Data preprocessing can refer to manipulation, filtration or augmentation of data before it is analyzed, and is often an important step in the data mining process. Data collection methods are often loosely controlled, resulting in out-of-range values, impossible data combinations, and missing values, amongst other issues. Preprocessing is the process by which unstructured data is transformed into intelligible representations suitable for machine-learning models. This phase of model deals with noise in order to arrive at better and improved results from the original data set which was noisy. This dataset also has some level of missing value present in it. The preprocessing pipeline used can often have large effects on the conclusions drawn from the downstream analysis. Thus, representation and quality of data is necessary before running any analysis. If there is a high proportion of irrelevant and redundant information present or noisy and unreliable data, then knowledge discovery during the training phase may be more difficult. Data preparation and filtering steps can take a considerable amount of processing time. Examples of methods used in data preprocessing include cleaning, instance selection, normalization, one-hot encoding, data transformation, feature extraction and feature selection. == Applications == === Data mining === Data preprocessing allows for the removal of unwanted data with the use of data cleaning, this allows the user to have a dataset to contain more valuable information after the preprocessing stage for data manipulation later in the data mining process. Editing such dataset to either correct data corruption or human error is a crucial step to get accurate quantifiers like true positives, true negatives, false positives and false negatives found in a confusion matrix that are commonly used for a medical diagnosis. Users are able to join data files together and use preprocessing to filter any unnecessary noise from the data which can allow for higher accuracy. Users use Python programming scripts accompanied by the pandas library which gives them the ability to import data from a comma-separated values as a data-frame. The data-frame is then used to manipulate data that can be challenging otherwise to do in Excel. Pandas (software) which is a powerful tool that allows for data analysis and manipulation; which makes data visualizations, statistical operations and much more, a lot easier. Many also use the R programming language to do such tasks as well. The reason why a user transforms existing files into a new one is because of many reasons. Aspects of data preprocessing may include imputing missing values, aggregating numerical quantities and transforming continuous data into categories (data binning). More advanced techniques like principal component analysis and feature selection are working with statistical formulas and are applied to complex datasets which are recorded by GPS trackers and motion capture devices. === Semantic data preprocessing === Semantic data mining is a subset of data mining that specifically seeks to incorporate domain knowledge, such as formal semantics, into the data mining process. Domain knowledge is the knowledge of the environment the data was processed in. Domain knowledge can have a positive influence on many aspects of data mining, such as filtering out redundant or inconsistent data during the preprocessing phase. Domain knowledge also works as constraint. It does this by using working as set of prior knowledge to reduce the space required for searching and acting as a guide to the data. Simply put, semantic preprocessing seeks to filter data using the original environment of said data more correctly and efficiently. There are increasingly complex problems which are asking to be solved by more elaborate techniques to better analyze existing information. Instead of creating a simple script for aggregating different numerical values into a single value, it make sense to focus on semantic based data preprocessing. The idea is to build a dedicated ontology, which explains on a higher level what the problem is about. In regards to semantic data mining and semantic pre-processing, ontologies are a way to conceptualize and formally define semantic knowledge and data. The Protégé (software) is the standard tool for constructing an ontology. In general, the use of ontologies bridges the gaps between data, applications, algorithms, and results that occur from semantic mismatches. As a result, semantic data mining combined with ontology has many applications where semantic ambiguity can impact the usefulness and efficiency of data systems. Applications include the medical field, language processing, banking, and even tutoring, among many more. There are various strengths to using a semantic data mining and ontological based approach. As previously mentioned, these tools can help during the per-processing phase by filtering out non-desirable data from the data set. Additionally, well-structured formal semantics integrated into well designed ontologies can return powerful data that can be easily read and processed by machines. A specifically useful example of this exists in the medical use of semantic data processing. As an example, a patient is having a medical emergency and is being rushed to hospital. The emergency responders are trying to figure out the best medicine to administer to help the patient. Under normal data processing, scouring all the patient’s medical data to ensure they are getting the best treatment could take too long and risk the patients’ health or even life. However, using semantically processed ontologies, the first responders could save the patient’s life. Tools like a semantic reasoner can use ontology to infer the what best medicine to administer to the patient is based on their medical history, such as if they have a certain cancer or other conditions, simply by examining the natural language used in the patient's medical records. This would allow the first responders to quickly and efficiently