A large language model (LLM) is a neural network trained on a vast amount of text for natural language processing tasks, especially language generation. LLMs can typically generate, summarize, translate and analyze text in many contexts, and are a foundational technology behind modern chatbots. Biased or inaccurate training data can make an LLM's output less reliable. As of 2026, the most capable LLMs are based on transformer architectures, which, according to the 2017 paper "Attention Is All You Need", can be more efficient and parallelizable than earlier statistical and recurrent neural network models. Benchmark evaluations for LLMs attempt to measure model reasoning, factual accuracy, alignment, and safety. == History == Before the emergence of transformer-based models in 2017, some language models were considered large relative to the computational and data constraints of their time. In the early 1990s, IBM's statistical models pioneered word alignment techniques for machine translation, laying the groundwork for corpus-based language modeling. In 2001, a smoothed n-gram model, such as those employing Kneser–Ney smoothing, trained on 300 million words, achieved state-of-the-art perplexity on benchmark tests. During the 2000s, with the rise of widespread internet access, researchers began compiling massive text datasets from the web ("web as corpus") to train statistical language models. Moving beyond n-gram models, researchers started in 2000 to use neural networks as language models. Following the breakthrough of deep neural networks in image classification around 2012, similar architectures were adapted for language tasks. This shift was marked by the development of word embeddings (e.g., Word2Vec by Mikolov in 2013) and sequence-to-sequence (seq2seq) models using LSTM. In 2016, Google transitioned its translation service to neural machine translation (NMT), replacing statistical phrase-based models with deep recurrent neural networks. These early NMT systems used LSTM-based encoder-decoder architectures, as they preceded the invention of transformers. At the 2017 NeurIPS conference, Google researchers introduced the transformer architecture in their landmark paper "Attention Is All You Need". This paper's goal was to improve upon 2014 seq2seq technology, and was based mainly on the attention mechanism developed by Bahdanau et al. in 2014. The following year in 2018, BERT was introduced and quickly became "ubiquitous". Though the original transformer has both encoder and decoder blocks, BERT is an encoder-only model. Academic and research usage of BERT began to decline in 2023, following rapid improvements in the abilities of decoder-only models (such as GPT) to solve tasks via prompting. Although decoder-only GPT-1 was introduced in 2018, it was GPT-2 in 2019 that caught widespread attention because OpenAI claimed to have initially deemed it too powerful to release publicly, out of fear of malicious use. GPT-3 in 2020 went a step further and as of 2025 is available only via API with no offering of downloading the model to execute locally. But it was the consumer-facing chatbot ChatGPT in late 2022 that received extensive media coverage and public attention by 2023. The 2023 GPT-4 was praised for its increased accuracy and as a "holy grail" for its multimodal capabilities. OpenAI did not reveal the high-level architecture and the number of parameters of GPT-4. The release of ChatGPT led to an uptick in LLM usage across several research subfields of computer science, including robotics, software engineering, and societal impact work. In 2024, OpenAI released the reasoning model OpenAI o1, which generates long chains of thought before returning a final answer. Many LLMs with parameter counts comparable to those of OpenAI's GPT series have been developed. Since 2022, weights-available models have been gaining popularity, especially at first with BLOOM and LLaMA, though both have restrictions on usage and deployment. Mistral AI's open-weight models Mistral 7B and Mixtral 8x7B have a more permissive Apache License. In January 2025, DeepSeek released DeepSeek R1, a 671-billion-parameter open-weight model that performs comparably to OpenAI o1 but at a much lower price per token for users. Since 2023, many LLMs have been trained to be multimodal, having the ability to also process or generate other types of data, such as images, audio, or 3D meshes. Open-weight LLMs have become more influential since 2023. Per Vake et al. (2025), community-driven contributions to open-weight models improve their efficiency and performance via collaborative platforms such as Hugging Face. == Dataset preprocessing == === Tokenization === As machine learning algorithms process numbers rather than text, the text must be converted to numbers. In the first step, a vocabulary is decided upon, then integer indices are arbitrarily but uniquely assigned to each vocabulary entry, and finally, an embedding is associated with the integer index. Algorithms include byte-pair encoding (BPE) and WordPiece. There are also special tokens serving as control characters, such as [MASK] for masked-out token (as used in BERT), and [UNK] ("unknown") for characters not appearing in the vocabulary. Also, some special symbols are used to denote