Digital signage is a segment of electronic signage that uses digital display technologies to present multimedia content in both public and private environments. Content may include video, images, text, or interactive media and is typically displayed for purposes such as advertising, information dissemination, branding, or entertainment. Digital signage systems can be either networked or standalone. Networked systems are managed through centralized content management systems (CMS), often cloud-based, enabling remote updates, scheduling, real-time data integration, and dynamic content delivery. These systems may also incorporate audience analytics, IoT sensors, or AI-driven personalization. Standalone systems, by contrast, operate without a network connection. They rely on local media playback via USB drives, SD cards, or internal storage. These solutions are simpler and suitable for locations where connectivity is limited or content changes infrequently. == Applications of digital signage == Digital signage is widely used in transportation hubs, retail stores, restaurants, corporate buildings, hotels, educational institutions, healthcare facilities, and public spaces. One prominent application of digital signage is Digital Out-of-Home (DOOH) advertising, which leverages digital signage displays in public spaces to deliver targeted advertisements to people outside of their homes. DOOH has become a significant segment of digital signage, providing advertisers with a dynamic and contextually relevant way to engage with audiences. == Components == === Hardware components === Digital signage hardware includes the physical equipment used to show multimedia content in public and private spaces. ==== Display devices ==== Display devices are the most prominent components of a digital signage system, serving as the primary medium for presenting content. Display devices come in various technologies, such as LCD, LED, and OLED formats, each offering different advantages in terms of clarity, color reproduction, and energy efficiency. In addition to flat-panel displays, projectors are also commonly used in digital signage, particularly in large-scale settings. Projectors can cast large-format visuals onto walls, screens, or other surfaces, providing flexibility in display size and positioning. Screen sizes vary widely to suit different applications. Smaller panels are often used in kiosks and point-of-sale systems, while larger displays, such as video walls and projection surfaces, are deployed in venues like stadiums, auditoriums, and other public spaces. Many digital signage displays are also equipped with touchscreen capabilities, allowing for interactive applications. These interactive displays are commonly used in information kiosks, wayfinding systems, and self-service applications. ==== Playback devices ==== Playback devices are specialized hardware components that manage the storage, processing, and transmission of multimedia content to digital signage displays and projectors. They serve as the crucial link between the content management system (CMS) and the visual output, ensuring seamless playback of static images, video files, animated graphics, and real-time content, such as news feeds. Playback devices can be standalone units or integrated into display hardware using System-on-Chip (SoC) technology. The latter reduces hardware complexity and installation time, making the system more efficient. These devices support remote or local content updates, allowing digital signage operators to manage networks effectively. Content can be updated via cloud-based platforms for centralized control or through direct interfaces on-site, depending on the system's configuration and deployment requirements. ==== Mounting systems ==== Mounting systems provide structural support for digital signage displays, enabling deployment across diverse environments. Typical configurations include wall mounts, ceiling mounts, and floor stands each engineered to meet specific spatial and functional requirements. === Software components === Digital signage software is responsible for content creation, scheduling, and management. It enables users to manage and distribute content to one or more playback devices. ==== Software compatibility ==== Digital signage software supports various operating systems, including Android, Windows, Linux, iOS, tvOS, webOS, Tizen, ChromeOS, macOS, and others. This allows customers to choose the hardware and software solution that best suits their digital signage needs. == Interactivity == Interactivity in digital signage allows users to interact directly with displays using input methods like touch, gestures, voice, or proximity sensors. This feature enables real-time responses and personalized content, improving the user experience. Interactive digital signage is commonly used in places