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They are defined by the following Bayesian program: Pr { D s { S p ( π ) { V a : S 0 , … , S T , O 0 , … , O T D c : { P ( S 0 ∧ ⋯ ∧ O T ∣ π ) = [ P ( S 0 ∧ O 0 ∣ π ) ∏ t = 1 T [ P ( S t ∣ S t − 1 ∧ π ) × P ( O t ∣ S t ∧ π ) ] ] F o : { P ( S 0 ∧ O 0 ∣ π ) ≡ Matrix P ( S t ∣ S t − 1 ∧ π ) ≡ Matrix P ( O t ∣ S t ∧ π ) ≡... | Wikipedia - Bayesian programming - Example > Bayesian filter, Kalman filter and hidden Markov model > Hidden Markov model | 332 | 679 | null |
_{t=1}^{T}\left[P\left(S^{t}\mid S^{t-1}\wedge \pi \right)\times P\left(O^{t}\mid S^{t}\wedge \pi \right)\right]\end{array}}\right]\end{cases}}\\Fo:\\{\begin{cases}P\left(S^{0}\wedge O^{0}\mid \pi \right)\equiv {\text{Matrix}}\\P\left(S^{t}\mid S^{t-1}\wedge \pi \right)\equiv {\text{Matrix}}\\P\left(O^{t}\mid S^{t}\wed... | Wikipedia - Bayesian programming - Example > Bayesian filter, Kalman filter and hidden Markov model > Hidden Markov model | 329 | 617 | null |
_{t=1}^{T}\left[P\left(S^{t}\mid S^{t-1}\wedge \pi \right)\times P\left(O^{t}\mid S^{t}\wedge \pi \right)\right]\end{array}}\right]\end{cases}}\\Fo:\\{\begin{cases}P\left(S^{0}\wedge O^{0}\mid \pi \right)\equiv {\text{Matrix}}\\P\left(S^{t}\mid S^{t-1}\wedge \pi \right)\equiv {\text{Matrix}}\\P\left(O^{t}\mid S^{t}\wed... | Wikipedia - Bayesian programming - Example > Bayesian filter, Kalman filter and hidden Markov model > Hidden Markov model | 423 | 871 | null |
The transition model P ( S t ∣ S t − 1 ∧ π ) {\displaystyle P\left(S^{t}\mid S^{t-1}\wedge \pi \right)} and the observation model P ( O t ∣ S t ∧ π ) {\displaystyle P\left(O^{t}\mid S^{t}\wedge \pi \right)} are both specified using probability matrices. The question most frequently asked of HMMs is: max S 1 ∧ ⋯ ∧ S T −... | Wikipedia - Bayesian programming - Example > Bayesian filter, Kalman filter and hidden Markov model > Hidden Markov model | 285 | 830 | null |
Section: Probabilistic programming. The purpose of probabilistic programming is to unify the scope of classical programming languages with probabilistic modeling (especially bayesian networks) to deal with uncertainty while profiting from the programming languages' expressiveness to encode complexity. Extended classica... | Wikipedia - Bayesian programming - Probabilistic programming | 237 | 1,284 | null |
Article: Behavior informatics. Behavior informatics (BI) is the informatics of behaviors so as to obtain behavior intelligence and behavior insights. BI is a research method combining science and technology, specifically in the area of engineering. The purpose of BI includes analysis of current behaviors as well as the... | Wikipedia - Behavior informatics - Summary | 258 | 1,508 | null |
Section: Research and applications. The first demonstrations of BC in humans and animals took place in the 1960s when Grey Walter demonstrated use of non-invasively recorded encephalogram (EEG) signals from a human subject to control a slide projector (Graimann et al., 2010). Soon after Jacques J. Vidal coined the term... | Wikipedia - Brain technology - Research and applications | 332 | 1,627 | null |
Article: Brilliant Labs. Brilliant Labs is a Singapore-based technology company that produces open source eyewear featuring artificial intelligence (AI). Brilliant Labs was founded in 2019 in Hong Kong by Bobak Tavangar, a former Apple program lead. Tavangar said he saw the potential for integrating the capabilities of... | Wikipedia - Brilliant Labs - Summary | 275 | 1,357 | null |
Section: Biography. Budapesti studied computational linguistics at Oxford University and Harvard University, Chinese Language at Tsinghua University and has an EMBA from Columbia Business School. When she was President of the Oxford computer science society, she was horrified to find out that only eight per cent of the... | Wikipedia - Ilona Budapesti - Biography | 213 | 1,128 | null |
Article: 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 wh... | Wikipedia - Case-based reasoning - Summary | 200 | 1,004 | null |
Section: 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 examp... | Wikipedia - Case-based reasoning - Process | 329 | 1,660 | null |
Section: 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... | Wikipedia - Case-based reasoning - Comparison to other methods | 347 | 1,758 | null |
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... | Wikipedia - Case-based reasoning - Comparison to other methods | 345 | 1,809 | null |
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 vi... | Wikipedia - Case-based reasoning - Comparison to other methods | 176 | 910 | null |
Section: 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, ... | Wikipedia - Case-based reasoning - History | 326 | 1,594 | null |
Article: Character computing. Character computing is a trans-disciplinary field of research at the intersection of computer science and psychology. It is any computing that incorporates the human character within its context. Character is defined as all features or characteristics defining an individual and guiding the... | Wikipedia - Character computing - Summary | 166 | 903 | null |
Section: Overview. Character computing can be viewed as an extension of the well-established field of affective computing. Based on the foundations of the different psychology branches, it advocates defining behavior as a compound attribute that is not driven by either personality, emotions, situation or cognition alon... | Wikipedia - Character computing - Overview | 328 | 1,821 | null |
