In decision tree learning, ID3 (Iterative Dichotomiser 3) is a greedy algorithm invented by Ross Quinlan used to generate a decision tree from a dataset. ID3 is the precursor to the C4.5 algorithm. The 3 in the name is meant to signify that this was Quinlan's third attempt at a model based on entropy-based splitting, and the term dichotimser is a misnomer as it implies a binary split, but the ID3 algorithm can split on multi-valued attributes. == Algorithm == The ID3 algorithm begins with the original set S {\displaystyle S} as the root node. On each iteration of the algorithm, it iterates through every unused attribute of the set S {\displaystyle S} and calculates the entropy H ( S ) {\displaystyle \mathrm {H} {(S)}} or the information gain I G ( S ) {\displaystyle IG(S)} of that attribute. It then selects the attribute which has the smallest entropy (or largest information gain) value. The set S {\displaystyle S} is then split or partitioned by the selected attribute to produce subsets of the data. (For example, a node can be split into child nodes based upon the subsets of the population whose ages are less than 50, between 50 and 100, and greater than 100.) The algorithm continues to recurse on each subset, considering only attributes never selected before. Recursion on a subset may stop in one of these cases: every element in the subset belongs to the same class; in which case the node is turned into a leaf node and labelled with the class of the examples. there are no more attributes to be selected, but the examples still do not belong to the same class. In this case, the node is made a leaf node and labelled with the most common class of the examples in the subset. there are no examples in the subset, which happens when no example in the parent set was found to match a specific value of the selected attribute. An example could be the absence of a person among the population with age over 100 years. Then a leaf node is created and labelled with the most common class of the examples in the parent node's set. Throughout the algorithm, the decision tree is constructed with each non-terminal node (internal node) representing the selected attribute on which the data was split, and terminal nodes (leaf nodes) representing the class label of the final subset of this branch. === Summary === Calculate the entropy of every attribute a {\displaystyle a} of the data set S {\displaystyle S} . Partition ("split") the set S {\displaystyle S} into subsets using the attribute for which the resulting entropy after splitting is minimized; or, equivalently, information gain is maximum. Make a decision tree node containing that attribute. Recurse on subsets using the remaining attributes. === Properties === ID3 does not guarantee an optimal solution. It can converge upon local optima. It uses a greedy strategy by selecting the locally best attribute to split the dataset on each iteration. The algorithm's optimality can be improved by using backtracking during the search for the optimal decision tree at the cost of possibly taking longer. ID3 can overfit the training data. To avoid overfitting, smaller decision trees should be preferred over larger ones. This algorithm usually produces small trees, but it does not always produce the smallest possible decision tree. ID3 is harder to use on continuous data than on factored data (factored data has a discrete number of possible values, thus reducing the possible branch points). If the values of any given attribute are continuous, then there are many more places to split the data on this attribute, and searching for the best value to split by can be time-consuming. === Usage === The ID3 algorithm is used by training on a data set S {\displaystyle S} to produce a decision tree which is stored in memory. At runtime, this decision tree is used to classify new test cases (feature vectors) by traversing the decision tree using the features of the datum to arrive at a leaf node. == The ID3 metrics == === Entropy === Entropy H ( S ) {\displaystyle \mathrm {H} {(S)}} is a measure of the amount of uncertainty in the (data) set S {\displaystyle S} (i.e. entropy characterizes the (data) set S {\displaystyle S} ). H ( S ) = ∑ x ∈ X − p ( x ) log 2 p ( x ) {\displaystyle \mathrm {H} {(S)}=\sum _{x\in X}{-p(x)\log _{2}p(x)}} Where, S {\displaystyle S} – The current dataset for which entropy is being calculated This changes at each step of the ID3 algorithm, either to a subset of the previous set in the case of splitting on an attribute or to a "sibling" partition of the parent in case the recursion terminated previously. X {\displaystyle X} – The set of classes in S {\displaystyle S} p ( x ) {\displaystyle p(x)} – The proportion of the number of elements in class x {\displaystyle x} to the number of elements in set S {\displaystyle S} When H ( S ) = 0 {\displaystyle \mathrm {H} {(S)}=0} , the set S {\displaystyle S} is perfectly classified (i.e. all elements in S {\displaystyle S} are of the same class). In ID3, entropy is calculated for each remaining attribute. The attribute with the smallest entropy is used to split the set S {\displaystyle S} on this iteration. Entropy in information theory measures how much information is expected to be gained upon measuring a random variable; as such, it can also be used to quantify the amount to which the distribution of the quantity's values is unknown. A constant quantity has zero entropy, as its distribution is perfectly known. In contrast, a uniformly distributed random variable (discretely or continuously uniform) maximizes entropy. Therefore, the greater the entropy at a node, the less information is known about the classification of data at this stage of the tree; and therefore, the greater the potential to improve the classification here. As such, ID3 is a greedy heuristic performing a best-first search for locally optimal entropy values. Its accuracy can be improved by preprocessing the data. === Information gain === Information gain I G ( A ) {\displaystyle IG(A)} is the measure of the difference in entropy from before to after the set S {\displaystyle S} is split on an attribute A {\displaystyle A} . In other words, how much uncertainty in S {\displaystyle S} was reduced after splitting set S {\displaystyle S} on attribute A {\displaystyle A} . I G ( S , A ) = H ( S ) − ∑ t ∈ T p ( t ) H ( t ) = H ( S ) − H ( S | A ) . {\displaystyle IG(S,A)=\mathrm {H} {(S)}-\sum _{t\in T}p(t)\mathrm {H} {(t)}=\mathrm {H} {(S)}-\mathrm {H} {(S|A)}.} Where, H ( S ) {\displaystyle \mathrm {H} (S)} – Entropy of set S {\displaystyle S} T {\displaystyle T} – The subsets created from splitting set S {\displaystyle S} by attribute A {\displaystyle A} such that S = ⋃ t ∈ T t {\displaystyle S=\bigcup _{t\in T}t} p ( t ) {\displaystyle p(t)} – The proportion of the number of elements in t {\displaystyle t} to the number of elements in set S {\displaystyle S} H ( t ) {\displaystyle \mathrm {H} (t)} – Entropy of subset t {\displaystyle t} In ID3, information gain can be calculated (instead of entropy) for each remaining attribute. The attribute with the largest information gain is used to split the set S {\displaystyle S} on this iteration.
Apertus (LLM)
Apertus is a public large language model, developed by the Swiss AI Initiative (a collaboration between EPFL, ETH Zurich, and the Swiss National Supercomputing Centre). It was released on September 2, 2025, under the free and open-source Apache 2.0 license. Designed initially for business and research use cases around the world, Apertus was trained on over 1800 languages, and comes in 8 billion or 70 billion parameter versions and is available on Hugging Face for download. The model was developed aiming to adhere to European copyright law, and is one of the first examples of AI as a public good in the vein of AI Sovereignty. It is also the first large model to comply with the European Union's Artificial Intelligence Act. At its launch, the model creators emphasized multilinguality, transparency, and auditability as priorities in contrast to commercial frontier model. While international reception was largely positive, the first iteration was significantly behind the capabilities of frontier models and needs adaptation for many use cases with chatbots being a secondary but not a primary use case. As of late 2025, it was considered the largest and most capable fully open model. The capability of future models will depend in part on how much more funding can be secured.