special text formatting. For example, "Ġ" denotes a preceding whitespace in RoBERTa and GPT and "##" denotes continuation of a preceding word in BERT. For example, the BPE tokenizer used by the legacy version of GPT-3 would split tokenizer: texts -> series of numerical "tokens" as Tokenization also compresses the datasets. Because LLMs generally require input to be an array that is not jagged, the shorter texts must be "padded" until they match the length of the longest one. ==== Byte-pair encoding ==== As an example, consider a tokenizer based on byte-pair encoding. In the first step, all unique characters (including blanks and punctuation marks) are treated as an initial set of n-grams (i.e. initial set of uni-grams). Successively the most frequent pair of adjacent characters is merged into a bi-gram and all instances of the pair are replaced by it. All occurrences of adjacent pairs of (previously merged) n-grams that most frequently occur together are then again merged into even lengthier n-gram, until a vocabulary of prescribed size is obtained. After a tokenizer is trained, any text can be tokenized by it, as long as it does not contain characters not appearing in the initial-set of uni-grams. === Dataset cleaning === In the context of training LLMs, datasets are typically cleaned by removing low-quality, duplicated, or toxic data. Cleaned datasets can increase training efficiency and lead to improved downstream performance. A trained LLM can be used to clean datasets for training a further LLM. With the increasing proportion of LLM-generated content on the web, data cleaning in the future may include filtering out such content. LLM-generated content can pose a problem if the content is similar to human text (making filtering difficult) but of lower quality (degrading performance of models trained on it). === Synthetic data === Training of largest language models might need more linguistic data than naturally available, or that the naturally occurring data is of insufficient quality. In these cases, synthetic data might be used. == Training == An LLM is a type of foundation model (large X model) trained on language. LLMs can be trained in different ways. In particular, GPT models are first pretrained to predict the next word on a large amount of data, before being fine-tuned. === Cost === Substantial infrastructure is necessary for training the largest models. The tendency towards larger models is visible in the list of large language models. For example, the training of GPT-2 (i.e. a 1.5-billion-parameter model) in 2019 cost $50,000, while training of the PaLM (i.e. a 540-billion-parameter model) in 2022 cost $8 million, and Megatron-Turing NLG 530B (in 2021) cost around $11 million. The qualifier "large" in "large language model" is inherently vague, as there is no definitive threshold for the number of parameters required to qualify as "large". === Fine-tuning === Before being fine-tuned, most LLMs are next-token predictors. The fine-tuning shapes the LLM's behavior via techniques like reinforcement learning from human feedback (RLHF) or constitutional AI. Instruction fine-tuning is a form of supervised learning used to teach LLMs to follow user instructions. In 2022, OpenAI demonstrated InstructGPT, a version of GPT-3 similarly fine-tuned to follow instructions. Reinforcement learning from human feedback (RLHF) involves training a reward model to predict which text humans prefer. Then, the LLM can be fine-tuned through reinforcement learning to better satisfy this reward model. Since humans typically prefer truthful, helpful and harmless answers, RLHF favors such answers. == Architecture == LLMs are generally based on the tra
Textual entailment
In natural language processing, textual entailment (TE), also known as natural language inference (NLI), is a directional relation between text fragments. The relation holds whenever the truth of one text fragment follows from another text. == Definition == In the TE framework, the entailing and entailed texts are termed text (t) and hypothesis (h), respectively. Textual entailment is not the same as pure logical entailment – it has a more relaxed definition: "t entails h" (t ⇒ h) if, typically, a human reading t would infer that h is most likely true. (Alternatively: t ⇒ h if and only if, typically, a human reading t would be justified in inferring the proposition expressed by h from the proposition expressed by t.) The relation is directional because even if "t entails h", the reverse "h entails t" is much less certain. Determining whether this relationship holds is an informal task, one which sometimes overlaps with the formal tasks of formal semantics (satisfying a strict condition will usually imply satisfaction of a less strict conditioned); additionally, textual entailment partially subsumes word entailment. == Examples == Textual entailment can be illustrated with examples of three different relations: An example of a positive TE (text entails hypothesis) is: text: If you help the needy, God will reward you. hypothesis: Giving money to a poor man has good consequences. An example of a negative TE (text contradicts hypothesis) is: text: If you help the needy, God will reward you. hypothesis: Giving money to a poor man has no consequences. An