Section: Character. The word character originates from the Greek word meaning “stamping tool”, referring to distinctive features and traits. Over the years it has been given many different connotations, like the moral character in philosophy, the temperament in psychology, a person in literature or an avatar in various... | Wikipedia - Character computing - Character | 199 | 1,120 | null |
Section: Areas. Research into character computing can be divided into three areas, which complement each other but can each be investigated separately. The first area is sensing and predicting character states and traits or ensuing behavior. The second area is adapting applications to certain character states or traits... | Wikipedia - Character computing - Areas | 186 | 1,053 | null |
Section: The Character-Behavior-Situation triad. Character computing is based on a holistic psychologically driven model of human behavior. Human behavior is modeled and predicted based on the relationships between a situation and a human's character. To further define character in a more formal or holistic manner, we ... | Wikipedia - Character computing - The Character-Behavior-Situation triad | 280 | 1,442 | null |
Section: Definition. At present, there is no widely agreed upon definition for cognitive computing in either academia or industry. In general, the term cognitive computing has been used to refer to new hardware and/or software that mimics the functioning of the human brain (2004). In this sense, cognitive computing is ... | Wikipedia - Cognitive computing - Definition | 305 | 1,605 | null |
Section: Applications. Education Even if cognitive computing can not take the place of teachers, it can still be a heavy driving force in the education of students. Cognitive computing being used in the classroom is applied by essentially having an assistant that is personalized for each individual student. This cognit... | Wikipedia - Cognitive computing - Applications | 324 | 1,823 | null |
This technology can also evaluate information about the patient, looking through every medical record in depth, searching for indications that can be the source of their problems. Commerce Together with Artificial Intelligence, it has been used in warehouse management systems to collect, store, organize and analyze all... | Wikipedia - Cognitive computing - Applications | 201 | 1,150 | null |
Section: Industry work. Cognitive computing in conjunction with big data and algorithms that comprehend customer needs, can be a major advantage in economic decision making. The powers of cognitive computing and artificial intelligence hold the potential to affect almost every task that humans are capable of performing... | Wikipedia - Cognitive computing - Industry work | 197 | 1,139 | null |
Article: Cognitive philology. Cognitive philology is the science that studies written and oral texts as the product of human mental processes. Studies in cognitive philology compare documentary evidence emerging from textual investigations with results of experimental research, especially in the fields of cognitive and... | Wikipedia - Cognitive philology - Summary | 337 | 1,948 | null |
Section: Concept. CEV proposes that an advanced AI system should derive its goals by extrapolating the idealized volition of humanity. This means aggregating and projecting human preferences into a coherent utility function that reflects what people would desire under ideal epistemic and moral conditions. Yudkowsky env... | Wikipedia - Coherent extrapolated volition - Concept | 199 | 978 | null |
Section: Criticism. Despite its philosophical appeal, CEV faces significant theoretical and practical challenges. One central critique is that human values are not stable or fixed; rather, they are deeply shaped by context, culture, and environment. The extrapolation of values could therefore lead to distortions, as in... | Wikipedia - Coherent extrapolated volition - Criticism | 299 | 1,513 | null |
Article: Commonsense knowledge (artificial intelligence). In artificial intelligence research, commonsense knowledge consists of facts about the everyday world, such as "Lemons are sour", or "Cows say moo", that all humans are expected to know. It is currently an unsolved problem in artificial general intelligence. The... | Wikipedia - Commonsense knowledge (artificial intelligence) - Summary | 343 | 1,658 | null |
Section: Commonsense reasoning. Commonsense reasoning simulates the human ability to use commonsense knowledge to make presumptions about the type and essence of ordinary situations they encounter every day, and to change their "minds" should new information come to light. This includes time, missing or incomplete info... | Wikipedia - Commonsense knowledge (artificial intelligence) - Commonsense reasoning | 224 | 1,235 | null |
Section: Commonsense knowledge base construction. Compiling comprehensive knowledge bases of commonsense assertions (CSKBs) is a long-standing challenge in AI research. From early expert-driven efforts like CYC and WordNet, significant advances were achieved via the crowdsourced OpenMind Commonsense project, which led ... | Wikipedia - Commonsense knowledge (artificial intelligence) - Commonsense knowledge base construction | 204 | 1,042 | null |
