Visio and Google Drawings. == Features == Collabora Online can be accessed from modern web browsers without the need for plug-ins or add-ons. It supports real-time collaborative editing of word processing documents, spreadsheets, presentations, and vector graphics. Collaboration features include commenting, version tracking with document comparison and restoration, and integration with communication tools such as chat or video calls. These functions are often enabled through integration with enterprise open-source cloud platforms like Nextcloud, ownCloud, Seafile, EGroupware, GroupOffice and others. Collabora Online can also be embedded or integrated into a variety of third-party applications. Although client apps are not required to use the web-based suite, optional applications are available for offline use on Android, ChromeOS, iOS, iPadOS, Linux distributions, macOS, and Windows. These apps share the same LibreOffice-based core as the server version, ensuring document compatibility across platforms. Development of the LibreOffice core benefits both the online server and the client applications simultaneously. The mobile apps offer touch-optimized interfaces that adapt to different screen sizes and can be used offline, with optional integration into cloud storage services. Collabora Online supports OpenDocument formats (ODF; .odt, .odp, .ods, .odg) in accordance with ISO/IEC 26300. It is also compatible with Microsoft Office formats, including Office Open XML (.docx, .pptx, .xlsx) and legacy binary formats (.doc, .ppt, .xls). Additional supported formats include PDF, PNG, CSV, TSV, RTF, EPUB, and others. The suite can import a range of formats supported by LibreOffice, including Microsoft Visio and Publisher files, Apple Keynote, Numbers, and Pages files, as well as legacy formats used by Lotus 1-2-3, Microsoft Works, and Quattro Pro. The core of Collabora Online is written in C++ and utilizes LibreOfficeKit, a programming interface that enables reuse of much of LibreOffice's existing code for document saving, loading, and rendering. Collabora Online operates on the principle that documents remain on the server, with users viewing tile-rendered images of the document and sending their edits back to the server. The user interface is implemented in JavaScript. For file access and authentication with file hosting services, Collabora Online uses Microsoft's WOPI protocol, allowing compatibility with any service supporting Microsoft 365 integration. == Server == The server component can be self-hosted or deployed through third-party enterprise open-source cloud platforms, allowing organizations to maintain control over data and infrastructure. It is available for various Linux distributions and as a Docker image. The server enables features such as in-browser document editing, file synchronization, and real-time communication. These third-party cloud platforms typically offer additional functionality comparable to services such as Dropbox, Google Workspace, Microsoft 365, or Zoom, including file sharing, calendars, email, contacts, chat, and video conferencing. Collabora Online can be integrated into these applications, as well as with other services such as learning management systems and enterprise content platforms, through open APIs and an SDK. == Reception == Various online and print publications have discussed Collabora Online. In December 2016 the technology website Softpedia mentioned the availability of collaborative editing in version 2.0 and the integration with ownCloud, Nextcloud, and other file synchronization and sharing solutions. In June 2020, ZDNET reported that Collabora Online would be included as the standard office suite in Nextcloud version 19, noting that direct document editing was added to the native video conferencing software Talk. The technology blog OMG! Ubuntu! covered the release of Collabora's Android and iOS apps, emphasizing their offline functionality. In September 2020, Linux Magazine compared Collabora Online with OnlyOffice, noting the flexibility and platform independence of both tools and highlighting Collabora's extensive feature set derived from LibreOffice. === Digital sovereignty === Collabora Online's open-source design and support for self-hosting have made it notable in discussions about digital sovereignty—the ability of users and organizations to control their own data. This is particularly relevant in Europe, where concerns about dependence on U.S.