Common Crawl
The Common Crawl Foundation (Common Crawl) is a nonprofit 501(c)(3) organization that crawls the web and freely provides its archives and datasets to the public. Common Crawl was founded by Gil Elbaz. The data had mostly been primarily used by researchers and some startups until the 2020s, when AI companies started training large language models using the data. In November 2025, an investigation by The Atlantic revealed that Common Crawl misled publishers when it claimed it respected paywalls in its scraping and it was not honoring requests from publishers to have their content removed from its databases. == History == Common Crawl was founded in 2007 in San Francisco. It began publishing its crawls in 2011. By 2013, sites like TinEye were building their products off of Common Crawl. The crawl reduces the reliance of companies and researchers on Google, which has the biggest dataset. Common Crawl was designed to have more and fresher data that was more efficient to analyze and utilize than the Wayback Machine created by the Internet Archive. By 2015, 1.8 billion webpages were on the Common Crawl, which started by crawling a list of URLs donated by the search engine Blekko. They use Amazon Web Services, which provides some of its services for free, allowing computing costs to average $2-4000/month. The Common Crawl website listed 30 studies based on Common Crawl data. Before 2023, Common Crawl was not very well known outside of academic researchers who utilize the data. Common Crawl received its first requests to redact information in 2023 and increasingly started seeing its crawler, CCBot, blocked. In 2023, it began receiving significant financial support from AI companies, including Anthropic and OpenAI, each of which donated $250,000. It was also used to train Google DeepMind's large language model Gemini. By April 2023, Common Crawl was capturing 3.1 billion webpages, with an estimated 5% of pages before 2021 containing hate speech or slurs. As of 2024, Common Crawl had been cited in more than 10,000 academic studies. By 2024, The Pile and Common Crawl had been the two main training datasets being used to train AI models. In November 2025, an investigation by technology journalist Alex Reisner for The Atlantic revealed that Common Crawl misled publishers when it claimed it respected paywalls in its scraping and when it said that it was honoring requests from publishers to have their content removed from its databases. It included misleading results in the public search function on its website that showed no entries for websites that had requested their archives be removed, when in fact those sites were still included in its scrapes used by AI companies. As of 2025, Reisner found that CCBot was the most widely-blocked bot by the top 1000 websites. A 2026 article in LWN.net discussed an advantage to services like Common Crawl being that it can limit the scraping costs to websites by allowing companies and researchers to download the data from Common Crawl instead of scraping it themselves. In April 2026, Common Crawl experimentally began to distribute its data through Hugging Face Storage Bucket, in addition to its standard storage on Amazon S3. == Organization == Peter Norvig and Joi Ito have served on the advisory board. Rich Skrenta is the executive director. It has received funding almost exclusively from the Elbaz Family Foundation Trust until 2023 when it started receiving donations from the AI industry. == Refined versions == A number of organizations take raw Common Crawl data and refine it into datasets that exclude edgy content or are otherwise higher-quality for their purposes, such as FineWeb, DCLM and C4. === Colossal Clean Crawled Corpus === Google version of the Common Crawl is called the Colossal Clean Crawled Corpus, or C4 for short. It was constructed for the training of the T5 language model series in 2019. As of 2023, there were some concerns over copyrighted content in the C4 as well as racist content. A 2024 study found that 45% of content was explicitly restricted by websites' terms of service to be used for purposes like AI training by for-profit companies.
Colossus (supercomputer)
Colossus is a supercomputer developed by xAI. Construction began in 2024 in Memphis, Tennessee; the system became operational in July 2024. It is currently the world's largest AI supercomputer. Colossus's primary purpose is to train the company's chatbot, Grok. In addition, Colossus provides computing support to the social-media platform X and to other projects of Elon Musk, such as SpaceX. In 2025, it expanded to neighboring Southaven, Mississippi across the Tennessee–Mississippi border. As of May 6, 2026, Anthropic has agreed to rent all compute capacity at the Colossus 1 data center. == Background == Colossus was launched in September 2024 at a former Electrolux site in South Memphis to train the AI language model Grok. Within 19 days of the project's conception, xAI was ready to begin construction. The site was chosen because the abandoned Electrolux building could be repurposed to expedite construction and its proximity to a nearby wastewater treatment facility provided a water source. As of February 2025, xAI plans to build an $80 million facility to process additional wastewater for use at the supercomputer. === xAI === Musk incorporated xAI in March 2023 with the stated purpose of understanding the "nature of the universe". The team includes former members of OpenAI, DeepMind, Microsoft, and Tesla. Musk was one of the founding members of the company OpenAI, investing up to US$45 million in 2015. He left OpenAI in 2018, reportedly to avoid conflicts of interest with Tesla. It has also been reported that he had made a bid for leadership at OpenAI and left when his proposal was rejected. The exact reasons for his departure from the company are unclear. Both Dell Technologies and Supermicro partnered with xAI to build the supercomputer. It was originally powered by 100,000 Nvidia