like retail, transportation, education, and public spaces to create engaging and informative interactions. Additionally, self-service kiosks are often integrated into interactive signage solutions, allowing users to perform tasks such as ordering products, checking in for flights, accessing information, or making payments. These kiosks empower users to complete transactions or obtain services independently, improving efficiency and convenience in high-traffic locations. == Audience measurement and context-aware content adaptation == === Audience measurement === Cameras can be integrated into digital signage systems to enable audience measurement. They are used to detect and count viewers, estimate demographics such as age and gender, measure dwell time and attention, and sometimes analyze emotional reactions using computer vision techniques. This process is valuable for understanding audience behavior and refining business strategies. Privacy concerns are addressed by anonymizing collected data and avoiding the storage of personally identifiable information. === Context-aware digital signage === Context-aware digital signage refers to systems that adjust content based on environmental or audience data. The infrastructure supporting context awareness, including sensors and analytics systems, also facilitates the collection of audience insights. While these insights may be primarily used for reporting, optimization, or planning future campaigns rather than immediate content adjustments, they play a crucial role in the overall context-aware ecosystem. ==== Contextual information ==== Contextual information in the realm of context-aware digital signage refers to data about the environment, audience, and other factors that influence how digital signage content is displayed. This information helps the system to deliver more relevant, timely, and personalized content to its audience. Contextual information can include, but is not limited to: Audience demographics — this can involve detecting the age, gender, or even emotional state of viewers through cameras or sensors. It helps tailor content to specific audience segments, improving engagement. Time and weather — the system may adjust content based on the time of day or current weather conditions. For example, weather-appropriate content (like a raincoat ad on a rainy day) or time-specific content (like dinner menu promotions in the evening) can be shown. Emergency information — in situations of emergency, systems can prioritize displaying urgent notifications such as fire alerts, disaster warnings, or evacuation instructions. This can be crucial for public safety in crowded environments or densely populated areas. The system may adapt content in real-time to inform and guide individuals to safety, offering location-specific instructions or emergency service contacts. == Challenges == === Display blindness === Digital signage in public spaces has been found to lose visibility, significantly diminishing its ability to capture attention. This issue, known as "Display Blindness", was identified by Müller et al. and refers to the phenomenon where digital advertisements are largely overlooked by passersby. Observations indicate that many of these advertisements fail to resonate with their audience, often being irrelevant or unengaging, which leads to passive reception and reduced interaction. == Comparison with print signage == Digital signage and traditional print signage serve similar purposes by delivering visual information to a target audience, but they differ significantly in terms of flexibility, cost, maintenance, and environmental impact. Digital signage is advantageous in low-light or nighttime environments, where its internal illumination ensures visibility without the need for external lighting, unlike printed signs, which may require additional fixtures to be seen after dark. === Content and flexibility === Digital signage allows for dynamic and real-time content updates, often controlled remotely through content management systems. This makes it well-suited for environments where information chan
Community cloud
A community cloud in computing is a collaborative effort in which infrastructure is shared between several organizations from a specific community with common concerns (security, compliance, jurisdiction, etc.), whether managed internally or by a third party and hosted internally or externally. This is controlled and used by a group of organizations that have shared interests. The costs are spread over fewer users than a public cloud (but more than a private cloud), so only some of the cost savings potential of cloud computing are realized. The community cloud is provisioned for use by a group of consumers from different organizations who share the same concerns (e.g., application, security, policy, and efficiency demands).