-based "big tech" companies and data privacy have grown in recent years. On 10th June 2025, Microsoft executives under oath in the French Senate admitted that they cannot guarantee data sovereignty and would be compelled to pass French (and by implication the wider European Union) information to the US administration if requested via a warrant or subpoena. The Cloud Act is a law that gives the US government authority to obtain digital data held by US-based tech corporations, irrespective of whether that data is stored on servers at home or on foreign soil. A 2020 briefing by the European Parliament highlighted risks associated with reliance on major technology companies that collect and exploit user data. Legal decisions such as the Schrems II ruling have further underscored these concerns. Several European government agencies have adopted private cloud solutions using Collabora Online and related platforms to enhance data security and maintain control over sensitive information. == History == The former LibreOffice development team from SUSE joined Collabora in September 2013, forming the subsidiary Collabora Productivity. In 2015 Collabora and IceWarp announced the development of an enterprise-ready version of LibreOffice Online to compete wi
Semantic space
Semantic spaces in the natural language domain aim to create representations of natural language that are capable of capturing meaning. The original motivation for semantic spaces stems from two core challenges of natural language: Vocabulary mismatch (the fact that the same meaning can be expressed in many ways) and ambiguity of natural language (the fact that the same term can have several meanings). The application of semantic spaces in natural language processing (NLP) aims at overcoming limitations of rule-based or model-based approaches operating on the keyword level. The main drawback with these approaches is their brittleness, and the large manual effort required to create either rule-based NLP systems or training corpora for model learning. Rule-based and machine learning based models are fixed on the keyword level and break down if the vocabulary differs from that defined in the rules or from the training material used for the statistical models. Research in semantic spaces dates back more than 20 years. In 1996, two papers were published that raised a lot of attention around the general idea of creating semantic spaces: latent semantic analysis and Hyperspace Analogue to Language. However, their adoption was limited by the large computational effort required to construct and use those semantic spaces. A breakthrough with regard to the accuracy of modelling associative relations between words (e.g. "spider-web", "lighter-cigarette", as opposed to synonymous relations such as "whale-dolphin", "astronaut-driver") was achieved by explicit semantic analysis (ESA) in 2007. ESA was a novel (non-machine learning) based approach that represented words in the form of vectors with 100,000 dimensions (where each dimension represents an Article in Wikipedia). However practical applications of the approach are limited due to the large number of required dimensions in the vectors. More recently, advances in neural network techniques in combination with other new approaches (tensors) led to a host of new recent developments: Word2vec from Google, GloVe from Stanford University, and fastText from Facebook AI Research (FAIR) labs.
List of speech recognition software
Speech recognition software is available for many computing platforms, operating systems, use models, and software licenses. Here is a listing of such, grouped in various useful ways. == Acoustic models and speech corpus (compilation) == The following list presents notable speech recognition software engines with a brief synopsis of characteristics. == Macintosh == == Cross-platform web apps based on Chrome == The following list presents notable speech recognition software that operate in a Chrome browser as web apps. They make use of HTML5 Web-Speech-API. == Mobile devices and smartphones == Many mobile phone handsets, including feature phones and smartphones such as iPhones and BlackBerrys, have basic dial-by-voice features built in. Many third-party apps have implemented natural-language speech recognition support, including: == Windows == === Windows built-in speech recognition === The Windows Speech Recognition version 8.0 by Microsoft comes built into Windows Vista, Windows 7, Windows 8 and Windows 10. Speech Recognition is available only in