graphics processing units (GPUs) and was constructed in 122 days. 3 months after the first 100,000 GPUs were deployed, xAI announced that they had increased the system to 200,000 GPUs and that they intended to continue increasing the computer's processing power to 1 million GPUs. As of April 2025, xAI claimed Colossus was the largest AI training platform in the world. == Choice of location == xAI selected Memphis, in southwestern Tennessee, as the site for Colossus in part because an existing industrial facility allowed the project to proceed more quickly than constructing a new data center. Elon Musk was initially told that building a data center would take 18–24 months. The company instead searched for a vacant facility and selected the former Electrolux factory in Memphis. Electrolux opened the facility in 2012 and operated it for about eight years before closing it in 2020 after relocating operations to Springfield, Tennessee. The building covered 785,000 sq ft (72,900 m2) and had been purchased by Phoenix Investors in December 2023 for $35 million . Because the structure was already in place, work on the supercomputer could begin immediately rather than waiting for a new facility to be constructed. According to Forbes, xAI considered seven or eight other sites before selecting Memphis, and Musk finalized the decision to build in Memphis in about a week. The decision was finalized in March 2024, after which construction began. xAI publicly announced in June 2024 that Colossus would be built in Memphis. The building itself was not the only reason xAI selected Memphis. According to the Greater Memphis Chamber, the company chose the city because of its "reliable power grid, ability to create a water recycling facility, proximity to the Mississippi River and ample land". The city was also able to provide the large amounts of electricity and water needed to operate the supercomputer. At full capacity, the system was expected to require 150 megawatts of electricity and millions of gallons of water per day. The project also relied on partnerships with local and regional organizations including Memphis Light, Gas and Water (MLGW), Tennessee Valley Authority (TVA), the City of Memphis, and Shelby County. The city also provided financial incentives for the project. == Environmental impact == AI data centers consume large amounts of energy. At the site of Colossus in South Memphis, the grid connection was only 8 MW, so xAI applied to temporarily set up more than a dozen gas turbines (Voltagrid’s 2.5 MW units and Solar Turbines’ 16 MW SMT-130s) which would steadily burn methane gas from a 16-inch natural gas main. Aerial imagery in April 2025 showed 35 gas turbines had been set up at a combined 422 MW. These turbines have been estimated to generate about "72 megawatts, which is approximately 3% of the (TVA) power grid". The higher number of gas turbines and the subsequent emissions requires xAI to have a major source permit. In Memphis, xAI was able to avoid some environmental rules in the construction of Colossus, such as operating without permits for the on-site methane gas turbines because they are "portable". The Shelby County Health Department told NPR that "it only regulates gas-burning generators if they're in the same location for more than 364 days". However, in a January 2026 ruling, the EPA revised its New Source Performance Standard and announced that large methane gas turbines require permits even for temporary operations. In November 2024, the grid connection was upgraded to 150 MW, and some turbines were removed. Along with high electricity needs, the expected water demand is over five million gallons of water per day. While xAI has stated they plan to work with MLGW on a wastewater treatment facility and the installation of 50 megawatts of large battery storage facilities, there are currently no concrete plans in place aside from a one-page factsheet shared by MLGW. == Community response == The plan to build Colossus in Memphis was unknown to residents, City Council members, and environmental agencies. Many did not find out about the project until the day before, or the day of, as they watched the announcement on the local news. Keshaun Pearson, president of Memphis Community Against Pollution, stated that there is a historical lack of transparency and communication surrounding environmental issues in Memphis. Some community members in Memphis have expressed concern about the potential for additional air and water pollution caused by the supercomputer. In a letter to the Shelby County Health Department, the Southern Environmental Law Center stated the emissions from the turbines make the facility "...likely the largest industrial emitter of NOx in Memphis..." This is due to data supplied by the manufacturer showing that "...xAI emits between 1,200 and 2,000 tons of smog-forming nitrogen oxides (NOx)..." At a public Shelby County Commissioner's hearing on April 9, 2025, residents living near the site of Colossus voiced complaints about air quality, noting that they have chronic respiratory issues related to living in a polluted section of Memphis. One woman said she smells "everything but the right thing and the right thing is the clean air." Other residents voiced frustration that Brent Mayo, the senior xAI official responsible for building out xAI's infrastructure, did not attend the meeting to discuss community concerns. Keshaun Pearson also stated that "We're getting more and more days a year where it is unhealthy for us to go outside." People living near the site of Colossus have said they were not offered the opportunity for a public review of the plans, nor were they provided with information on how their community could potentially benefit. The community is also concerned about the strain on the power grid. Memphis's peak demand is around 3 GW. In November 2024, TVA approved xAI's request for access to more than 100 megawatts of power to Colossus which is supplied by MLGW. In December 