search for medicine without having worry about the patient’s medical history themselves, as the semantic reasoner would already have analyzed this data and found solutions. In general, this illustrates the incredible strength of using semantic data mining and ontologies. They allow for quicker and more efficient data extraction on the user side, as the user has fewer variables to account for, since the semantically pre-processed data and ontology built for the data have already accounted for many of these variables. However, there are some drawbacks to this approach. Namely, it requires a high amount of computational power and complexity, even with relatively small data sets. This could result in higher costs and increased difficulties in building and maintaining semantic data processing systems. This can be mitigated somewhat if the data set is already well organized and formatted, but even then, the complexity is still higher when compared to standard data processing. Below is a simple a diagram combining some of the processes, in particular semantic data mining and their use in ontology. The diagram depicts a data set being broken up into two parts: the characteristics of its domain, or domain knowledge, and then the actual acquired data. The domain characteristics are then processed to become user understood domain knowledge that can be applied to the data. Meanwhile, the data set is processed and stored so that the domain knowledge can applied to it, so that the process may continue. This application forms the ontology. From there, the ontology can be used to analyze data and process results. Fuzzy preprocessing is another, more advanced technique for solving complex problems. Fuzzy preprocessing and fuzzy data mining make use of fuzzy sets. These data sets are composed of two elements: a set and a membership function for the set which comprises 0 and 1. Fuzzy preprocessing uses this fuzzy data set to ground numerical values with linguistic information. Raw data is then transformed into natural language. Ultimately, fuzzy data mining's goal is to help deal with inexact information, such as an incomplete database. Currently fuzzy preprocessing, as well as other fuzzy based data mining techniques see frequent use with neural networks and artificial intelligence.
And–or tree
An and–or tree is a graphical representation of the reduction of problems (or goals) to conjunctions and disjunctions of subproblems (or subgoals). == Example == The and–or tree: represents the search space for solving the problem P, using the goal-reduction methods: P if Q and R P if S Q if T Q if U == Definitions == Given an initial problem P0 and set of problem solving methods of the form: P if P1 and … and Pn the associated and–or tree is a set of labelled nodes such that: The root of the tree is a node labelled by P0. For every node N labelled by a problem or sub-problem P and for every method of the form P if P1 and ... and Pn, there exists a set of children nodes N1, ..., Nn of the node N, such that each node Ni is labelled by Pi. The nodes are conjoined by an arc, to distinguish them from children of N that might be associated with other methods. A node N, labelled by a problem P, is a success node if there is a method of the form P if nothing (i.e., P is a "fact"). The node is a failure node if there is no method for solving P. If all of the children of a node N, conjoined by the same arc, are success nodes, then the node N is also a success node. Otherwise the node is a failure node. == Search strategies == An and–or tree specifies only the search space for solving a problem. Different search strategies for searching the space are possible. These include searching the tree depth-first, breadth-first, or best-first using some measure of desirability of solutions. The search strategy can be sequential, searching or generating one node at a time, or parallel, searching or generating several nodes in parallel. == Relationship with logic programming == The methods used for generating and–or trees are propositional logic programs (without variables). In the case of logic programs containing variables, the solutions of conjoint sub-problems must be compatible. Subject to this complication, sequential and parallel search strategies for and–or trees provide a computational model for executing logic programs. == Relationship with two-player games == And–or trees can also be used to represent the search spaces for two-person games. The root node of such a tree represents the problem of one of the players winning the game, starting from the initial state of the game. Given a node N, labelled by the problem P of the player winning the game from a particular state of play, there exists a single set of conjoint children nodes, corresponding to all of the opponents responding moves. For each of these children nodes, there exists a set of non-conjoint children nodes, corresponding to all of the player's defending moves. For solving game trees with proof-number search family of algorithms, game trees are to be mapped to and–or trees. MAX-nodes (i.e. maximizing player to move) are represented as OR nodes, MIN-nodes map to AND nodes. The mapping is possible, when the search is done with only a binary goal, which usually is "player to move wins the game".
Data-centric AI
Data-centric AI is an approach within artificial intelligence that emphasizes on improving the quality, consistency and representativeness of the data used to train machine learning models, rather than focusing primarily on optimizing model architectures or algorithms. This idea has gained traction as researchers and practitioners have come to believe that many performance limitations of machine learning systems stem from issues such as noisy labels, biased datasets, and lack of coverage in the data. Data-centric AI involves disciplined approach to data cleaning, augmentation, labeling, and governance that improves model performance and reliability in applications such as computer vision, natural language processing, and further.