English, French, Spanish, German, Japanese, Simplified Chinese, and Traditional Chinese and only in the corresponding version of Windows; meaning you cannot use the speech recognition engine in one language if you use a version of Windows in another language. Windows 7 Ultimate and Windows 8 Pro allow you to change the system language, and therefore change which speech engine is available. Windows Speech Recognition evolved into Cortana (software), a personal assistant included in Windows 10. === Windows 7, 8, 10, 11 third-party speech recognition === Braina – Dictate into third party software and websites, fill web forms and execute vocal commands. Dragon NaturallySpeaking from Nuance Communications – Successor to the older DragonDictate product. Focus on dictation. 64-bit Windows support since version 10.1. Tazti – Create speech command profiles to play PC games and control applications – programs. Create speech commands to open files, folders, webpages, applications. Windows 7, Windows 8 and Windows 8.1 versions. Voice Finger – software that improves the Windows speech recognition system by adding several extensions to it. The software enables controlling the mouse and the keyboard by only using the voice. It is especially useful for aiding users to overcome disabilities or to heal from computer injuries. === Microsoft Speech API === The first version of the Microsoft Speech API was released for Windows NT 3.51 and Windows 95 in 1995, it was then part of Windows up to Windows Vista. This initial version already contained Direct Speech Recognition and Direct Text To Speech APIs which applications could use to directly control engines, as well as simplified 'higher-level' Voice Command and Voice Talk APIs. Speech recognition functionality included as part of Microsoft Office and on Tablet PCs running Microsoft Windows XP Tablet PC Edition. It can also be downloaded as part of the Speech SDK 5.1 for Windows applications, but since that is aimed at developers building speech applications, the pure SDK form lacks any user interface (numerous applications were available), and thus is unsuitable for end users. == Built-in software == Microsoft Kinect includes built-in software which allows speech recognition of commands. Older generations of Nokia phones like Nokia N Series (before using Windows 7 mobile technology) used speech-recognition with family names from contact list and a few commands. Siri, originally implemented in the iPhone 4S, Apple's personal assistant for iOS, which uses technology from Nuance Communications. Cortana (software), Microsoft's personal assistant built into Windows Phone and Windows 10. == Interactive voice response == The following are interactive voice response (IVR) systems: CSLU Toolkit Genesys HTK – copyrighted by Microsoft, but allows altering software for licensee's internal use LumenVox ASR Tellme Networks; acquired by Microsoft == Unix-like x86 and x86-64 speech transcription software == Janus Recognition Toolkit (JRTk) Mozilla DeepSpeech was developing an open-source Speech-To-Text engine based on Baidu's deep speech research paper. Weesper Neon Flow – professional voice-dictation software that provides offline speech-to-text processing on macOS and Windows using local AI models. It is not open source and offers a paid subscription after a 15‑day free trial. Vocalinux – open-source speech transcription software for Linux. == Discontinued software == IBM VoiceType (formerly IBM Personal Dictation System) IBM ViaVoice – Embedded version still maintained by IBM. No longer supported for versions above Windows Vista. Untested above macOS 10.4 or on Macintoshes with an Intel chipset. Quack.com; acquired by AOL; the name has now been reused for an iPad search app. SpeechWorks from Nuance Communications. Yap Speech Cloud – Speech-to-text platform acquired by Amazon.com.
17LIVE