2022, MLGW imposed (then rescinded) rolling blackouts during several days of extreme cold, straining the power grid. In a letter to the TVA, the SELC "urged the agency to 'prioritize Memphis families' access to reliable power over the 'secondary purpose' of serving xAI". == Current progress == In early December 2024, Ted Townsend detailed how the power of Colossus doubled in its processing capability. When it first went online in September 2024, it was using "100,000 Nvidia H100 processing chips". This initial launch demonstrated Colossus to be the largest supercomputer globally. The maximum power consumption increased from 150 to 250 MW. As of June 2025, the supercomputer consists of 150,000 H100 GPUs, 50,000 H200 GPUs, and 30,000 GB200 GPUs. Another 110,000 GB200 GPUs are to be brought online at a second data center, also in the Memphis area. The expansion of this supercomputer has already been discussed and will be the second phase of the project. xAI also plans to increase Colossus to 1 million GPUs. Because the supercomputer currently utilizes gas turbines for power, alongside 168 Tesla Megapack battery storage units. xAI is also looking to add more
DREAM Challenges
DREAM Challenges (Dialogue for Reverse Engineering Assessment and Methods) is a non-profit initiative for advancing biomedical and systems biology research via crowd-sourced competitions. Started in 2006, DREAM challenges collaborate with Sage Bionetworks to provide a platform for competitions run on the Synapse platform. Over 60 DREAM challenges have been conducted over the span of over 15 years. == Overview == DREAM Challenges were founded in 2006 by Gustavo Stolovizky from IBM Research and Andrea Califano from Columbia University. Current chair of the DREAM organization is Paul Boutros from University of California. Further organization spans emeritus chairs Justin Guinney and Gustavo Stolovizky, and multiple DREAM directors. Individual challenges focus on tackling a specific biomedical research question, typically narrowed down to a specific disease. A prominent disease focus has been on oncology, with multiple past challenges focused on breast cancer, acute myeloid leukemia, and prostate cancer or similar diseases. The data involved in an individual challenge reflects the disease context; while cancers typically involve data such as mutations in the human genome, gene expression and gene networks in transcriptomics, and large scale proteomics, newer challenges have shifted towards single cell sequencing technologies as well as emerging gut microbiome related research questions, thus reflecting trends in the wider research community. Motivation for DREAM Challenges is that via crowd-sourcing data to a larger audience via competitions, better models and insight is gained than if the analysis was conducted by a single entity. Past competitions have been published in such scientific venues as the flagship journals of the Nature Portfolio and PLOS publishing groups. Results of DREAM challenges are announced via web platforms, and the top performing participants are invited to present their results in the annual RECOMB/ISCB Conferences with RSG/DREAM organized by the ISCB. While DREAM Challenges have emphasized open science and data, in order to mitigate issues rising from highly sensitive data such as genomics in patient cohorts, "model to data" approaches have been adopted. In such challenges participants submit their models via containers such as Docker or Singularity. This allows retaining confidentiality of the original data as these containers are then run by the organizers on the confidential data. This differs from the more traditional open data model, where participants submit predictions directly based on the provided open data. == Challenge organization == DREAM challenge comprises a core DREAM/Sage Bionetworks organization group as well as an extended scientific expert group, who may have contributed to creation and conception of the challenge or by providing key data. Additionally, new DREAM challenges may be proposed by the wider research community. Pharmaceutical companies or other private entities may also be involved in DREAM challenges, for example in providing data. == Challenge structure == Timelines for key stages (such as introduction webinars, model submission deadlines, and final deadline for participation) are provided in advance. After the winners are announced, organizers start collaborating with the top performing participants to conduct post hoc analyses for a publication describing key findings from the competition. Challenges may be split into sub-challenges, each addressing a different subtopic within the research question. For example, regarding cancer treatment efficacy predictions, these may be separate predictions for progression-free survival, overall survival, best overall response according to RECIST, or exact time until event (progression or death). == Participation == During DREAM challenges, participants typically build models on provided data, and submit predictions or models that are then validated on held-out data by the organizers. While DREAM challenges avoid leaking validation data to participants, there are typically mid-challenge submission leaderboards available to assist participants in evaluating their performance on a sub-sampled or scrambled dataset. DREAM challenges are free for participants. During the open phase anybody can register via Synapse to participate either individually or as a team. A person may only register once and may not use any aliases. There are some exceptions, which disqualify an individual from participating, for example: Person has privileged access to the data for the particular challenge, thus providing them with an unfair advantage. Person has been caught or is under suspicion of cheating or abusing previous DREAM Challenges. Person is a minor (under age 18 or the age of majority in jurisdiction of residence). This may be alleviated via parental consent.