Spike-and-slab regression
Spike-and-slab regression is a type of Bayesian linear regression in which a particular hierarchical prior distribution for the regression coefficients is chosen such that only a subset of the possible regressors is retained. The technique is particularly useful when the number of possible predictors is larger than the number of observations. The idea of the spike-and-slab model was originally proposed by Mitchell & Beauchamp (1988). The approach was further significantly developed by Madigan & Raftery (1994) and George & McCulloch (1997). A recent and important contribution to this literature is Ishwaran & Rao (2005). == Model description == Suppose we have P possible predictors in some model. Vector γ has a length equal to P and consists of zeros and ones. This vector indicates whether a particular variable is included in the regression or not. If no specific prior information on initial inclusion probabilities of particular variables is available, a Bernoulli prior distribution is a common default choice. Conditional on a predictor being in the regression, we identify a prior distribution for the model coefficient, which corresponds to that variable (β). A common choice on that step is to use a normal prior with a mean equal to zero and a large variance calculated based on ( X T X ) − 1 {\displaystyle (X^{T}X)^{-1}} (where X {\displaystyle X} is a design matrix of explanatory variables of the model). A draw of γ from its prior distribution is a list of the variables included in the regression. Conditional on this set of selected variables, we take a draw from the prior distribution of the regression coefficients (if γi = 1 then βi ≠ 0 and if γi = 0 then βi = 0). βγ denotes the subset of β for which γi = 1. In the next step, we calculate a posterior probability for both inclusion and coefficients by applying a standard statistical procedure. All steps of the described algorithm are repeated thousands of times using the Markov chain Monte Carlo (MCMC) technique. As a result, we obtain a posterior distribution of γ (variable inclusion in the model), β (regression coefficient values) and the corresponding prediction of y. The model got its name (spike-and-slab) due to the shape of the two prior distributions. The "spike" is the probability of a particular coefficient in the model to be zero. The "slab" is the prior distribution for the regression coefficient values. An advantage of Bayesian variable selection techniques is that they are able to make use of prior knowledge about the model. In the absence of such knowledge, some reasonable default values can be used; to quote Scott and Varian (2013): "For the analyst who prefers simplicity at the cost of some reasonable assumptions, useful prior information can be reduced to an expected model size, an expected R2, and a sample size ν determining the weight given to the guess at R2." Some researchers suggest the following default values: R2 = 0.5, ν = 0.01, and π = 0.5 (parameter of a prior Bernoulli distribution).
Outline of deep learning
The following outline is provided as an overview of, and topical guide to, deep learning: Deep learning is a subfield of machine learning and artificial intelligence based on artificial neural networks with multiple processing layers. It emphasizes representation learning and is widely used in areas such as computer vision, natural language processing, speech recognition, recommender systems, robotics, and generative artificial intelligence. == Ways to categorize deep learning == A field of study A branch of artificial intelligence A subfield of machine learning A subfield of computer science A form of representation learning A class of methods based on artificial neural networks An approach used in computational statistics == History == === Precursors === Cybernetics Perceptron Connectionism Neocognitron Backpropagation === Milestones === LeNet Long short-term memory Deep belief network AlexNet Sequence to sequence learning Generative adversarial network Residual neural network Transformer BERT Generative pre-trained transformer Diffusion model === Related histories === History of artificial intelligence History of machine learning Timeline of machine learning == Core concepts == == Learning settings == Supervised learning Unsupervised learning Self-supervised learning Semi-supervised learning Reinforcement learning Transfer learning Multitask learning Multimodal learning Online machine learning Continual learning == Common tasks == Image classification Object detection Image segmentation Automatic speech recognition Neural machine translation Question answering Automatic summarization Text-to-image model Protein structure prediction == Architectures == === Feedforward and convolutional architectures === Feedforward neural network Multilayer perceptron Convolutional neural network Radial basis function network Residual neural network U-Net === Recurrent and sequence architectures === Recurrent neural network Long short-term memory Gated recurrent unit Sequence