17LIVE is an international entertainment platform. As of 2024, 17LIVE is the #3 live broadcasting platform globally, formed by its flagship live stream app 17LIVE (LIVIT in English markets), MEME Live and live stream e-commerce platforms HandsUP and OrderPally. == History == 17LIVE was first founded in Taiwan in 2015 by Jeffery Huang. The company has maintained its leading position since its entry into the Japan market in 2017, becoming the biggest platform for live entertainment in Japan, Taiwan, Hong Kong, and other countries. In 2017, 17 closed out US$33M in series B round to merge with dating software Paktor, with Joseph Phua (Co-founder of Paktor) taking over the leadership of 17LIVE as CEO and Co-founder, as well as to enter the Japan and Hong Kong market. Within one year, 17 Media became the #1 market leader in Japan. In 2018, the company raised $25M in series C round as it got ready for US IPO, which failed to materialize. 17LIVE had an unsuccessful US IPO attempt in 2018. Since then, the company reformed and transformed the business. Some key initiatives include the hiring of current CEO Hirofumi Ono, spin-off of Paktor (dating software business unit), full buy-out of founder Jeffery Huang, acquisition of MEME and HandsUp, and more. Despite the failed IPO attempt, the company continued to push for international expansion, including creating ‘LIVIT’ for the English-speaking markets to enter US, India, and North Africa. In 2019, 17's flagship live streaming app reached 10M downloads in Japan, and the business continues to push for both organic and inorganic expansion. Some key M&A highlights in the year include the acquisition of MEME Live in Southeast Asia, as well as HandsUp, a live e-commerce platform. In 2020, M17 closed out $26.5M in Series D round to continue organic growth in Japan, US and Middle East. In the same year, the company also sold its dating app business, Parktor, to rationalise M17 into a live-stream pure play business, followed by the appointment of its current Chairman, Joseph Phua, and previous Global CEO, Hirofumi Ono. With the buy-out and departure of founder Jeff Huang, the parent holding company M17 Entertainment Limited was officially renamed as 17 LIVE Group. An estimated 60 million users registered in 154 countries and territories in April 2022. In 2022, September, 17LIVE announced Group CEO Hirofumi Ono steps down. Alex Lien takes over the leadership as new Group COO; Jing Shen Ng appointed Group CTO. In 2023, March, 17LIVE announced Alex Lien promoted to Global CEO. Kenta Masuda appointed as Global CFO. === Collaboration with Ayumi Hamasaki === To celebrate its 4th anniversary, 17LIVE collaborated with Japanese singer-songwriter Ayumi Hamasaki, who led the 17LIVE 4th Anniversary meets Ayumi Hamasaki series starting October 18, 2021. Along with composer and arranger Yuta Nakano, Hamasaki judged auditioning artists competing for the chance to work with her and her production team for a debut single. The series was streamed live on the 17LIVE website, the final airing on November 11. The eventual winner was named as Yoshitaka_song. When asked why she collaborated with 17LIVE as a producer, Hamasaki commented: "Although the world has become like this (during COVID-19), I believe that the art of entertainment can give people dreams, hope, courage, and strength. I hope that kind of light will continue to shine through the entertainment industry." == Features == On 17LIVE, artists (LIVERs) are able to broadcast live, and post photos and videos from their album. The app has been designed for LIVERs to simply open the App, and start sharing contents without the need to edit or professionally curate their videos. The platform cultivates LIVERs, supports them with a local content management team, and provides artists with various functions, such as real time chatting, gifting, fan clubs, interactive competition and events. Today, 17LIVE has 46 thousands contracted artists and more than 2.3 million MAU, who spend 44 minutes on the platform every day. 17LIVE continues to advocate content-driven philosophy and delivers diverse topics, from politics and music to entertainment, to broaden its audience groups. 17LIVE also hosts offline flash events and concerts to attract new users and support LIVERs better connect with their fans. == Operation == 17LIVE has over 700 employees globally. The app provides few monetization models for LIVERs on the platform, including: Gifting: user / fans buy virtual gifts on the app to send to their favored LIVERs. Subscription: monthly subscription fan club service for access to exclusive content Pay-per-view: ticket service for online streaming concerts E-commerce: live e-commerce platform In the past, 17LIVE has encountered some regulatory headwinds with reported incidents of inappropriate livestream content on the platform. The incidents were direct results of the lack of oversight and supervision capability in place in the business at the time. Over the years, 17LIVE claims to have put in tremendous manpower and effort into improving, monitoring and maintaining control over both the live stream content and the KYC procedures and systems.