Dynamic Graphics Project
The Dynamic Graphics Project (commonly referred to as DGP) is an interdisciplinary research laboratory at the University of Toronto devoted to projects involving computer graphics, computer vision, human computer interaction, and visualization. The lab began as the computer graphics research group of Department of Computer Science Professor Leslie Mezei in 1967. Mezei invited Bill Buxton, a pioneer of human–computer interaction (HCI) to join. In 1972, Ronald Baecker, another HCI pioneer joined, establishing DGP as the first Canadian university group focused on computer graphics and human-computer interaction. According to csrankings.org, the DGP is the top research institution in the world for the combined subfields of computer graphics, HCI, and visualization. Since then, DGP has hosted many well known faculty and students in computer graphics, computer vision and HCI (e.g., Alain Fournier, Bill Reeves, Jos Stam, Demetri Terzopoulos, Marilyn Tremaine). DGP also occasionally hosts artists in residence (e.g., Oscar-winner Chris Landreth). Many past and current researchers at Autodesk (and before that Alias Wavefront) graduated after working at DGP. DGP is located in the St. George campus of University of Toronto in the Bahen Centre for Information Technology. DGP researchers regularly publish at ACM SIGGRAPH, ACM SIGCHI and ICCV. DGP hosts the Toronto User Experience (TUX) Speaker Series and the Sanders Series Lectures. == Notable alumni == Bill Buxton (MS 1978) James McCrae (PhD 2013) Dimitris Metaxas (PhD 1992) Bill Reeves (MS 1976, Ph.D. 1980) Jos Stam (MS 1991, Ph.D. 1995)
Ontology components
Contemporary ontologies share many structural similarities, regardless of the ontology language in which they are expressed. Most ontologies describe individuals (instances), classes (concepts), attributes, and relations. == List == Common components of ontologies include: Individuals instances or objects (the basic or "ground level" objects; the tokens). Classes sets, collections, concepts, types of objects, or kinds of things. Attributes aspects, properties, features, characteristics, or parameters that individuals (and classes and relations) can have. Relations ways in which classes and individuals can be related to one another. Relations can carry attributes that specify the relation further. Function terms complex structures formed from certain relations that can be used in place of an individual term in a statement. Restrictions formally stated descriptions of what must be true in order for some assertion to be accepted as input. Rules statements in the form of an if-then (antecedent-consequent) sentence that describe the logical inferences that can be drawn from an assertion in a particular form. Axioms assertions (including rules) in a logical form that together comprise the overall theory that the ontology describes in its domain of application. This definition differs from that of "axioms" in generative grammar and formal logic. In these disciplines, axioms include only statements asserted as a priori knowledge. As used here, "axioms" also include the theory derived from axiomatic statements. Events the changing of attributes or relations. Actions types of events. Ontologies are commonly encoded using ontology languages. == Individuals == Individuals (instances) are the basic, "ground level" components of an ontology. The individuals in an ontology may include concrete objects such as people, animals, tables, automobiles, molecules, and planets, as well as abstract individuals such as numbers and words (although there are differences of opinion as to whether numbers and words are classes or individuals). Strictly speaking, an ontology need not include any individuals, but one of the general purposes of an ontology is to provide a means of classifying individuals, even if those individuals are not explicitly part of the ontology. In formal extensional ontologies, only the utterances of words and numbers are considered individuals – the numbers and names themselves are classes. In a 4D ontology, an individual is identified by its spatio-temporal extent. Examples of formal extensional ontologies are BORO, ISO 15926 and the model in development by the IDEAS Group. == Classes == == Attributes == Objects in an ontology can be described by relating them to other things, typically aspects or parts. These related things are often called attributes, although they may be independent things. Each attribute can be a class or an individual. The kind of object and the kind of attribute determine the kind of relation between them. A relation between an object and an attribute express a fact that is specific to the object to which it is