Abeba Birhane

Abeba Birhane is an Ethiopian-born cognitive scientist who works at the intersection of complex adaptive systems, machine learning, algorithmic bias, and critical race studies. Birhane's work with Vinay Prabhu uncovered that large-scale image datasets commonly used to develop AI systems, including ImageNet and 80 Million Tiny Images, carried racist and misogynistic labels and offensive images. She has been recognized by VentureBeat as a top innovator in computer vision and named as one of the 100 most influential persons in AI 2023 by TIME magazine. == Early life and education == Birhane was born in Ethiopia. She received her Bachelors of Science in Psychology and a Bachelors of Arts in Philosophy from The Open University. In 2015, she completed her Master of Science in Cognitive Science and, in 2021, her Ph.D. at the Complex Software Lab in the School of Computer Science at University College Dublin. == Career and research == Birhane studied the impacts of emerging AI technologies and how they shape individuals and local communities. She found that AI algorithms tend to disproportionately impact vulnerable groups such as older workers, trans people, immigrants, and children. Her research on relational ethics won the best paper award at NeurIPS’s Black in AI workshop in 2019. She has also studied and written about algorithmic colonization driven by corporate agendas. Her work in decolonizing computational sciences addressed the inherited oppressions in current systems especially towards women of color. In 2020, Birhane and Vinay Prabhu, principal machine learning scientist at UnifyID, published a paper examining the problematic data collection, labelling, classification, and consequences of large image datasets. These datasets, including ImageNet and MIT's 80 Million Tiny Images, have been used to develop thousands of AI algorithms and systems. Birhane and Prabhu found that they contained many racist and misogynistic labels and slurs as well as offensive images. This resulted in MIT voluntarily and formally taking down the 80 Million Tiny Images dataset. More recently, Birhane has worked with Rediet Abebe, George Obaido, and Sekou Remy on researching the barriers to data sharing in Africa. They found that power imbalances are significant in the data sharing process, even when the data comes from Africa. Their research was published at the ACM Conference on Fairness, Accountability, and Transparency. In 2024, Birhane established the AI Accountability Lab research group at Trinity College Dublin. == Selected awards == 2019 NeurIPS Black in AI Workshop Best Paper Award 2020 Venture Beat AI Innovations Award in the category Computer Vision Innovation (received with Vinay Prabhu) 2021 100 Brilliant Women in AI Ethics Hall of Fame Honoree 2022 Lero Director’s Prize for PhD/PostDoctoral Contribution. 2023 100 Most Influential People in AI by TIME magazine

N-jet

An N-jet is the set of (partial) derivatives of a function f ( x ) {\displaystyle f(x)} up to order N. Specifically, in the area of computer vision, the N-jet is usually computed from a scale space representation L {\displaystyle L} of the input image f ( x , y ) {\displaystyle f(x,y)} , and the partial derivatives of L {\displaystyle L} are used as a basis for expressing various types of visual modules. For example, algorithms for tasks such as feature detection, feature classification, stereo matching, tracking and object recognition can be expressed in terms of N-jets computed at one or several scales in scale space.

Grok sexual deepfake scandal

From 2025 onwards, X (formerly Twitter)'s integrated chatbot, Grok, has allowed users to nonconsensually alter images of individuals, including minors, to show them in bikinis or transparent clothing, or in sexually suggestive contexts. The majority of these prompts were targeted at women and girls. Users were able to generate such images by responding to a photo with a request to Grok, such as "put her in a bikini", to which the chatbot would publicly reply with a generated image. The scandal drew significant criticism from lawmakers across the world, and there were calls for bans on X, as well as legal crackdowns on X and xAI for, amongst other reasons, the facilitation of sexual abuse, revenge porn, and child pornography. == Background == Deepfake pornography emerged in the late 2010s with the advent of machine learning. Originally, it was created on a small individual scale using a combination of machine learning algorithms, computer vision techniques, and AI software. However, the production process has significantly evolved since 2018, with the advent of several public apps that have largely automated the process. Since 2023, several AI apps available on Google Play and the Apple App Store are capable of "nudify-ing" user provided photos to generate non-consensual deepfake pornography. Grok would first be proposed by Elon Musk in 2023, when he expressed an intention to create his own AI chatbot to "combat bias". Grok version 2.0, released on August 14, 2024, would introduce image generation capabilities, ones which would be improved over successive updates. == Grok deepfake generation == Cases of Grok being used to remove the clothes from women in pictures, replacing them with bikinis or lingerie, began to surface in May 2025. By late December 2025, a trend of X users requesting such edits to women's photos without