AstroPay
AstroPay is a global digital wallet that provides users with a way to pay, send, and receive money. The app provides online payments, virtual and physical debit cards, peer-to-peer money transfers, and more. == History == AstroPay was founded in Uruguay in 2009 as a payment processing company. Over time, it expanded its services across Latin America, EMEA, and APAC. A significant milestone occurred in 2016, when AstroPay spun off dLocal, focusing on cross-border payments for emerging markets. dLocal became Uruguay's first unicorn and eventually went public through a successful IPO. In 2020, AstroPay spun off its payment processing services into a new entity, D24, to focus on mobile wallet for cross border. Between 2023 and 2024 the Company brought new leadership to guide its transition towards becoming a fully focused global digital multicurrency wallet where users save, send, and spend globally. This shift introduced enhanced features, including loyalty prepaid cards and multicurrency accounts. == Services == AstroPay offers three main products: AstroPay Wallet, AstroPay check-out, and AstroPay Platform. AstroPay Wallet is a digital wallet for consumers, where they have multicurrency accounts, prepaid card and marketplace. With AstroPay check-out, businesses can tap into AstroPay's wallet user base by accepting AstroPay as a payment method in their check-out options. Lastly, AstroPay Platform enables other businesses to use the AstroPay network to launch their own global wallet. == Brand endorsements, partnerships == AstroPay's marketing strategy has included the development of co-branded products with sports teams and other brand. The company sponsored Burnley Football Club during the 2018–19 Premier League season, renewing the partnership for the 2021–22 Premier League season when it became the club's official payment service partner. In August 2021, AstroPay entered into a partnership with the Wolverhampton Wanderers for the 2021-22 Premier League season, and the following year, became the team's shirt sponsor. Later, in September 2021, AstroPay expanded its partnership with Wolverhampton Wanderers, which included becoming the team's official payment partner and later, in 2023, co-launching a co-branded card. Other partnerships include Newcastle United in 2021 in the English Premier League. AstroPay made arrangements to ensure that branding and logo would be visible on the pitch-side LED advertising during Premier League matches. Furthermore, in June 2022, the company renewed it's partnership with Wolverhampton Wanderers for the 2022-23 Premier League season and launched its Wolves debit card in February 2023. Some other notable partnerships include: Universidad de Chile in 2024, Tottenham Hotspurs in 2023-25, and even a collaboration with Lionel Messi across all of Latin America. == Recent developments == AstroPay has refocused its strategy since 2023, pivoting from payment processing to concentrate on its global digital wallet. This move reflects a broader effort to redefine the company's market positioning by emphasizing global user-friendly financial services, while separating its identity from previous operations managed by dLocal and D24.
Argumentation framework
In artificial intelligence and related fields, an argumentation framework is a way to deal with contentious information and draw conclusions from it using formalized arguments. In an abstract argumentation framework, entry-level information is a set of abstract arguments that, for instance, represent data or a proposition. Conflicts between arguments are represented by a binary relation on the set of arguments. In concrete terms, an argumentation framework is represented with a directed graph such that the nodes are the arguments, and the arrows represent the attack relation. There exist some extensions of the Dung's framework, like the logic-based argumentation frameworks or the value-based argumentation frameworks. == Abstract argumentation frameworks == === Formal framework === Abstract argumentation frameworks, also called argumentation frameworks à la Dung, are defined formally as a pair: A set of abstract elements called arguments, denoted A {\displaystyle A} A binary relation on A {\displaystyle A} , called attack relation, denoted R {\displaystyle R} For instance, the argumentation system