Section: Data. As an example, as of 2012 ConceptNet includes these 21 language-independent relations: IsA (An "RV" is a "vehicle") UsedFor HasA (A "rabbit" has a "tail") CapableOf Desires CreatedBy ("cake" can be created by "baking") PartOf Causes LocatedNear AtLocation (Somewhere a "Cook" can be at a "restaurant") Def... | Wikipedia - Commonsense knowledge (artificial intelligence) - Data | 207 | 712 | null |
Article: Computational heuristic intelligence. Computational heuristic intelligence (CHI) refers to specialized programming techniques in computational intelligence (also called artificial intelligence, or AI). These techniques have the express goal of avoiding complexity issues, also called NP-hard problems, by using ... | Wikipedia - Computational heuristic intelligence - Summary | 335 | 1,774 | null |
Of course, real programs and real problems both contain both feedforward and feedback components. A real example which illustrates this point is that of human cognition, which clearly involves both perceptual (bottom-up, feedback, sensor-oriented) and conceptual (top-down, feedforward, motor-oriented) information flows... | Wikipedia - Computational heuristic intelligence - Summary | 339 | 1,657 | null |
Section: Joke generators > Pun generation. An approach to analysis of humor is classification of jokes. A further step is an attempt to generate jokes basing on the rules that underlie classification. Simple prototypes for computer pun generation were reported in the early 1990s, based on a natural language generator p... | Wikipedia - Computational humor - Joke generators > Pun generation | 336 | 1,594 | null |
Section: Applications. A possible application for assistance in language acquisition is described in the section "Pun generation". Another envisioned use of joke generators is in cases of a steady supply of jokes where quantity is more important than quality. Another obvious, yet remote, direction is automated joke app... | Wikipedia - Computational humor - Applications | 224 | 1,152 | null |
Article: Computational intelligence. In computer science, computational intelligence (CI) refers to concepts, paradigms, algorithms and implementations of systems that are designed to show "intelligent" behavior in complex and changing environments. These systems are aimed at mastering complex tasks in a wide variety o... | Wikipedia - Computational intelligence - Summary | 307 | 1,711 | null |
Traditionally the three main pillars of CI have been Neural Networks, Fuzzy Systems and Evolutionary Computation. ... CI is an evolving field and at present in addition to the three main constituents, it encompasses computing paradigms like ambient intelligence, artificial life, cultural learning, artificial endocrine ... | Wikipedia - Computational intelligence - Summary | 334 | 1,838 | null |
Section: Relationship between hard and soft computing and artificial and computational intelligence. Artificial intelligence (AI) is used in the media, but also by some of the scientists involved, as a kind of umbrella term for the various techniques associated with it or with CI. Craenen and Eiben state that attempts ... | Wikipedia - Computational intelligence - Relationship between hard and soft computing and artificial and computational intelligence | 349 | 1,852 | null |
It requires a precisely stated analytical model of the task to be processed and a prewritten program, i.e. a fixed set of instructions. The models used are based on Boolean logic (also called crisp logic), where e.g. an element can be either a member of a set or not and there is nothing in between. When applied to real... | Wikipedia - Computational intelligence - Relationship between hard and soft computing and artificial and computational intelligence | 329 | 1,546 | null |
Section: History. In 1950, Alan Turing, one of the founding fathers of computer science, developed a test for computer intelligence known as the Turing test. In this test, a person can ask questions via a keyboard and a monitor without knowing whether his counterpart is a human or a computer. A computer is considered i... | Wikipedia - Computational intelligence - History | 341 | 1,827 | null |
Section: The main algorithmic approaches of CI and their applications > Fuzzy logic. Unlike conventional Boolean logic, fuzzy logic is based on fuzzy sets. In both models, a property of an object is defined as belonging to a set; in fuzzy logic, however, the membership is not sharply defined by a yes/no distinction, bu... | Wikipedia - Computational intelligence - The main algorithmic approaches of CI and their applications > Fuzzy logic | 297 | 1,541 | null |
Section: The main algorithmic approaches of CI and their applications > Neural networks. An important field of CI is the development of artificial neural networks (ANN) based on the biological ones, which can be defined by three main components: the cell-body which processes the information, the axon, which is a device... | Wikipedia - Computational intelligence - The main algorithmic approaches of CI and their applications > Neural networks | 292 | 1,532 | null |
Section: The main algorithmic approaches of CI and their applications > Evolutionary computation. Evolutionary computation can be seen as a family of methods and algorithms for global optimization, which are usually based on a population of candidate solutions. They are inspired by biological evolution and are often su... | Wikipedia - Computational intelligence - The main algorithmic approaches of CI and their applications > Evolutionary computation | 228 | 1,329 | null |