to sequence learning Recursive neural network === Representation-learning architectures === Autoencoder Denoising autoencoder Sparse autoencoder Variational autoencoder Restricted Boltzmann machine Deep belief network === Attention and transformer architectures === Attention (machine learning) Transformer BERT Generative pre-trained transformer Vision transformer === Generative and probabilistic architectures === Autoregressive model Diffusion model Energy-based model Generative adversarial network Mixture of experts === Graph and memory architectures === Graph neural network Graph convolutional network Siamese network Neural Turing machine Memory network Echo state network Capsule neural network == Neural network components and techniques == Artificial neuron Activation function Rectified linear unit Sigmoid function Softmax function Embedding Convolution Pooling layer Attention Batch normalization Layer normalization Residual connections == Training and optimization == Backpropagation Gradient descent Stochastic gradient descent Adam optimization Learning rate Loss function Cross-entropy Mean squared error Regularization Dropout Early stopping Batch normalization Data augmentation Transfer learning Knowledge distillation Ensemble learning Curriculum learning == Datasets and benchmarks == CIFAR-10 ImageNet MNIST database Common Objects in Context (COCO) General Language Understanding Evaluation (GLUE) benchmark LibriSpeech SQuAD == Applications == === Computer vision === Computer vision Facial recognition system Image classification Image segmentation Medical imaging Object detection Optical character recognition === Natural language processing === Automatic summarization Chatbot Information retrieval Large language model Natural language processing Neural machine translation Question answering Sentiment analysis === Speech and audio === Automatic speech recognition Music information retrieval Speaker recognition Speech synthesis === Science and medicine === Bioinformatics Computational biology Drug discovery Medical diagnosis Protein structure prediction === Robotics and control === Autonomous car Computer game bot Control theory Robotics === Recommendation, search, and forecasting === Anomaly detection Forecasting Fraud detection Recommender system Search engine === Generative artificial intelligence === Deepfake Generative artificial intelligence Large language model Speech synthesis Text-to-image model === Computer graphics and video games === Deep Learning Anti-Aliasing (DLAA) Deep Learning Super Sampling (DLSS) == Hardware == AMD Instinct AMD XDNA Application-specific integrated circuit Deep learning processor, Neural processing unit (NPU), or Neural Engine Field-programmable gate array General-purpose computing on graphics processing units (GPGPU) Graphics processing unit NVIDIA Deep Learning Accelerator (NVDLA) Tensor processing unit Vision processing unit Wafer-scale integration === Supporting software platforms === CUDA Metal ROCm == Software == === Open-source frameworks and libraries === === Neural network software === EDLUT Emergent Encog JOONE Neuroph NeuroSolutions OpenNN Peltarion Synapse SNNS === Platforms, tools, and deployment === Amazon SageMaker Google Colab Hugging Face Kaggle Kubeflow MLflow ONNX OpenVINO TensorFlow Hub == Algorithms for deep learning and neural networks == Backpropagation Conjugate gradient method Generalized Hebbian algorithm Gradient descent Levenberg–Marquardt algorithm Perceptron Quasi-Newton method Wake-sleep algorithm == Methods and related topics == === Representation and metric learning === Contrastive learning Embedding Feature learning Manifold learning Metric learning === Generative modeling === Autoregressive model Diffusion model Generative adversarial network Generative model Variational inference === Efficient and scalable deep learning === Knowledge distillation Low-rank approximation Mixture of experts Quantization Sparsity === Reliability, safety, and interpretability === Adversarial machine learning AI alignment Algorithmic bias Catastrophic forgetting Differential privacy Explainable artificial intelligence Federated learning Hallucination (artificial intelligence) == Conferences and workshops == Annual Meeting of the Association for Computational Linguistics Conference on Computer Vision and Pattern Recognition Conference on Neural Information Processing Systems International Conference on Computer Vision International Conference on Learning Representations International Conference on Machine Learning == Organizations == === Research laboratories and institutions === Allen Institute for AI Alberta Machine Intelligence Institute European Laboratory for Learning and Intelligent Systems Google DeepMind Meta AI Mila Microsoft Research Vector Institute === Companies === Anthropic Cerebras Cohere DeepSeek Mistral AI OpenAI Stability AI xAI == Publications == === Books === Deep Learning – Ian Goodfellow and Yoshua Bengio Neural Networks and Deep Learning – Michael Nielsen Perceptrons – Marvin Minsky and Seymour Papert === Journals === IEEE Transactions on Neural Networks and Learning Systems Neural Networks Neural Computation == Influential persons ==