S = ⟨ A , R ⟩ {\displaystyle S=\langle A,R\rangle } with A = { a , b , c , d } {\displaystyle A=\{a,b,c,d\}} and R = { ( a , b ) , ( b , c ) , ( d , c ) } {\displaystyle R=\{(a,b),(b,c),(d,c)\}} contains four arguments ( a , b , c {\displaystyle a,b,c} and d {\displaystyle d} ) and three attacks ( a {\displaystyle a} attacks b {\displaystyle b} , b {\displaystyle b} attacks c {\displaystyle c} and d {\displaystyle d} attacks c {\displaystyle c} ). Dung defines some notions : an argument a ∈ A {\displaystyle a\in A} is acceptable with respect to E ⊆ A {\displaystyle E\subseteq A} if and only if E {\displaystyle E} defends a {\displaystyle a} , that is ∀ b ∈ A {\displaystyle \forall b\in A} such that ( b , a ) ∈ R , ∃ c ∈ E {\displaystyle (b,a)\in R,\exists c\in E} such that ( c , b ) ∈ R {\displaystyle (c,b)\in R} , a set of arguments E {\displaystyle E} is conflict-free if there is no attack between its arguments, formally : ∀ a , b ∈ E , ( a , b ) ∉ R {\displaystyle \forall a,b\in E,(a,b)\not \in R} , a set of arguments E {\displaystyle E} is admissible if and only if it is conflict-free and all its arguments are acceptable with respect to E {\displaystyle E} . === Different semantics of acceptance === ==== Extensions ==== To decide if an argument can be accepted or not, or if several arguments can be accepted together, Dung defines several semantics of acceptance that allows, given an argumentation system, sets of arguments (called extensions) to be computed. For instance, given S = ⟨ A , R ⟩ {\displaystyle S=\langle A,R\rangle } , E {\displaystyle E} is a complete extension of S {\displaystyle S} only if it is an admissible set and every acceptable argument with respect to E {\displaystyle E} belongs to E {\displaystyle E} , E {\displaystyle E} is a preferred extension of S {\displaystyle S} only if it is a maximal element (with respect to the set-theoretical inclusion) among the admissible sets with respect to S {\displaystyle S} , E {\displaystyle E} is a stable extension of S {\displaystyle S} only if it is a conflict-free set that attacks every argument that does not belong in E {\displaystyle E} (formally, ∀ a ∈ A ∖ E , ∃ b ∈ E {\displaystyle \forall a\in A\backslash E,\exists b\in E} such that ( b , a ) ∈ R {\displaystyle (b,a)\in R} , E {\displaystyle E} is the (unique) grounded extension of S {\displaystyle S} only if it is the smallest element (with respect to set inclusion) among the complete extensions of S {\displaystyle S} . There exists some inclusions between the sets of extensions built with these semantics : Every stable extension is preferred, Every preferred extension is complete, The grounded extension is complete, If the system is well-founded (there exists no infinite sequence a 0 , a 1 , … , a n , … {\displaystyle a_{0},a_{1},\dots ,a_{n},\dots } such that ∀ i > 0 , ( a i + 1 , a i ) ∈ R {\displaystyle \forall i>0,(a_{i+1},a_{i})\in R} ), all these semantics coincide—only one extension is grounded, stable, preferred, and complete. Some other semantics have been defined. One introduce the notation E x t σ ( S ) {\displaystyle Ext_{\sigma }(S)} to note the set of σ {\displaystyle \sigma } -extensions of the system S {\displaystyle S} . In the case of the system S {\displaystyle S} in the figure above, E x t σ ( S ) = { { a , d } } {\displaystyle Ext_{\sigma }(S)=\{\{a,d\}\}} for every Dung's semantic—the system is well-founded. That explains why the semantics coincide, and the accepted arguments are: a {\displaystyle a} and d {\displaystyle d} . ==== Labellings ==== Labellings are a more expressive way than extensions to express the acceptance of the arguments. Concretely, a labelling is a mapping that associates every argument with a label in (the argument is accepted), out (the argument is rejected), or undec (the argument is undefined—not accepted or refused). One can also note a labelling as a set of pairs ( a r g u m e n t , l a b e l ) {\displaystyle ({\mathit {argument}},{\mathit {label}})} . Such a mapping does not make sense without additional constraint. The notion of reinstatement labelling guarantees the sense of the mapping. L {\displaystyle L} is a reinstatement labelling on the system S = ⟨ A , R ⟩ {\displaystyle S=\langle A,R\rangle } if and only if : ∀ a ∈ A , L ( a ) = i n {\displaystyle \forall a\in A,L(a)={\mathit {in}}} if