permission had taken root, and this received significant media attention in the first few days of January 2026. Some users prompted Grok to edit photos of women into sexualized poses, and others to add blood and bruising, with the chatbot publicly posting these graphic images in response. Grok's X account was restricted on January 9 from posting image generation responses to users who are not paid subscribers, providing a link to "subscribe to unlock these features". All users were still able to generate Grok-altered images using X's "Edit image" feature, and the standalone Grok website and app. However, by March 19, Grok’s Imagine feature was fully restricted to paid subscribers only (SuperGrok tier) for both the standalone Grok website and mobile app. == Analysis == An analysis of 20,000 images generated by Grok between December 25, 2025, and January 1, 2026, showed 2% appeared to be 18 or younger, including 30 of "young or very young" women or girls in bikinis or transparent clothes. A Reuters review of Grok requests over 10 minutes on January 2nd found 102 attempts to put women in bikinis. A separate analysis conducted over 24 hours from January 5 to 6 calculated that users had Grok create 6,700 sexually suggestive or nudified images per hour — 84 times more so than the top 5 deepfake websites combined. Wired reported that far more graphic AI-generated sexual imagery was being created by Grok on its website and app, which are separate to X, including female celebrities removing their clothes and engaging in sexual acts. An analysis of 800 pieces of recovered content by the Paris-based nonprofit AI Forensics found that almost 10% were "instances of photorealistic people, very young, doing sexual activities". AI-generated deepfakes have been described as sexual assault, and as a means to push women out of the public sphere. AI-generated sexually explicit or exploitative image claims are now being treated more like product safety or personal injury harms, not just privacy violations. Because harm may occur the moment an image is generated, some plaintiffs argue liability should focus on the system’s design and safety safeguards. == Reactions == On January 15, the Get Grok Gone campaign delivered letters to Apple and Google, demanding the removal of the app from Apple Store and Google Play Store respectively. The campaign accused both companies of profiting from nonconsensual intimate imagery and child sexual abuse imagery, which were also banned by the companies own policies. The Get Grok Gone campaign argues that the restrictions placed on Grok by xAI are not enough and that Apple and Google are enabling the distribution of harmful material by hosting the apps. === Elon Musk and xAI === xAI responded to requests for comment from media organizations with the automated reply, "Legacy Media Lies." On January 2, Elon Musk reacted "Not sure why, but I couldn’t stop laughing about this one 🤣🤣" to an image of a toaster dressed in a bikini by Grok. Later, on January 14, Elon Musk said that he was "not aware of any naked underage images generated by Grok. Literally zero." Later that same day, xAI announced that X users will no longer be able to use Grok to alter images of real people to portray them in revealing clothing. However, verified X users, as well as users of the standalone Grok app and website, were still able to generate such images. ==== Elon Musk's family ==== Ashley St. Clair, mother of one of Elon Musk's children, reported that Grok users were creating fake sexualized images from her photos, including a photo of her as a child. She considers the photos to be a form of revenge porn, and considered suing under the Take It Down Act. A spokesperson for X stated, "We take action against illegal content on X, including child sexual abuse material (CSAM), by removing it, permanently suspending accounts, and working with local governments and law enforcement as necessary. Anyone using or prompting Grok to make illegal content will suffer the same consequences as if they upload illegal content." However, Grok continued to post non-consensual sexual images. On January 15, St. Clair filed a lawsuit against xAI in the New York Supreme Court. === Canada === In response to the Grok deepfake scandal, individuals have asked that the government of Canada boycott X. On January 10, 2026, Canadian MP and Minister of AI Evan Solomon declared that Canada "is not considering a ban on X". In April 2026, Bill C-16, An Act to amend certain Acts in relation to criminal and correctional matters (child protection, gender-based violence, delays and other measures), was amended following a proposal by Conservative MP Andrew Lawton to ensure that AI-generated images and "nearly nude" intimate images are criminalized. A further proposal by NDP MP Leah Gazan to encompass "sexualized or humiliating contexts, such transparent bathing suits or being covered in blood or bruises" was voted down. === France === On January 2, 2026, French ministers reported the AI tool to prosecutors, calling the content "manifestly illegal", and also asked regulators to check compliance with the Digital Services Act. On February 3, Paris prosecutors office, a cybercrime team employed by them and Europol searched the Paris offices of X. The investigation started as one into allegations of abuse of algorithms and fraudulent data extraction, but has expanded into spreading Holocaust denial and