example of a non-TE (text does not entail nor contradict) is: text: If you help the needy, God will reward you. hypothesis: Giving money to a poor man will make you a better person. == Ambiguity of natural language == A characteristic of natural language is that there are many different ways to state what one wants to say: several meanings can be contained in a single text and the same meaning can be expressed by different texts. This variability of semantic expression can be seen as the dual problem of language ambiguity. Together, they result in a many-to-many mapping between language expressions and meanings. The task of paraphrasing involves recognizing when two texts have the same meaning and creating a similar or shorter text that conveys almost the same information. Textual entailment is similar but weakens the relationship to be unidirectional. Mathematical solutions to establish textual entailment can be based on the directional property of this relation, by making a comparison between some directional similarities of the texts involved. == Approaches == Textual entailment measures natural language understanding as it asks for a semantic interpretation of the text, and due to its generality remains an active area of research. Many approaches and refinements of approaches have been considered, such as word embedding, logical models, graphical models, rule systems, contextual focusing, and machine learning. Practical or large-scale solutions avoid these complex methods and instead use only surface syntax or lexical relationships, but are correspondingly less accurate. As of 2005, state-of-the-art systems are far from human performance; a study found humans to agree on the dataset 95.25% of the time. Algorithms from 2016 had not yet achieved 90%. == Applications == Many natural language processing applications, like question answering, information extraction, summarization, multi-document summarization, and evaluation of machine translation systems, need to recognize that a particular target meaning can be inferred from different text variants. Typically entailment is used as part of a larger system, for example in a prediction system to filter out trivial or obvious predictions. Textual entailment also has applications in adversarial stylometry, which has the objective of removing textual style without changing the overall meaning of communication. == Datasets == Some of available English NLI datasets include: SNLI MultiNLI SciTail SICK MedNLI QA-NLI In addition, there are several non-English NLI datasets, as follows: XNLI DACCORD, RTE3-FR, SICK-FR for French FarsTail for Farsi OCNLI for Chinese SICK-NL for Dutch IndoNLI for Indonesian
Label noise
Label noise refers to errors or inaccuracies in the class labels of data instances. This is a widespread issue in machine learning datasets, arising from human annotator mistakes, unclear labeling instructions, automated labeling methods, or adversarial attacks in supervised learning. Label noise can be roughly divided into random noise, where labels are flipped independently of input features, and systematic noise, where mislabeling is dependent on certain patterns or biases in the data. Label noise can be damaging to model performance, especially for complex models that may overfit to noisy labels rather than generalizable patterns. Many approaches have been proposed to deal with the effects of label noise, including robust loss functions, noise-tolerant algorithms, data cleaning methods, and semi-supervised learning approaches. To reduce the impact of wrong labels during training, techniques like label smoothing, sample reweighting and using trusted validation sets are used. The role of noise-robust training paradigms and curriculum learning strategies to improve resilience against mislabeled data is also explored in recent research.
Expectation propagation
Expectation propagation (EP) is a technique in Bayesian machine learning. EP finds approximations to a probability distribution. It uses an iterative approach that uses the factorization structure of the target distribution. It differs from other Bayesian approximation approaches such as variational Bayesian methods. More specifically, suppose we wish to approximate an intractable probability distribution p ( x ) {\displaystyle p(\mathbf {x} )} with a tractable distribution q ( x ) {\displaystyle q(\mathbf {x} )} . Expectation propagation achieves this approximation by minimizing the Kullback–Leibler divergence K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} . Variational Bayesian methods minimize K L ( q | | p ) {\displaystyle \mathrm {KL} (q||p)} instead. If q ( x ) {\displaystyle q(\mathbf {x} )} is a Gaussian N ( x | μ , Σ ) {\displaystyle {\mathcal {N}}(\mathbf {x} |\mu ,\Sigma )} , then K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} is minimized with μ {\displaystyle \mu } and Σ {\displaystyle \Sigma } being equal to the mean of p ( x ) {\displaystyle p(\mathbf {x} )} and the covariance of p ( x ) {\displaystyle p(\mathbf {x} )} , respectively; this is called moment matching. == Applications == Expectation propagation via moment matching plays a vital role in approximation for indicator functions that appear when deriving the message passing equations for TrueSkill.