and only if ∀ b ∈ A {\displaystyle \forall b\in A} such that ( b , a ) ∈ R , L ( b ) = o u t {\displaystyle (b,a)\in R,L(b)={\mathit {out}}} ∀ a ∈ A , L ( a ) = o u t {\displaystyle \forall a\in A,L(a)={\mathit {out}}} if and only if ∃ b ∈ A {\displaystyle \exists b\in A} such that ( b , a ) ∈ R {\displaystyle (b,a)\in R} and L ( b ) = i n {\displaystyle L(b)={\mathit {in}}} ∀ a ∈ A , L ( a ) = u n d e c {\displaystyle \forall a\in A,L(a)={\mathit {undec}}} if and only if L ( a ) ≠ i n {\displaystyle L(a)\neq {\mathit {in}}} and L ( a ) ≠ o u t {\displaystyle L(a)\neq {\mathit {out}}} One can convert every extension into a reinstatement labelling: the arguments of the extension are in, those attacked by an argument of the extension are out, and the others are undec. Conversely, one can build an extension from a reinstatement labelling just by keeping the arguments in. Indeed, Caminada proved that the reinstatement labellings and the complete extensions can be mapped in a bijective way. Moreover, the other Datung's semantics can be associated to some particular sets of reinstatement labellings. Reinstatement labellings distinguish arguments not accepted because they are attacked by accepted arguments from undefined arguments—that is, those that are not defended cannot defend themselves. An argument is undec if it is attacked by at least another undec. If it is attacked only by arguments out, it must be in, and if it is attacked some argument in, then it is out. The unique reinstatement labelling that corresponds to the system S {\displaystyle S} above is L = { ( a , i n ) , ( b , o u t ) , ( c , o u t ) , ( d , i n ) } {\displaystyle L=\{(a,{\mathit {in}}),(b,{\mathit {out}}),(c,{\mathit {out}}),(d,{\mathit {in}})\}} . === Inference from an argumentation system === In the general case when several extensions are computed for a given semantic σ {\displaystyle \sigma } , the agent that reasons from the system can use several mechanisms to infer information: Credulous inference: the agent accepts an argument if it belongs to at least one of the σ {\displaystyle \sigma } -extensions—in which case, the agent risks accepting some arguments that are not acceptable together ( a {\displaystyle a} attacks b {\displaystyle b} , and a {\displaystyle a} and b {\displaystyle b} each belongs to an extension) Skeptical inference: the agent accepts an argument only if it belongs to every σ {\displaystyle \sigma } -extension. In this case, the agent risks deducing too little information (if the intersection of the extensions is empty or has a very small cardinal). For these two methods to infer information, one can identify the set of accepted arguments, respectively C r σ ( S ) {\displaystyle Cr_{\sigma }(S)} the set of the arguments credulously accepted under the semantic σ {\displaystyle \sigma } , and S c σ ( S ) {\displaystyle Sc_{\sigma }(S)} the set of arguments accepted skeptically under the semantic σ {\displaystyle \sigma } (the σ {\displaystyle \sigma } can be missed if there is no possible ambiguity about the semantic). Of course, when there is only one extension (for instance, when the system is well-founded), this problem is very simple: the agent accepts arguments of the unique extension and rejects others. The same reasoning can be done with labellings that correspond to the chosen semantic : an argument can be accepted if it is in for each labelling and refused if it is out for each labelling, the others being in an undecided state (the status of the arguments can remind the
Google Tasks
Google Tasks is a task management application developed by Google and included with Google Workspace. Included initially as a feature in Gmail and Google Calendar, Google Tasks launched as a core product with a standalone app in 2018. It is available for Android and iOS, as well as in the right-hand side panel on Google Workspace apps on the web and in Google Calendar. == History and development == Google Tasks began as an integration within other apps in G Suite (now Google Workspace), allowing to-do items to be created in Calendar and Gmail. Upon graduating to a core service on June 28, 2018, Google Tasks launched as a dedicated mobile app in which tasks can be sorted into lists, managed, and completed. Google Tasks launched the ability to create tasks from Google Chat messages in 2022.