sexual deepfakes. Elon Musk and former CEO Linda Yaccarino have been summoned to a hearing on April 20, with other X staff as witnesses. On April 20, Musk did not turn up for the hearing. The Paris prosecutors office told the BBC on April 20 that it had "taken note of the absence of the people summoned", adding "the presence or absence (of the people summoned) is not an obstacle to continuing the investigation". === India === Indian Member of Parliament Priyanka Chaturvedi filed a complaint to India's IT ministry, demanding a review of Grok's safety mechanisms. === Indonesia === On January 10, Indonesia announced that Grok will be temporarily blocked, becoming the first country to do so. Meutya Hafid, the Minister of Communication and Digital Affairs, stated that "the government views the practice of non-consensual sexual deepfakes as a serious violation of human rights, dignity, and the security of citizens in the digital space." Access to Grok in the country was later restored on February 1. === Ireland === On January 6, Coimisiún na Meán, the Irish media commission, said they were consulting with the European Commission about concerns that Grok was generating sexualized images of women and children. The same day, Ofcom of the United Kingdom contacted X concerning complaints about these images. On January 13, Micheál Martin, Taoiseach of Ireland, announced he would talk with Rossa Fanning, the country's Attorney General, about the Grok chatbot being used to produce sexually explicit images of women and minors. On January 14, the Garda Síochána announced there are 200 investigations into child sex abuse images generated by Grok. The Garda National Cyber Crime Bureau has al

Tales from the Loop (role-playing game)

Tales from the Loop (Swedish: Ur Varselklotet), subtitled "Roleplaying in the '80s That Never Was", is an alternative history science fiction tabletop role-playing game published in 2017 by Free League Publishing, the international arm of Swedish game and book publisher Fria Ligan AB, and Modiphius Entertainment. The game, based on the art of Simon Stålenhag, envisions an alternative world where a group of bored and ignored preteens and teens solve mysteries caused by new technology near their hometown. == Description == === Setting === Tales from the Loop is set in an alternative history world taken from the artwork of Simon Stålenhag. According to this alternative timeline, back in the 1940s, research began on particle accelerators. In the 1960s, two massive underground particle accelerators were built in Sweden and Colorado with the promise of a harvest of technological marvels that would change everyone's lives. Tales from the Loop is set twenty years later, in the late 1980s, and the better life has not materialized. Although the particle accelerators have created robots and large skyships, the detritus of failed experiments and the ruins of abandoned high tech company buildings litter the landscape. Generally the life of the average family has not changed for the better. A campaign can either be set in the Mälaren Islands, west of the Swedish capital of Stockholm, or in a city in the Southwest United States that resembles Boulder City, Nevada. There is also a step-by-step guide for the gamemaster to use their own hometown. === Character generation === Player characters are preteens and young teenagers age 10–15 who live in a society where they are bored and largely left to themselves. Players can choose archetypes for their characters including Bookworm, Jock, Troublemaker, Popular Kid and Weirdo. Unlike most role-playing games, characters in Tales from the Loop cannot be killed, although in an ongoing campaign or due to an in-game effect, they are removed from the game if they reach the age of sixteen. === Game system === The game uses the Year Zero Engine first developed by Tomas Härenstam for the post-apocalyptic role-playing game Mutant: Year Zero. (Härenstam served as the editor and project manager for Tales from the Loop.) Problems are resolved by rolling a pool of six-sided dice, with any 6 rolled marking success. Attributes and skills (Sneak, Force, Move, Build, Tinker, Calculate, Contact, Charm, Lead, Investigate, Comprehend, and Empathize) may allow the player to add more dice to the dice pool, increasing the chances of success. However, if a character has earned a condition such as Scared or Injured, dice are removed from the dice pool. === Gameplay === The game principles are that life for the characters is dull and boring, but the area around the town is full of wonderful, mysterious things. An adventure is set up as a Mystery, and in order to successfully resolve the Mystery, characters must overcome a series of Troubles, which can range from having to be home by a certain time to dealing with a bully to disarming or otherwise overcoming a booby-trap on a door that must be opened. Each Mystery is played as a series of scenes, much like a TV drama. Although the gamemaster leads the players into the Mystery, each scene is set collaboratively with the players before action continues. As critic Jukka Kauppinen noted, "The players and the gamemaster take turns verbally staging a new scene — where we are, what it's like there — and only then what we do." === Campaign === The book presents a chronologically-linked set of four Mysteries called "The Four Seasons of Mad Science" that take place over a calendar year: "Summer Break and Killer Birds": The Kids hears pigeons having a conversation and investigate "Grown-Up Attraction": Adults start disappearing without any sign of struggle. "Creatures from the Cretaceous": The search for a missing dog leads to the discovery of creatures that don't belong in our time "I, Wagner": The Kids discover a body in a stream, and are drawn into a Mystery with robots and humans that may affect them closely. == Publication history == In 2017, Swedish artist Simon Stålenhag was raising money on Kickstarter to publish a book of his art titled Tales from the Loop. One of the stretch goals offered was the creation of a role-playing game. A second Kickstarter campaign to publish the role-playing game was initiated by Fria Ligan AB, who surpassed their crowdfunding goal and raised a total of 3,745,896 kr from 5,600 backers. The role-playing game Tales from the Loop was subsequently published as a 184-page hardcover book in 2017 by Free League Publishing, the international arm of Swedish game and book publisher Fria Ligan AB, and Modiphius Entertainment. Cover art and interior art were by Stålenhag, and cartography was by Christian Granath. A stand-alone expansion, Things from the Flood (Swedish: Flodskörden), based on Stålenhag's art book of the same name, was created by Nils Hintze, Rickard Antroia, and Tomas Härenstam. The 216-page hardcover book was published in 2019 with cover art by Stålenhag, interior art by Stålenhag and Reine Rosenberg, and cartography by Christian Granath. In 2020, the setting of the role-playing game was transferred to the TV series Tales from the Loop developed by Nathanial Halpern and Simon Stålenhag. The series tells eight stories of children's encounters with strange technology. == Reception == Shut Up & Sit Down praised Tales from the Loop for its comfortable, contemporary setting, simple rules that make the game easy to run, and the alternation between sci-fi and the kids' lives, but criticized the Type system for characters, noting "a suggested 'Pride' for the Weirdo involved being homosexual –– the only mention of queerness in the entire game. Those of us who identify as GLBTQ bristled at that: why was only the Weirdo queer, with queerness as a (possibly secret) Pride? Why not more fully address being a GLBTQ kid in the 1980s?" The review concluded, "For new RPG players, Tales is a decent game that you'll enjoy and that will make your heart burst. But you need an experienced GM who’s able to either alter the book’s mysteries or create their own, and who can put in work when poor dice rolls hold the players back." Rob Weiland of Geek & Sundry named Tales from the Loop 2017's best RPG release and praised Stålenhag's art, the collaborative nature between the GM and players, and the simplicity of running the game. Weiland concluded, "It has a simple system that is easy to explain but holds up under several plays. It has a setting that’s immediately evocative but also leaves plenty of room for GMs to build out their own world. It offers players a chance to experience the rush of memory, the pain of childhood and the wonder of movies." In a review of Tales from the Loop in Black Gate, Andrew Zimmerman Jones said, "Though not based directly on an established franchise, it draws richly from elements of popular culture that will make it resonate with many players. The focus on narrative play also means it’s a good game for people who aren’t necessarily big into learning a ton of new rules." Jukka Kauppinen, writing for the Finnish games magazine Skrolli, called the game, "downright delicious in its diversity. The science fiction world created by the Swedish artist Simon Stälenhag is, after all, both delightful vintage and tickling novelty." Kauppinen concluded, "This mutual storytelling and interaction makes this game more of a campfire circle than a traditional role-playing game. At the same time, its setting in the real world, tinged with science fiction and even horror, creates a delicious and unique adventure environment." In his 2023 book Monsters, Aliens, and Holes in the Ground, RPG historian Stu Horvath noted that the game system "pushes the players to constantly reevaluate their characters' relationships with the everyday world, for better or worse. It won't be long before navigating entanglements with parents, teachers, siblings and bullies proves just as risky to the characters, and central to the players' experience, as trying to find out what happened with the time portal or dealing with a rampaging robot." Horvath concluded, "The appeal of Tales from the Loop is Stålenhag's deep shadows and purple dusks. They hide the dangers and mysteries that often act [as] an escape hatch, a way to avoid prosaic problems." == Awards == At the 2017 Golden Geek Awards, Tales of the Loop won "RPG of the Year", and was a finalist for " Best RPG Artwork/Presentation" At the 2017 ENnie Awards, Tales from the Loops won five Gold Medals: Product of the Year Best Writing Best Setting Best Game Best Art, Interior

Fuzzy measure theory