Case-based reasoning
Case-based reasoning (CBR), broadly construed, is the process of solving new problems based on the solutions of similar past problems. In everyday life, an auto mechanic who fixes an engine by recalling another car that exhibited similar symptoms is using case-based reasoning. A lawyer who advocates a particular outcome in a trial based on legal precedents or a judge who creates case law is using case-based reasoning. So, too, an engineer copying working elements of nature (practicing biomimicry) is treating nature as a database of solutions to problems. Case-based reasoning is a prominent type of analogy solution making. It has been argued that case-based reasoning is not only a powerful method for computer reasoning, but also a pervasive behavior in everyday human problem solving; or, more radically, that all reasoning is based on past cases personally experienced. This view is related to prototype theory, which is most deeply explored in cognitive science. == Process == Case-based reasoning has been formalized for purposes of computer reasoning as a four-step process: Retrieve: Given a target problem, retrieve cases relevant to solving it from memory. A case consists of a problem, its solution, and, typically, annotations about how the solution was derived. For example, suppose Fred wants to prepare blueberry pancakes. Being a novice cook, the most relevant experience he can recall is one in which he successfully made plain pancakes. The procedure he followed for making the plain pancakes, together with justifications for decisions made along the way, constitutes Fred's retrieved case. Reuse: Map the solution from the previous case to the target problem. This may involve adapting the solution as needed to fit the new situation. In the pancake example, Fred must adapt his retrieved solution to include the addition of blueberries. Revise: Having mapped the previous solution to the target situation, test the new solution in the real world (or a simulation) and, if necessary, revise. Suppose Fred adapted his pancake solution by adding blueberries to the batter. After mixing, he discovers that the batter has turned blue – an undesired effect. This suggests the following revision: delay the addition of blueberries until after the batter has been ladled into the pan. Retain: After the solution has been successfully adapted to the target problem, store the resulting experience as a new case in memory. Fred, accordingly, records his new-found procedure for making blueberry pancakes, thereby enriching his set of stored experiences, and better preparing him for future pancake-making demands. == Comparison to other methods == At first glance, CBR may seem similar to the rule induction algorithms of machine learning. Like a rule-induction algorithm, CBR starts with a set of cases or training examples; it forms generalizations of these examples, albeit implicit ones, by identifying commonalities between a retrieved case and the target problem. If for instance a procedure for plain pancakes is mapped to blueberry pancakes, a decision is made to use the same basic batter and frying method, thus implicitly generalizing the set of situations under which the batter and frying method can be used. The key difference, however, between the implicit generalization in CBR and the generalization in rule induction lies in when the generalization is made. A rule-induction algorithm draws its generalizations from a set of training examples before the target problem is even known; that is, it performs eager generalization. For instance, if a rule-induction algorithm were given recipes for plain pancakes, Dutch apple pancakes, and banana pancakes as its training examples, it would have to derive, at training time, a set of general rules for making all types of pancakes. It would not be until testing time that it would be given, say, the task of cooking blueberry pancakes. The difficulty for the rule-induction algorithm is in anticipating the different directions in which it should attempt to generalize its training examples. This is in contrast to CBR, which delays (implicit) generalization of its cases until testing time – a strategy of lazy generalization. In the pancake example, CBR has already been given the target problem of cooking blueberry pancakes; thus it can generalize its cases exactly as needed to cover this situation. CBR therefore tends to be a good approach for rich, complex domains in which there are myriad ways to generalize a case. In law, there is often explicit delegation of CBR to courts, recognizing the limits of rule based reasons: limiting delay, limited knowledge of future context, limit of negotiated agreement, etc. While CBR in law and cognitively inspired CBR have long been associated, the former is more clearly an interpolation of rule based reasoning, and judgment, while the latter is more closely tied to recall and process adaptation. The difference is clear in their attitude toward error and appellate review. Another name for case-based reasoning in problem solving is symptomatic strategies. It does require à priori domain knowledge that is gleaned from past experience which established connections between symptoms and causes. This knowledge is referred to as shallow, compiled, evidential, history-based as well as case-based knowledge. This is the strategy most associated with diagnosis by experts. Diagnosis of a problem transpires as a rapid recognition process in which symptoms evoke appropriate situation categories. An expert knows the cause by virtue of having previously encountered similar cases. Case-based