Artificial consciousness
Artificial consciousness, also known as machine consciousness, synthetic consciousness, or digital consciousness, is consciousness hypothesized to be possible for artificial intelligence. It is also the corresponding field of study, which draws insights from philosophy of mind, philosophy of artificial intelligence, cognitive science and neuroscience. The term "sentience" can be used when specifically designating ethical considerations stemming from a form of phenomenal consciousness (P-consciousness, or the ability to feel qualia). Since sentience involves the ability to experience ethically positive or negative (i.e., valenced) mental states, it may justify welfare concerns and legal protection, as with non-human animals. Some scholars believe that consciousness is generated by the interoperation of various parts of the brain; these mechanisms are labeled the neural correlates of consciousness (NCC). Some further believe that constructing a system (e.g., a computer system) that can emulate this NCC interoperation would result in a system that is conscious. Some scholars reject the possibility of non-biological conscious beings. == Philosophical views == As there are many hypothesized types of consciousness, there are many potential implementations of artificial consciousness. In the philosophical literature, perhaps the most common taxonomy of consciousness is into "access" and "phenomenal" variants. Access consciousness concerns those aspects of experience that can be apprehended, while phenomenal consciousness concerns those aspects of experience that seemingly cannot be apprehended, instead being characterized qualitatively in terms of "raw feels", "what it is like" or qualia. === Plausibility debate === Type-identity theorists and other skeptics hold the view that consciousness can be realized only in particular physical systems because consciousness has properties that necessarily depend on physical constitution. In his 2001 article "Artificial Consciousness: Utopia or Real Possibility," Giorgio Buttazzo says that a common objection to artificial consciousness is that, "Working in a fully automated mode, they [the computers] cannot exhibit creativity, unreprogrammation (which means can 'no longer be reprogrammed', from rethinking), emotions, or free will. A computer, like a washing machine, is a slave operated by its components." For other theorists (e.g., functionalists), who define mental states in terms of causal roles, any system that can instantiate the same pattern of causal roles, regardless of physical constitution, will instantiate the same mental states, including consciousness. ==== Thought experiments ==== David Chalmers proposed two thought experiments intending to demonstrate that "functionally isomorphic" systems (those with the same "fine-grained functional organization", i.e., the same information processing) will have qualitatively identical conscious experiences, regardless of whether they are based on biological neurons or digital hardware. The "fading qualia" is a reductio ad absurdum thought experiment. It involves replacing, one by one, the neurons of a brain with a functionally identical component, for example based on a silicon chip. Chalmers makes the hypothesis, knowing it in advance to be absurd, that "the qualia fade or disappear" when neurons are replaced one-by-one with identical silicon equivalents. Since the original neurons and their silicon counterparts are functionally identical, the brain's information processing should remain unchanged, and the subject's behaviour and introspective reports would stay exactly the same. Chalmers argues that this leads to an absurd conclusion: the subject would continue to report normal conscious experiences even as their actual qualia fade away. He concludes that the subject's qualia actually don't fade, and that the resulting robotic brain, once every neuron is replaced, would remain just as sentient as the original biological brain. Similarly, the "dancing qualia" thought experiment is another reductio ad absurdum argument. It supposes that two functionally isomorphic systems could have different perceptions (for instance, seeing the same object in different colors, like red and blue). It involves a switch that alternates between a chunk of brain that causes the perception of red, and a functionally isomorphic silicon chip, that causes the perception of blue. Since both perform the same function within the brain, the subject would not notice any change during the switch. Chalmers argues that this would be highly implausible if the qualia were truly switching between red and blue, hence the contradiction. Therefore, he concludes that the equivalent digital system would not only experience qualia, but it would perceive the same qualia as the biological system (e.g., seeing the same color). Greg Egan's short story Learning To Be Me (mentioned in §In fiction), illustrates how undetectable duplication of the brain and its functionality could be from a first-person perspective. Critics object that Chalmers' proposal begs the question in assuming that all mental properties and external connections are already sufficiently captured by abstract causal organization. Van Heuveln et al. argue that the dancing qualia argument contains an equivocation fallacy, conflating a "change in experience" between two systems with an "experience of change" within a single system. Mogensen argues that the fading qualia argument can be resisted by appealing to vagueness at the boundaries of consciousness and the holistic structure of conscious neural activity, which suggests consciousness may require specific