In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity. The central concept of fuzzy measure theory is the fuzzy measure (also capacity, see ), which was introduced by Choquet in 1953 and independently defined by Sugeno in 1974 in the context of fuzzy integrals. There exists a number of different classes of fuzzy measures including plausibility/belief measures, possibility/necessity measures, and probability measures, which are a subset of classical measures. == Definitions == Let X {\displaystyle \mathbf {X} } be a universe of discourse, C {\displaystyle {\mathcal {C}}} be a class of subsets of X {\displaystyle \mathbf {X} } , and E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} . A function g : C → R {\displaystyle g:{\mathcal {C}}\to \mathbb {R} } where ∅ ∈ C ⇒ g ( ∅ ) = 0 {\displaystyle \emptyset \in {\mathcal {C}}\Rightarrow g(\emptyset )=0} E ⊆ F ⇒ g ( E ) ≤ g ( F ) {\displaystyle E\subseteq F\Rightarrow g(E)\leq g(F)} is called a fuzzy measure. A fuzzy measure is called normalized or regular if g ( X ) = 1 {\displaystyle g(\mathbf {X} )=1} . == Properties of fuzzy measures == A fuzzy measure is: additive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) = g ( E ) + g ( F ) . {\displaystyle g(E\cup F)=g(E)+g(F).} ; supermodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have g ( E ∪ F ) + g ( E ∩ F ) ≥ g ( E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\geq g(E)+g(F)} ; submodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have g ( E ∪ F ) + g ( E ∩ F ) ≤ g ( E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\leq g(E)+g(F)} ; superadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) ≥ g ( E ) + g ( F ) {\displaystyle g(E\cup F)\geq g(E)+g(F)} ; subadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) ≤ g ( E ) + g ( F ) {\displaystyle g(E\cup F)\leq g(E)+g(F)} ; symmetric if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have | E | = | F | {\displaystyle |E|=|F|} implies g ( E ) = g ( F ) {\displaystyle g(E)=g(F)} ; Boolean if for any E ∈ C {\displaystyle E\in {\mathcal {C}}} , we have g ( E ) = 0 {\displaystyle g(E)=0} or g ( E ) = 1 {\displaystyle g(E)=1} . Understanding the properties of fuzzy measures is useful in application. When a fuzzy measure is used to define a function such as the Sugeno integral or Choquet integral, these properties will be crucial in understanding the function's behavior. For instance, the Choquet integral with respect to an additive fuzzy measure reduces to the Lebesgue integral. In discrete cases, a symmetric fuzzy measure will result in the ordered weighted averaging (OWA) operator. Submodular fuzzy measures result in convex functions, while supermodular fuzzy measures result in concave functions when used to define a Choquet integral. == Möbius representation == Let g be a fuzzy measure. The Möbius representation of g is given by the set function M, where for every E , F ⊆ X {\displaystyle E,F\subseteq X} , M ( E ) = ∑ F ⊆ E ( − 1 ) | E ∖ F | g ( F ) . {\displaystyle M(E)=\sum _{F\subseteq E}(-1)^{|E\backslash F|}g(F).} The equivalent axioms in Möbius representation are: M ( ∅ ) = 0 {\displaystyle M(\emptyset )=0} . ∑ F ⊆ E | i ∈ F M ( F ) ≥ 0 {\displaystyle \sum _{F\subseteq E|i\in F}M(F)\geq 0} , for all E ⊆ X {\displaystyle E\subseteq \mathbf {X} } and all i ∈ E {\displaystyle i\in E} A fuzzy measure in Möbius representation M is called normalized if ∑ E ⊆ X M ( E ) = 1. {\displaystyle \sum _{E\subseteq \mathbf {X} }M(E)=1.} Möbius representation can be used to give an indication of which subsets of X interact with one another. For instance, an additive fuzzy measure has Möbius values all equal to zero except for singletons. The fuzzy measure g in standard representation can be recovered from the Möbius form using the Zeta transform: g ( E ) = ∑ F ⊆ E M ( F ) , ∀ E ⊆ X . {\displaystyle g(E)=\sum _{F\subseteq E}M(F),\forall E\subseteq \mathbf {X} .} == Simplification assumptions for fuzzy measures == Fuzzy measures are defined on a semiring of sets or monotone class, which may be as granular as the power set of X, and even in discrete cases the number of variables can be as large as 2|X|. For this reason, in the context of multi-criteria decision analysis and other disciplines, simplification assumptions on the fuzzy measure have been introduced so that it is less computationally expensive to determine and use. For instance, when it is assumed the fuzzy measure is additive, it will hold that g ( E ) = ∑ i ∈ E g ( { i } ) {\displaystyle g(E)=\sum _{i\in E}g(\{i\})} and the values of the fuzzy measure can be evaluated from the values on X. Similarly, a symmetric fuzzy measure is defined uniquely by |X| values. Two important fuzzy measures that can be used are the Sugeno- or λ {\displaystyle \lambda } -fuzzy measure and k-additive measures, introduced by Sugeno and Grabisch respectively. === Sugeno λ-measure === The Sugeno λ {\displaystyle \lambda } -measure is a special case of fuzzy measures defined iteratively. It has the following definition: ==== Definition ==== Let X = { x 1 , … , x n } {\displaystyle \mathbf {X} =\left\lbrace x_{1},\dots ,x_{n}\right\rbrace } be a finite set and let λ ∈ ( − 1 , + ∞ ) {\displaystyle \lambda \in (-1,+\infty )} . A Sugeno λ {\displaystyle \lambda } -measure is a function g : 2 X → [ 0 , 1 ] {\displaystyle g:2^{X}\to [0,1]} such that g ( X ) = 1 {\displaystyle g(X)=1} . if A , B ⊆ X {\displaystyle A,B\subseteq \mathbf {X} } (alternatively A , B ∈ 2 X {\displaystyle A,B\in 2^{\mathbf {X} }} ) with A ∩ B = ∅ {\displaystyle A\cap B=\emptyset } then g ( A ∪ B ) = g ( A ) + g ( B ) + λ g ( A ) g ( B ) {\displaystyle g(A\cup B)=g(A)+g(B)+\lambda g(A)g(B)} . As a convention, the value of g at a singleton set { x i } {\displaystyle \left\lbrace x_{i}\right\rbrace } is called a density and is denoted