NASA AI Assisted-Air Quality Monitoring Project
The NASA Expert-System Ion Trap Mass Spectrometer (ES-ITMS) Project was a public-private partnership to develop an artificial intelligence assisted, air quality monitoring system and was qualified for use on the Space Shuttle. The partnership was also the first cost and intellectual property shared public-partnership implemented by NASA, which used the commercial Research and Development Limited Partnership (RDLP) model that had been adopted by the Reagan Administration for Department of Defense semiconductor development, and recommended for use by NASA for space commercialization. The project partners included NASA, the University of Florida and Finnigan MAT Corporation, was organized and administered by the NASA Joint Enterprise Institute (subsequently NASA Joint Sponsored Program) and ran from 1988 through 1990. The partnership concluded final testing in 1991, generating four patents, expert system software and application protocol reports. The system was space qualified for use on the Shuttle and elements of the ES-ITMS system were integrated into the product Improvements for Finnigan MAT corporation. The success of the partnership lead NASA to create a pilot program to develop partnership business models as an ongoing management practice. == Purpose and objectives == The need to monitor air quality in confined spaces represented an increasing challenge for NASA's planned space missions and private sector facility managers facing the increased scrutiny of possible air contaminants. Up to the early 1980's, air quality monitors generally required large spaces and human technicians to interpret readings. This created a need for miniaturized air quality monitors that could generate reliable and accurate analytic results without on-site technician presence. NASA initiated projects to develop..."mobile and/or portable mass spectrometers" that evaluated the "tradeoff between instrumentation capabilities and space, weight and power considerations." NASA selected a "commercial ITMS instrument capable of generating electron ionization, chemical ionization and mass spectrometry data", to develop a linked expert system to accomplish analysis without human intervention. The commercial instrumentation was from Finnigan MAT corporation while the scientific expertise to support expert system development was available at the University of Florida. The project managers at NASA Ames created a single, integrated project using the RDLP model with objectives to: Develop AI/expert system software for instrument control (NASA's role) Expand sensitivity, selectivity and speed of the spectrometer (Univ Florida role) Expand the spectrometer analytic capability and automate the screening (Finnigan role) == Membership == The partnership included seven specialists from five member organizations: Federal Government National Aeronautics and Space Administration (NASA) NASA Ames Research Center (ARC) NASA Kennedy Space Center (KSC) Commercial Finnigan MAT Corporation (Thermo-Fisher Scientific) TGS Technology, Inc. Research Management University of Florida == Organization, management and administration == The technical project was organized into two development teams, one located in at the NASA Ames Research Center covering expert systems and analytic capabilities and one in Florida covering improved sensitivity and testing. The partnership management and administration was provided by a non-profit, partnership support organization: the Joint Enterprise Institute operating through San Francisco State University Foundation (SFSUF) with a NASA employee liaison, Syed Shariq. == Public-private partnership == The partnership structure was as a prototype test of a pilot NASA program to develop public-private partnership business models. The pilot program was known as the NASA Joint Sponsored Research Program (JSRP), which operated as the NASA Joint Enterprise Institute between 1988 and 1991. The partnership was the first public-private, research and development partnership implemented by NASA in response to national policy shifts to increase technology transfer and space commercialization. The partnership structure included a two year technology development and testing plan that cost $610,000, of which NASA funded $310,000, Finnigan $175,000 and the University of Florida $95,000. == Results and commercialization == The project generated patents (4), software (2) and application protocol reports (8). NASA gained use of the patents and jointly development software while Finnigan received commercial utilization rights. The results were commercialized within eighteen months of project completion. == Recognition == NASA recognized the project as a space qualified instrument. Its achievements were reported to the NASA Administrator, directly leading to establishment of the agency-wide Joint Sponsored Research Program.