reasoning is the most powerful strategy, and that used most commonly. However, the strategy won't work independently with truly novel problems, or where deeper understanding of whatever is taking place is sought. An alternative approach to problem solving is the topographic strategy which falls into the category of deep reasoning. With deep reasoning, in-depth knowledge of a system is used. Topography in this context means a description or an analysis of a structured entity, showing the relations among its elements. Also known as reasoning from first principles, deep reasoning is applied to novel faults when experience-based approaches aren't viable. The topographic strategy is therefore linked to à priori domain knowledge that is developed from a more a fundamental understanding of a system, possibly using first-principles knowledge. Such knowledge is referred to as deep, causal or model-based knowledge. Hoc and Carlier noted that symptomatic approaches may need to be supported by topographic approaches because symptoms can be defined in diverse terms. The converse is also true – shallow reasoning can be used abductively to generate causal hypotheses, and deductively to evaluate those hypotheses, in a topographical search. == Criticism == Critics of CBR argue that it is an approach that accepts anecdotal evidence as its main operating principle. Without statistically relevant data for backing and implicit generalization, there is no guarantee that the generalization is correct. However, all inductive reasoning where data is too scarce for statistical relevance is inherently based on anecdotal evidence. == History == CBR traces its roots to the work of Roger Schank and his students at Yale University in the early 1980s. Schank's model of dynamic memory was the basis for the earliest CBR systems: Janet Kolodner's CYRUS and Michael Lebowitz's IPP. Other schools of CBR and closely allied fields emerged in the 1980s, which directed at topics such as legal reasoning, memory-based reasoning (a way of reasoning from examples on massively parallel machines), and combinations of CBR with other reasoning methods. In the 1990s, interest in CBR grew internationally, as evidenced by the establishment of an International Conference on Case-Based Reasoning in 1995, as well as European, German, British, Italian, and other CBR workshops. CBR technology has resulted in the deployment of a number of successful systems, the earliest being Lockheed's CLAVIER, a system for laying out composite parts to be baked in an industrial convection oven. CBR has been used extensively in applications such as the Compaq SMART system and has found a major application area in the health sciences, as well as in structural safety management. There is recent work that develops CBR within a statistical framework and formalizes case-based inference as a specific type of probabilistic inference. Thus, it becomes possible to produce case-based predictions equipped with a certain level of confidence. One description of the difference between CBR and induction from instances is that statistical inference aims to find what tends to make cases similar while CBR aims to encode what suffices to claim similarly.
World model (artificial intelligence)
A world model in artificial intelligence is a machine learning system that builds an internal representation of an environment. The model predicts how that environment changes over time in response to actions. Researchers design world models to help agents plan, reason, and act without constant real-world trial and error. World models differ from systems that merely classify or generate outputs. They simulate dynamics such as physics, object interactions, and causality. Early ideas date to the 1990s. Modern versions power robots, autonomous driving, and interactive video generation. == History == Jürgen Schmidhuber introduced the term world model in machine learning in 1990. He proposed recurrent neural networks that predict future states from observations and use those predictions to train agents. David Ha and Schmidhuber revived the concept in a 2018 paper. Their agents learned to drive virtual cars and play video games inside self-generated simulations. Yann LeCun advanced the idea in a 2022 position paper titled "A Path Towards Autonomous Machine Intelligence". He argued that intelligence requires predictive models of the world rather than pure pattern matching. LeCun proposed the joint embedding predictive architecture (JEPA) as a practical foundation. LeCun and collaborators developed several JEPA variants. V-JEPA 2 reached state-of-the-art performance on video understanding and physical reasoning at the time. It supports zero-shot robot control in unfamiliar environments. Introduced in March 2026, LeWorldModel trains stably end-to-end from raw pixels and uses two loss terms and avoids hand-crafted heuristics. LeCun founded Advanced Machine Intelligence Labs in 2026 to further develop world models. Google DeepMind introduced Genie in 2024. The model learned interactive environments from unlabeled internet videos. Genie 2 followed in late 2024 and added three-dimensional generation. The Genie series set benchmarks for general-purpose simulation. Genie 3 was introduced in August 2025. It produces photorealistic, real-time interactive worlds from text prompts which are displayed at 24 frames per second and explored in real time with text or image prompts. The model supports persistent three-dimensional worlds and real-time interaction. Waymo adopted Genie 3 in February 2026 and used it to create a specialized world model