by g i = g ( { x i } ) {\displaystyle g_{i}=g(\left\lbrace x_{i}\right\rbrace )} . In addition, we have that λ {\displaystyle \lambda } satisfies the property λ + 1 = ∏ i = 1 n ( 1 + λ g i ) {\displaystyle \lambda +1=\prod _{i=1}^{n}(1+\lambda g_{i})} . Tahani and Keller as well as Wang and Klir have shown that once the densities are known, it is possible to use the previous polynomial to obtain the values of λ {\displaystyle \lambda } uniquely. === k-additive fuzzy measure === The k-additive fuzzy measure limits the interaction between the subsets E ⊆ X {\displaystyle E\subseteq X} to size | E | = k {\displaystyle |E|=k} . This drastically reduces the number of variables needed to define the fuzzy measure, and as k can be anything from 1 (in which case the fuzzy measure is additive) to X, it allows for a compromise between modelling ability and simplicity. ==== Definition ==== A discrete fuzzy measure g on a set X is called k-additive ( 1 ≤ k ≤ | X | {\displaystyle 1\leq k\leq |\mathbf {X} |} ) if its Möbius representation verifies M ( E ) = 0 {\displaystyle M(E)=0} , whenever | E | > k {\displaystyle |E|>k} for any E ⊆ X {\displaystyle E\subseteq \mathbf {X} } , and there exists a subset F with k elements such that M ( F ) ≠ 0 {\displaystyle M(F)\neq 0} . == Shapley and interaction indices == In game theory, the Shapley value or Shapley index is used to indicate the weight of a game. Shapley values can be calculated for fuzzy measures in order to give some indication of the importance of each singleton. In the case of additive fuzzy measures, the Shapley value will be the same as each singleton. For a given fuzzy measure g, and | X | = n {\displaystyle |\mathbf {X} |=n} , the Shapley index for every i , … , n ∈ X {\displaystyle i,\dots ,n\in X} is: ϕ ( i ) = ∑ E ⊆ X ∖ { i } ( n − | E | − 1 ) ! | E | ! n ! [ g ( E ∪ { i } ) − g ( E ) ] . {\displaystyle \phi (i)=\sum _{E\subseteq \mathbf {X} \backslash \{i\}}{\frac {(n-|E|-1)!|E|!}{n!}}[g(E\cup \{i\})-g(E)].} The Shapley value is the vector ϕ ( g ) = ( ψ ( 1 ) , … , ψ ( n ) ) . {\displaystyle \mathbf {\phi } (g)=(\psi (1),\dots ,\psi (n)).}

Security type system

In computer science, a type system can be described as a syntactic framework which contains a set of rules that are used to assign a type property (int, boolean, char etc.) to various components of a computer program, such as variables or functions. A security type system works in a similar way, only with a main focus on the security of the computer program, through information flow control. Thus, the various components of the program are assigned security types, or labels. The aim of a such system is to ultimately be able to verify that a given program conforms to the type system rules and satisfies non-interference. Security type systems is one of many security techniques used in the field of language-based security, and is tightly connected to information flow and information flow policies. In simple terms, a security type system can be used to detect if there exists any kind of violation of confidentiality or integrity in a program, i.e. the programmer wants to detect if the program is in line with the information flow policy or not. == A simple information flow policy == Suppose there are two users, A and B. In a program, the following security classes (SC) are introduced: SC = {∅, {A}, {B}, {A,B}}, where ∅ is the empty set. The information flow policy should define the direction that information is allowed to flow, which is dependent on whether the policy allows read or write operations. This example considers read operations (confidentiality). The following flows are allowed: → = {({A}, {A}), ({B}, {B}), ({A,B}, {A,B}), ({A,B}, {A}), ({A,B}, {B}), ({A}, ∅), ({B}, ∅), ({A,B}, ∅)} This can also be described as a superset (⊇). In words: information is allowed to flow towards stricter levels of confidentiality. The combination operator (⊕) can express how security classes can perform read operations with respect to other security classes. For example: {A} ⊕ {A,B} = {A} — the only security class that can read from both {A} and {A,B} is {A}. {A} ⊕ {B} = ∅ — neither {A} nor {B} are allowed to read from both {A} and {B}. This can also be described as an intersection (∩) between security classes. An information flow policy can be illustrated as a Hasse diagram. The policy should also be a lattice, that is, it has a greatest lower-bound and least upper-bound (there always exists a combination between security classes). In the case of integrity, information will flow in the opposite direction, thus the policy will be inverted. == Information flow policy in security type systems == Once the policy is in place, the software developer can apply the security classes to the program components. Use of a security type system is usually combined with a compiler that can perform the verification of the information flow according to the type system rules. For the sake of simplicity, a very simple computer program, together with the information flow policy as described in the previous section, can be used as a demonstration. The simple program is given in the following pseudocode: if y{A} = 1 then x{A,B} := 0 else x{A,B} := 1 Here, an equality check is made on a variable y that is assigned the security class {A}. A variable x with a lower security class ({A,B}) is influenced by this check. This means that information is leaking from class {A} to