related. For example, the Ford Explorer object has attributes such as: ⟨has as name⟩ Ford Explorer ⟨as by definition as part⟩ 6-speed transmission ⟨as by definition as part⟩ door (with as minimum and maximum cardinality: 4) ⟨as by definition as part one of⟩ {4.0L engine, 4.6L engine} The value of an attribute can be a complex data type; in this example, the related engine can only be one of a list of subtypes of engines, not just a single thing. Ontologies are only true ontologies if concepts are related to other concepts (the concepts do have attributes). If that is not the case, then you would have either a taxonomy (if hyponym relationships exist between concepts) or a controlled vocabulary. These are useful, but are not considered true ontologies. == Relations == Relations (also known as relationships) between objects in an ontology specify how objects are related to other objects. Typically a relation is of a particular type (or class) that specifies in what sense the object is related to the other object in the ontology. For example, in the ontology that contains the concept Ford Explorer and the concept Ford Bronco might be related by a relation of type ⟨is defined as a successor of⟩. The full expression of that fact then becomes: Ford Explorer is defined as a successor of : Ford Bronco This tells us that the Explorer is the model that replaced the Bronco. This example also illustrates that the relation has a direction of expression. The inverse expression expresses the same fact, but with a reverse phrase in natural language. Much of the power of ontologies comes from the ability to describe relations. Together, the set of relations describes the semantics of the domain: that is, its various semantic relations, such as synonymy, hyponymy and hypernymy, coordinate relation, and others. The set of used relation types (classes of relations) and their subsumption hierarchy describe the expression power of the language in which the ontology is expressed. An important type of relation is the subsumption relation (is-a-superclass-of, the converse of is-a, is-a-subtype-of or is-a-subclass-of). This defines which objects are classified by which class. For example, we have already seen that the class Ford Explorer is-a-subclass-of 4-Wheel Drive Car, which in turn is-a-subclass-of Car. The addition of the is-a-subclass-of relationships creates a taxonomy; a tree-like structure (or, more generally, a partially ordered set) that clearly depicts how objects relate to one another. In such a structure, each object is the 'child' of a 'parent class' (Some languages restrict the is-a-subclass-of relationship to one parent for all nodes, but many do not). Another common type of relations is the mereology relation, written as part-of, that represents how objects combine to form composite objects. For example, if we extended our example ontology to include concepts like Steering Wheel, we would say that a "Steering Wheel is-by-definition-a-part-of-a Ford Explorer" since a steering wheel is always one of the components of a Ford Explorer. If we introduce meronymy relationships to our ontology, the hierarchy that emerges is no longer able to be held in a simple tree-like structure since now members can appear under more than one parent or branch. Instead this new structure that emerges is known as a directed acyclic graph. As well as the standard is-a-subclass-of and is-by-definition-a-part-of-a relations, ontologies often include additional types of relations that further refine the semantics they model. Ontologies might distinguish between different categories of relation types. For example: relation types for relations between classes relation types for relations between individuals relation types for relations between an individual and a class relation types for relations between a single object and a collection relation types for relations between collections Relation types are sometimes domain-specific and are then used to store specific kinds of facts or to answer particular types of questions. If the definitions of the relation types are included in an ontology, then the ontology defines its own ontology definition language. An example of an ontology that defines its own relation types and distinguishes between various categories of relation types is the Gellish ontology. For example, in the domain of automobiles, we might need a made-in type relationship which tells us where each car is built. So the Ford Explorer is made-in Louisville. The ontology may also know that Louisville is-located-in Kentucky and Kentucky is-classified-as-a state and is-a-part-of the U.S. Software using this ontology could now answer a question like "which cars are made in the U.S.?"