biological substrates rather than being substrate-independent. Anil Seth argues that the complexity of brain neurons intrinsically matters in addition to their function and that it is not possible to replace any part of the brain with a perfect silicon equivalent. He points out that some of biological neurons exhibit activity aimed at cleaning up metabolic waste products, and writes that a perfect silicon replacement would require a silicon-based metabolism, but silicon is not suitable for creating such artificial metabolism. ==== In large language models ==== In 2022, Google engineer Blake Lemoine made a viral claim that Google's LaMDA chatbot was sentient. Lemoine supplied as evidence the chatbot's humanlike answers to many of his questions; however, the chatbot's behavior was judged by the scientific community as likely a consequence of mimicry, rather than machine sentience. Lemoine's claim was widely derided for being ridiculous. Moreover, attributing consciousness based solely on the basis of LLM outputs or the immersive experience created by an algorithm is considered a fallacy. However, while philosopher Nick Bostrom states that LaMDA is unlikely to be conscious, he additionally poses the question of "what grounds would a person have for being sure about it?" One would have to have access to unpublished information about LaMDA's architecture, and also would have to understand how consciousness works, and then figure out how to map the philosophy onto the machine: "(In the absence of these steps), it seems like one should be maybe a little bit uncertain. [...] there could well be other systems now, or in the relatively near future, that would start to satisfy the criteria." David Chalmers argued in 2023 that LLMs today display impressive conversational and general intelligence abilities, but are likely not conscious yet, as they lack some features that may be necessary, such as recurrent processing, a global workspace, and unified agency. Nonetheless, he considers that non-biological systems can be conscious, and suggested that future, extended models (LLM+s) incorporating these elements might eventually meet the criteria for consciousness, raising both profound scientific questions and significant ethical challenges. However, the view that consciousness can exist without biological phenomena is controversial and some reject it. Kristina Šekrst cautions that anthropomorphic terms such as "hallucination" can obscure important ontological differences between artificial and human cognition. While LLMs may produce human-like outputs, she argues that it does not justify ascribing mental states or consciousness to them. Instead, she advocates for an epistemological framework (such as reliabilism) that recognizes the distinct nature of AI knowledge production. She suggests that apparent understanding in LLMs may be a sophisticated form of AI hallucination. She also questions what would happen if an LLM were trained without any mention of consciousness. === Testing === Sentience is an inherently first-person phenomenon. Because of that, and due to the lack of an empirical definition of sentience, directly measuring it may be impossible. Although systems may display numerous behaviors correlated with sentience, determining whether a system is sentient is known as the hard pr
Artificial Linguistic Internet Computer Entity
A.L.I.C.E. (Artificial Linguistic Internet Computer Entity), also referred to as Alicebot, or simply Alice, is a natural language processing chatbot—a program that engages in a conversation with a human by applying some heuristical pattern matching rules to the human's input. It was inspired by Joseph Weizenbaum's classical ELIZA program. It is one of the strongest programs of its type and has won the Loebner Prize, awarded to accomplished humanoid, talking robots, three times (in 2000, 2001, and 2004). The program is unable to pass the Turing test, as even the casual user will often expose its mechanistic aspects in short conversations. Alice was originally composed by Richard Wallace; it "came to life" on November 23, 1995. The program was rewritten in Java beginning in 1998. The current incarnation of the Java implementation is Program D. The program uses an XML Schema called AIML (Artificial Intelligence Markup Language) for specifying the heuristic conversation rules. Alice code has been reported to be available as open source. The AIML source is available from ALICE A.I. Foundation on Google Code and from the GitHub account of Richard Wallace. These AIML files can be run using an AIML interpreter like Program O or Program AB. == In popular culture == Spike Jonze has cited ALICE as the inspiration for his academy award-winning film Her, in which a human falls in love with a chatbot. In a New Yorker article titled “Can Humans Fall in Love with Bots?” Jonze said “that the idea originated from a program he tried about a decade ago called the ALICE bot, which engages in friendly conversation.” The Los Angeles Times reported:Though the film’s premise evokes comparisons to Siri, Jonze said he actually had the idea well before the Apple digital assistant came along, after using a program called Alicebot about ten years ago. As geek nostalgists will recall, that intriguing if at times crude software (it flunked the industry-standard Turing Test) would attempt to engage users in everyday chatter based on a database of prior conversations. Jonze liked it, and decided to apply a film genre to it. “I thought about that idea, and what if you had a real relationship with it?” Jonze told reporters. “And I used that as a way to write a relationship movie and a love story.”