for autonomous driving simulation, called the Waymo World Model. It produces synchronized camera and lidar outputs and creates edge cases that real robotaxis rarely encounter. The edge cases were reported to be unusual by PCMag. General Intuition announced a $133.7 million seed round. World Labs raised $1 billion. AMI raised $1.03 billion. In April 2026, Alibaba announced Happy Oyster, its world model designed for real-time and “flowy” world model. It includes a directing mode for world building based on text and image prompts and a wandering mode for exploring the resulting world. It can generate 3-minute in-world video clips. Also in April, World Labs, co-founded by Li Fei Fei, unveiled Spark 2.0, an open-source 3D Gaussian splatting rendering engine that targets smartphone-class devices. In June 2026, Nvidia released Cosmos 3, a family of open-weight models. It combines previously independent physical reasoning, world simulation, and action generation. Cosmos 3 integrates can process and generate text, image, video, audio, and action sequences. The model employs a Mixture-of-Transformers" (MoT) approach. An autoregressive (AR) transformer handles reasoning and next-token prediction, while a diffusion transformer (DT) does multimodal generation. Encoders (ViT for vision, VAE for visual/audio, and domain-specific for actions) and generate a shared representation space using 3D multi-dimensional rotary position embedding (mRoPE) for spatial and temporal information. The family includes Cosmos3-Nano (16B parameters) for workstations; Cosmos3-Super (64B parameters) for research. == Architecture == World models process raw sensory data such as video frames or lidar scans. They compress this input into compact latent representations. The system then predicts future representations rather than pixel-by-pixel reconstructions. Many modern world models use joint embedding predictive architecture (JEPA). An encoder turns observations into embeddings. A predictor estimates one or a suite of embeddings from the current one and an action. In some cases a critic chooses one embedding as the best result. A regularizer keeps embeddings well-behaved. The model trains by minimizing prediction error in embedding space. This approach avoids the high cost of generating every detail. Some architectures add explicit components. A fast reactive path handles immediate responses. A slower deliberative path performs longer-horizon planning. Video prediction accuracy or robot success rates are key metrics, but do not always predict real-world performance. Generative world models such as Genie 3 combine these with a simulator. They accept text prompts or layouts and output consistent video, lidar, or three-dimensional scenes. World models often train with self-supervised learning. They use large unlabeled datasets of video or robot interactions. Self-supervised learning can speed learning. Reinforcement learning can fine-tune a model for specific tasks. == Applications == World models support robot learning. Agents train inside simulations and transfer skills to the physical world. This reduces the need for dangerous or expensive real-world trials. Autonomous vehicles use world models to test rare events. Waymo's system simulates tornadoes or unusual pedestrian behavior. Companies train planners without putting vehicles on public roads. Interactive entertainment benefits from world models. Genie 3 lets users generate playable environments from simple descriptions. Game studios prototype levels faster. Scientific simulation gains from these models. Researchers model physical systems or biological processes at scale. Planners in logistics or urban design test strategies inside accurate digital twins. == Comparison with large language models == Both world models and large language models (LLMs) use inferencing on their inputs to make predictions. LLMs operate on textual inputs. They predict the next token in text sequences. They excel at language-oriented tasks such as translation or summarization. However, they lack understanding of physics. World models operate on sensor inputs such as pixels. They predict state changes in that data in latent space. This design supports planning and causal reasoning. LLMs generate fluent text but often fail at consistent physical predictions. Their architecture employs transformers with refinements such as mixture of experts. World models divide an inferencing task into work performed by encoders, predictors, simulators, and other pieces. They typically handle multimodal inputs such as video, lidar, radar, and audio, guided by textual prompting. LLMs power chatbots and code assistants. World models drive embodied agents that act in dynamic environments, such as autonomous driving. The two may be combined in hybrid systems. For example, a LLM handles instructions, while a world model manages low-level control. World model proponents such as LeCun claim that because LLMs are trained only on text, they have no ability to predict anything beyond text, such as real-world events. == Benchmarks == World model benchmarks test physical understanding, long-term consistency, planning, and generalization from sensor data. Meta introduced three benchmarks for V-JEPA 2. IntPhys 2 measures a model's ability to detect physics violations. It presents pairs of videos that diverge when one breaks physical rules. Humans score near 100% accuracy. V-JEPA 2 achieves little better than random chance on many conditions. Minimal Video Pairs (MVPBench) tests physical understanding through multiple-choice questions based on short video clips. It probes object interactions and causality. Something-Something tests action recognition. Epic-Kitchens-100 tests human action anticipation. DeepMind benchmark: Interactive evaluation measures consistency over minutes of interaction, memory of off-screen objects, and response to user actions or text prompts. Waymo benchmark: Output generation quality: Metrics include realism, controllability (via text prompts), and usefulness for training planners in simulated worlds. However, pixel reconstruction error rate with episodic rewards often fails. Other: Epic-Kitchens-100 (often measured with Recall@5) Ego4D 50 Salads, Breakfast, etc. Potential benchmarks: Zero-shot transfer to robots Long-horizon planning Implausible prediction rate