class {A,B}, which is a violation of the confidentiality policy. This leak should be detected by the security type system. === Example === Designing a security type system requires a function (also known as a security environment) that creates a mapping from variables to security types, or classes. This function can be called Γ, such that Γ(x) = τ, where x is a variable and τ is the security class, or type. Security classes are assigned (also called "judgement") to program components, using the following notation: Types are assigned to read operations by: Γ ⊢ e : τ. Types are assigned to write operations by: Γ ⊢ S : τ cmd. Constants can be assigned any type. The following bottom-up notation can be used to decompose the program: ⁠assumption1 ... assumptionn/conclusion⁠. Once the program is decomposed into trivial judgements, by which the type can easily be determined, the types for the less trivial parts of the program can be derived. Each "numerator" is considered in isolation, looking at the type of each statement to see if an allowed type can be derived for the "denominator", based on the defined type system "rules". ==== Rules ==== The main part of the security type system is the rules. They say how the program should be decomposed and how type verification should be performed. This toy program consists of a conditional test and two possible variable assignments. Rules for these two events are defined as follows: Applying this to the simple program introduced above yields: The type system detects the policy violation in line 2, where a read operation of security class {A} is performed, followed by two write operations of a less strict security class {A,B}. In more formalized terms, {A} ⋢ {A,B}, {A,B} (from the rule of the conditional test). Thus, the program is classified as "not typeable". === Soundness === The soundness of a security type system can be informally defined as: If program P is well typed, P satisfies non-interference. Volpano, Smith and Irvine were the first to prove soundness of a security type system for a deterministic imperative programming language with a standard (non-instrumented) semantics using the notion of non-interference.

Argument technology

Argument technology is a sub-field of collective intelligence and artificial intelligence that focuses on applying computational techniques to the creation, identification, analysis, navigation, evaluation and visualisation of arguments and debates. In the 1980s and 1990s, philosophical theories of arguments in general, and argumentation theory in particular, were leveraged to handle key computational challenges, such as modeling non-monotonic and defeasible reasoning and designing robust coordination protocols for multi-agent systems. At the same time, mechanisms for computing semantics of Argumentation frameworks were introduced as a way of providing a calculus of opposition for computing what it is reasonable to believe in the context of conflicting arguments. With these foundations in place, the area was kick-started by a workshop held in the Scottish Highlands in 2000, the result of which was a book coauthored by philosophers of argument, rhetoricians, legal scholars and AI researchers. Since then, the area has been supported by various dedicated events such as the International Workshop on Computational Models of Natural Argument (CMNA) which has run annually since 2001; the International Workshop on Argument in Multi Agent Systems (ArgMAS) annually since 2004; the Workshop on Argument Mining, annually since 2014, and the Conference on Computational Models of Argument (COMMA), biennially since 2006. Since 2010, the field has also had its own journal, Argument & Computation, which was published by Taylor & Francis until 2016 and since then by IOS Press. One of the challenges that argument technology faced was a lack of standardisation in the representation and underlying conception of argument in machine readable terms. Many different software tools for manual argument analysis, in particular, developed idiosyncratic and ad hoc ways of representing arguments which reflected differing underlying ways of conceiving of argumentative structure. This lack of standardisation also meant that there was no interchange between tools or between research projects, and little re-use of data resources that were often expensive to create. To tackle this problem, the Argument Interchange Format set out to establish a common standard that captured the minimal common features of argumentation which could then be extended in different settings. Since about 2018, argument technology has been growing rapidly, with, for example, IBM's Grand Challenge, Project Debater, results for which were published in Nature in March 2021; German research funder, DFG's nationwide research programme on Robust Argumentation Machines, RATIO, begun in 2019; and UK nationwide deployment of The Evidence Toolkit by the BBC in 2019. A 2021 video narrated by Stephen Fry provides a summary of the societal motivations for work in argument technology. Argument technology has applications in a variety of domains, including education, healthcare, policy making, political science, intelligence analysis and risk management and has a variety of sub-fields, methodologies and technologies. == Technologies == === Argument assistant === An argument assistant is a software tool which support users when writing