Description logic
Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order logic. In contrast to the latter, the core reasoning problems for DLs are (usually) decidable, and efficient decision procedures have been designed and implemented for these problems. There are general, spatial, temporal, spatiotemporal, and fuzzy description logics, and each description logic features a different balance between expressive power and reasoning complexity by supporting different sets of mathematical constructors. DLs are used in artificial intelligence to describe and reason about the relevant concepts of an application domain (known as terminological knowledge). It is of particular importance in providing a logical formalism for ontologies and the Semantic Web: the Web Ontology Language (OWL) and its profiles are based on DLs. A major area of application of DLs and OWL is in biomedical informatics, where they assist in the codification of biomedical knowledge. DLs and OWL are also applied in other domains, including defense, climate modeling, and large-scale industrial knowledge graphs. == Introduction == A DL models concepts, roles and individuals, and their relationships. The fundamental modeling concept of a DL is the axiom—a logical statement relating roles and/or concepts. This is a key difference from the frames paradigm where a frame specification declares and completely defines a class. == Nomenclature == === Terminology compared to FOL and OWL === The description logic community uses different terminology than the first-order logic (FOL) community for operationally equivalent notions; some examples are given below. The Web Ontology Language (OWL) uses again a different terminology, also given in the table below. === Naming convention === There are many varieties of description logics and there is an informal naming convention, roughly describing the operators allowed. The expressivity is encoded in the label for a logic starting with one of the following basic logics: Followed by any of the following extensions: ==== Exceptions ==== Some canonical DLs that do not exactly fit this convention are: ==== Examples ==== As an example, A L C {\displaystyle {\mathcal {ALC}}} is a centrally important description logic from which comparisons with other varieties can be made. A L C {\displaystyle {\mathcal {ALC}}} is simply A L {\displaystyle {\mathcal {AL}}} with complement of any concept allowed, not just atomic concepts. A L C {\displaystyle {\mathcal {ALC}}} is used instead of the equivalent A L U E {\displaystyle {\mathcal {ALUE}}} . A further example, the description logic S H I Q {\displaystyle {\mathcal {SHIQ}}} is the logic A L C {\displaystyle {\mathcal {ALC}}} plus extended cardinality restrictions, and transitive and inverse roles. The naming conventions aren't purely systematic so that the logic A L C O I N {\displaystyle {\mathcal {ALCOIN}}} might be referred to as A L C N I O {\displaystyle {\mathcal {ALCNIO}}} and other abbreviations are also made where possible. The Protégé ontology editor supports S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} . Three major biomedical informatics terminology bases, SNOMED CT, GALEN, and GO, are expressible in E L {\displaystyle {\mathcal {EL}}} (with additional role properties). OWL 2 provides the expressiveness of S R O I Q ( D ) {\displaystyle {\mathcal {SROIQ}}^{\mathcal {(D)}}} , OWL-DL is based on S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} , and for OWL-Lite it is S H I F ( D ) {\displaystyle {\mathcal {SHIF}}^{\mathcal {(D)}}} . == History == Description logic was given its current name in the 1980s. Previous to this it was called (chronologically): terminological systems, and concept languages. === Knowledge representation === Frames and semantic networks lack formal (logic-based) semantics. DL was first introduced into knowledge representation (KR) systems to overcome this deficiency. The first DL-based KR system was KL-ONE (by Ronald J. Brachman and Schmolze, 1985). During the '80s other DL-based systems using structural subsumption algorithms were developed including KRYPTON (1983), LOOM (1987), BACK (1988), K-REP (1991) and CLASSIC (1991). This approach featured DL with limited expressiveness but relatively efficient (polynomial time) reasoning. In the early '90s, the introduction of a new tableau based algorithm paradigm allowed efficient reasoning on more expressive DL. DL-based