Seam carving
Seam carving (or liquid rescaling) is an algorithm for content-aware image resizing, developed by Shai Avidan, of Mitsubishi Electric Research Laboratories (MERL), and Ariel Shamir, of the Interdisciplinary Center and MERL. It functions by establishing a number of seams (paths of least importance) in an image and automatically removes seams to reduce image size or inserts seams to extend it. Seam carving also allows manually defining areas in which pixels may not be modified, and features the ability to remove whole objects from photographs. The purpose of the algorithm is image retargeting, which is the problem of displaying images without distortion on media of various sizes (cell phones, projection screens) using document standards, like HTML, that already support dynamic changes in page layout and text but not images. Image Retargeting was invented by Vidya Setlur, Saeko Takage, Ramesh Raskar, Michael Gleicher and Bruce Gooch in 2005. The work by Setlur et al. won the 10-year impact award in 2015. == Seams == Seams can be either vertical or horizontal. A vertical seam is a path of pixels connected from top to bottom in an image with one pixel in each row. A horizontal seam is similar with the exception of the connection being from left to right. The importance/energy function values a pixel by measuring its contrast with its neighbor pixels. == Process == The below example describes the process of seam carving: The seams to remove depends only on the dimension (height or width) one wants to shrink. It is also possible to invert step 4 so the algorithm enlarges in one dimension by copying a low energy seam and averaging its pixels with its neighbors. === Computing seams === Computing a seam consists of finding a path of minimum energy cost from one end of the image to another. This can be done via Dijkstra's algorithm, dynamic programming, greedy algorithm or graph cuts among others. ==== Dynamic programming ==== Dynamic programming is a programming method that stores the results of sub-calculations in order to simplify calculating a more complex result. Dynamic programming can be used to compute seams. If attempting to compute a vertical seam (path) of lowest energy, for each pixel in a row we compute the energy of the current pixel plus the energy of one of the three possible pixels above it. The images below depict a DP process to compute one optimal seam. Each square represents a pixel, with the top-left value in red representing the energy value of that pixel. The value in black represents the cumulative sum of energies leading up to and including that pixel. The energy calculation is trivially parallelized for simple functions. The calculation of the DP array can also be parallelized with some interprocess communication. However, the problem of making multiple seams at the same time is harder for two reasons: the energy needs to be regenerated for each removal for correctness and simply tracing back multiple seams can form overlaps. Avidan 2007 computes all seams by removing each seam iteratively and storing an "index map" to record all the seams generated. The map holds a "nth seam" number for each pixel on the image, and can be used later for size adjustment. If one ignores both issues however, a greedy approximation for parallel seam carving is possible. To do so, one starts with the minimum-energy pixel at one end, and keep choosing the minimum energy path to the other end. The used pixels are marked so that they are not picked again. Local seams can also be computed for smaller parts of the image in parallel for a good approximation. == Issues == The algorithm may need user-provided information to reduce errors. This can consist of painting the regions which are to be preserved. With human faces it is possible to use face detection. Sometimes the algorithm, by removing a low energy seam, may end up inadvertently creating a seam of higher energy. The solution to this is to simulate a removal of a seam, and then check the energy delta to see if the energy increases (forward energy). If it does, prefer other seams instead. == Implementations == Adobe Systems acquired a non-exclusive license to seam carving technology from MERL, and implemented it as a feature in Photoshop CS4, where it is called Content Aware Scaling. As the license is non-exclusive, other popular computer graphics applications (e. g. GIMP, digiKam, and ImageMagick) as well as some stand-alone programs (e. g. iResizer) also have implementations of this technique, some of which are released as free and open source software. There also exists an implementation for webpages. == Improvements and extensions == Better energy function and application to video by introducing 2D (time+1D) seams. Faster implementation on GPU. Application of this forward energy function to static images. Multi-operator: Combine with cropping and scaling. Much faster removal of multiple seams. Removing seams through neural deformation fields to extend to continuous domains like 3D scenes. A 2010 review of eight image retargeting methods found that seam carving produced output that was ranked among the worst of the tested algorithms. It was, however, a part of one of the highest-ranking algorithms: the multi-operator extension mentioned above (combined with cropping and scaling).
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