arguments. Argument assistants can help users compose content, review content from one other, including in dialogical contexts. In addition to Web services, such functionalities can be provided through the plugin architectures of word processor software or those of Web browsers. Internet forums, for instance, can be greatly enhanced by such software tools and services. === Argument blogging === ArguBlogging is software which allows its users to select portions of hypertext on webpages in their Web browsers and to agree or disagree with the selected content, posting their arguments to their blogs with linked argument data. It is implemented as a bookmarklet, adding functionality to Web browsers and interoperating with blogging platforms such as Blogger and Tumblr. === Argument mapping === Argument maps are visual, diagrammatic representations of arguments. Such visual diagrams facilitate diagrammatic reasoning and promote one's ability to grasp and to make sense of information rapidly and readily. Argument maps can provide structured, semi-formal frameworks for representing arguments using interactive visual language. One avenue of research and development is the design of online platforms to leverage collective intelligence to populate such maps and to integrate data, optimize and assess arguments. === Argument mining === Argument mining, or argumentation mining, is a research area within the natural language processing field. The goal of argument mining is the automatic extraction and identification of argumentative structures from natural language text with the aid of computer programs. === Argument search === An argument search engine is a search engine that is given a topic as a user query and returns a list of arguments for and against the topic or about that topic. Such engines could be used to support informed decision-making or to help debaters prepare for debates. === Automated argumentative essay scoring === The goal of automated argumentative essay scoring systems is to assist students in improving their writing skills by measuring the quality of their argumentative content. === Debate technology === Debate technology focuses on human-machine interaction and in particular providing systems that support, monitor and engage in debate. One of the most high-profile examples of debating technology is IBM's Project Debater which combines scripted communication with very large-scale processing of news articles to identify and construct arguments on the fly in a competitive debating setting. Debating technology also encompasses tools aimed at providing insight into debates, typically using techniques from data science. These analytics have been developed in both academic and commercial settings. === Decision support system === Argument technology can reduce both individual and group biases and facilitate more accurate decisions. Argument-based decision support systems do so by helping users to distinguish between claims and the evidence supporting them, and express their confidence in and evaluate the strength of evidence of competing claims. They have been used to improve predictions of housing market trends, risk analysis, ethical and legal decision making. ==== Ethical decision support system ==== An ethical decision support system is a decision support system which supports users in moral reasoning and decision-making. ==== Legal decision support system ==== A legal decision support system is a decision support system which supports users in legal reasoning and decision-making. === Explainable artificial intelligence === An explainable or transparent artificial intelligence system is an artificial intelligence system whose actions can be easily understood by humans. === Intelligent tutoring system === An intelligent tutoring system is a computer system that aims to provide immediate and customized instruction or feedback to learners, usually without requiring intervention from a human teacher. The intersection of argument technology and intelligent tutoring systems includes computer systems which aim to provide instruction in: critical thinking, argumentation, ethics, law, mathematics, and philosophy. === Legal expert system === A legal expert system is a domain-specific expert system that uses artificial intelligence to emulate the decision-making abilities of a human expert in the field of law. === Machine ethics === Machine ethics is a part of the ethics of artificial intelligence concerned with the moral behavior of artificially intelligent beings. As humans argue with respect to morality and moral behavior, argument can be envisioned as a component of machine ethics systems and moral reasoning components. === Proof assistant === In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. === Ethical considerations === Ethical considerations of argument technology include privacy, transparency, societal concerns, and diversity in representation. These factors cut across different levels such as technology, user interface design, user, service context, and society. There is concern about unethical misuse for "generating arguments on controversial topics with specific stances and deploying them on social platforms". Another issue may concern the design of conclusion-making algorithms, such as e.g. enabling such to conclude that certain key data is needed instead of only making lists of best-fit conclusions or enabling the generation of multi