systems using these algorithms — such as KRIS (1991) — show acceptable reasoning performance on typical inference problems even though the worst case complexity is no longer polynomial. From the mid '90s, reasoners were created with good practical performance on very expressive DL with high worst case complexity. Examples from this period include FaCT, RACER (2001), CEL (2005), and KAON 2 (2005). DL reasoners, such as FaCT, FaCT++, RACER, DLP and Pellet, implement the method of analytic tableaux. KAON2 is implemented by algorithms which reduce a SHIQ(D) knowledge base to a disjunctive datalog program. === Semantic web === The DARPA Agent Markup Language (DAML) and Ontology Inference Layer (OIL) ontology languages for the Semantic Web can be viewed as syntactic variants of DL. In particular, the formal semantics and reasoning in OIL use the S H I Q {\displaystyle {\mathcal {SHIQ}}} DL. The DAML+OIL DL was developed as a submission to—and formed the starting point of—the World Wide Web Consortium (W3C) Web Ontology Working Group. In 2004, the Web Ontology Working Group completed its work by issuing the OWL recommendation. The design of OWL is based on the S H {\displaystyle {\mathcal {SH}}} family of DL with OWL DL and OWL Lite based on S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} and S H I F ( D ) {\displaystyle {\mathcal {SHIF}}^{\mathcal {(D)}}} respectively. The W3C OWL Working Group began work in 2007 on a refinement of - and extension to - OWL. In 2009, this was completed by the issuance of the OWL2 recommendation. OWL2 is based on the description logic S R O I Q ( D ) {\displaystyle {\mathcal {SROIQ}}^{\mathcal {(D)}}} . Practical experience demonstrated that OWL DL lacked several key features necessary to model complex domains. == Modeling == === TBox vs Abox === In DL, a distinction is drawn between the so-called TBox (terminological box) and the ABox (assertional box). In general, the TBox contains sentences describing concept hierarchies (i.e., relations between concepts) while the ABox contains ground sentences stating where in the hierarchy, individuals belong (i.e., relations between individuals and concepts). For example, the statement: belongs in the TBox, while the statement: belongs in the ABox. Note that the TBox/ABox distinction is not significant, in the same sense that the two "kinds" of sentences are not treated differently in first-order logic (which subsumes most DL). When translated into first-order logic, a subsumption axiom like (1) is simply a conditional restriction to unary predicates (concepts) with only variables appearing in it. Clearly, a sentence of this form is not privileged or special over sentences in which only constants ("grounded" values) appear like (2). === Motivation for having Tbox and Abox === So why was the distinction introduced? The primary reason is that the separation can be useful when describing and formulating decision-procedures for various DL. For example, a reasoner might process the TBox and ABox separately, in part because certain key inference problems are tied to one but not the other one ('classification' is related to the TBox, 'instance checking' to the ABox). Another example is that the complexity of the TBox can greatly affect the performance of a given decision-procedure for a certain DL, independently of the ABox. Thus, it is useful to have a way to talk about that specific part of the knowledge base. The secondary reason is that the distinction can make sense from the knowledge base modeler's perspective. It is plausible to distinguish between our conception of terms/concepts in the world (class axioms in the TBox) and particular manifestations of those terms/concepts (instance assertions in the ABox). In the above example: when the hierarchy within a company is the same in every branch but the assignment to employees is different in every department (because there are other people working there), it makes sense to reuse the TBox for different branches that do not use the same ABox. There are two features of description logic that are not shared by most other data description formalisms: DL does not make the unique name assumption (UNA) or the closed-world assumption (CWA). Not having UNA means that two concepts with different names may be allowed by some inference to be shown to be equivalent. Not having CWA, or rather having the open world assumption (OWA) means that