Enterprise cognitive system
Enterprise cognitive systems (ECS) are part of a broader shift in computing, from a programmatic to a probabilistic approach, called cognitive computing. An Enterprise Cognitive System makes a new class of complex decision support problems computable, where the business context is ambiguous, multi-faceted, and fast-evolving, and what to do in such a situation is usually assessed today by the business user. An ECS is designed to synthesize a business context and link it to the desired outcome. It recommends evidence-based actions to help the end-user achieve the desired outcome. It does so by finding past situations similar to the current situation, and extracting the repeated actions that best influence the desired outcome. While general-purpose cognitive systems can be used for different outputs, prescriptive, suggestive, instructive, or simply entertaining, an enterprise cognitive system is focused on action, not insight, to help in assessing what to do in a complex situation. == Key characteristics == ECS have to be: Adaptive: They must learn as information changes, and as goals and requirements evolve. They must resolve ambiguity and tolerate unpredictability. They must be engineered to feed on dynamic data in real time, or near real time. In the Enterprise, near-real time learning from data requires an agile information federation approach to ingest incremental data updates as they occur, and an unsupervised learning approach to ensure that new best practice is leveraged across the organization in a timely manner. Interactive: They must interact easily with users so that those users can define their needs comfortably. They may also interact with other processors, devices, and Cloud services, as well as with people. In the Enterprise, interactions are controlled via existing workflows and UIs. Therefore, embedding best practices directly into these existing interfaces, in the context of a specific step, is critical to ensure maximum end-user adoption. Iterative and stateful: They must aid in defining a problem by asking questions or finding additional source input if a problem statement is ambiguous or incomplete. They must “remember” previous interactions in a process and return information that is suitable for the specific application at that point in time. In the Enterprise, business context is often structured by a business process, and therefore sufficiently data-rich to make relevant recommendations without significant iterations from the end-user. A stateful memory of overall interactions across communication channels is critical for understanding of context, as a static profile will not capture intent and outcome potential the way behavior does. Contextual: They must understand, identify, and extract contextual elements such as meaning, syntax, time, location, appropriate domain, regulations, user's profile, process, task and goal. They may draw on multiple sources of information, including both structured and unstructured digital information, as well as sensory inputs (visual, gestural, auditory, or sensor-provided). In the Enterprise, Context is fragmented and must be aggregated across data types, sources, and locations. In most business environments, such data is captured in existing enterprise information systems, and the effort is linked to quickly source and unify such information. It is rare to have to directly process sensor, audio or visual data in real-time as direct input into the enterprise cognitive system. Instead, these data types are captured by Enterprise Applications and pre-processed into a binary or text format prior to consumption by the System. == Business applications powered by an ECS == Bottlenose – trends and brands monitoring Cybereason – security threat monitoring Dataminr – social media monitoring
Decision list
Decision lists are a representation for Boolean functions which can be easily learned from examples. Single term decision lists are more expressive than disjunctions and conjunctions; however, 1-term decision lists are less expressive than the general disjunctive normal form and the conjunctive normal form. The language specified by a k-length decision list includes as a subset the language specified by a k-depth decision tree. Learning decision lists can be used for attribute efficient learning, a type of machine learning. == Definition == A decision list (DL) of length r is of the form: if f1 then output b1 else if f2 then output b2 ... else if fr then output br where fi is the ith formula and bi is the ith boolean for i ∈ { 1... r } {\displaystyle i\in \{1...r\}} . The last if-then-else is the default case, which means formula fr is always equal to true. A k-DL is a decision list where all of formulas have at most k terms. Sometimes "decision list" is used to refer to a 1-DL, where all of the formulas are either a variable or its negation.