Section: The main algorithmic approaches of CI and their applications > Swarm intelligence. Swarm intelligence is based on the collective behavior of decentralized, self-organizing systems, typically consisting of a population of simple agents that interact locally with each other and with their environment. Despite th... | Wikipedia - Computational intelligence - The main algorithmic approaches of CI and their applications > Swarm intelligence | 164 | 984 | null |
Section: The main algorithmic approaches of CI and their applications > Bayesian networks. In complex application domains, Bayesian networks provide a means to efficiently store and evaluate uncertain knowledge. A Bayesian network is a probabilistic graphical model that represents a set of random variables and their co... | Wikipedia - Computational intelligence - The main algorithmic approaches of CI and their applications > Bayesian networks | 170 | 900 | null |
Section: Impact on university education. According to bibliometrics studies, computational intelligence plays a key role in research. All the major academic publishers are accepting manuscripts in which a combination of Fuzzy logic, neural networks and evolutionary computation is discussed. On the other hand, Computati... | Wikipedia - Computational intelligence - Impact on university education | 258 | 1,438 | null |
Article: Computer audition. Computer audition (CA) or machine listening is the general field of study of algorithms and systems for audio interpretation by machines. Since the notion of what it means for a machine to "hear" is very broad and somewhat vague, computer audition attempts to bring together several disciplin... | Wikipedia - Computer audition - Summary | 204 | 1,197 | null |
Section: Areas of study. Since audio signals are interpreted by the human ear–brain system, that complex perceptual mechanism should be simulated somehow in software for "machine listening". In other words, to perform on par with humans, the computer should hear and understand audio content much as humans do. Analyzing... | Wikipedia - Computer audition - Areas of study | 343 | 1,857 | null |
Section: Areas of study > Representation issues. Computer audition deals with audio signals that can be represented in a variety of fashions, from direct encoding of digital audio in two or more channels to symbolically represented synthesis instructions. Audio signals are usually represented in terms of analogue or di... | Wikipedia - Computer audition - Areas of study > Representation issues | 223 | 1,308 | null |
Section: Areas of study > Source separation. Since one of the basic characteristics of general audio is that it comprises multiple simultaneously sounding sources, such as multiple musical instruments, people talking, machine noises or animal vocalization, the ability to identify and separate individual sources is very... | Wikipedia - Computer audition - Areas of study > Source separation | 220 | 1,301 | null |
Article: Concurrent MetateM. Concurrent MetateM is a multi-agent language in which each agent is programmed using a set of (augmented) temporal logic specifications of the behaviour it should exhibit. These specifications are executed directly to generate the behaviour of the agent. As a result, there is no risk of inv... | Wikipedia - Concurrent MetateM - Summary | 174 | 916 | null |
Section: Temporal Connectives. The Temporal Connectives of Concurrent MetateM can divided into two categories, as follows: Strict past time connectives: '●' (weak last), '◎' (strong last), '◆' (was), '■' (heretofore), 'S' (since), and 'Z' (zince, or weak since). Present and future time connectives: '◯' (next), '◇' (som... | Wikipedia - Concurrent MetateM - Temporal Connectives | 152 | 441 | null |
Article: DABUS. DABUS (Device for the Autonomous Bootstrapping of Unified Sentience) is an artificial intelligence (AI) system created by Stephen Thaler. It reportedly conceived of two novel products — a food container constructed using fractal geometry, which enables rapid reheating, and a flashing beacon for attracti... | Wikipedia - DABUS - Summary | 279 | 1,434 | null |
Section: History in different jurisdictions > Australia. On 17 September 2019, Thaler filed an application to patent a "Food container and devices and methods for attracting enhanced attention," naming DABUS as the inventor. On 21 September 2020, IP Australia found that section 15(1) of the Patents Act 1990 (Cth) is in... | Wikipedia - DABUS - History in different jurisdictions > Australia | 211 | 999 | null |
Section: History in different jurisdictions > European Patent Office. On 17 October 2018 and 7 November 2018, Thaler filed two European patent applications with the European Patent Office. The first claimed invention was a "Food Container" and the second was "Devices and Methods for Attracting Enhanced Attention." On 2... | Wikipedia - DABUS - History in different jurisdictions > European Patent Office | 193 | 893 | null |
Section: History in different jurisdictions > United Kingdom. Similar applications were filed by Thaler to the United Kingdom Intellectual Property Office on 17 October and 7 November 2018. The Office asked Thaler to file statements of inventorship and of right of grant to a patent (Patent Form 7) in respect of each in... | Wikipedia - DABUS - History in different jurisdictions > United Kingdom | 331 | 1,610 | null |
Section: History in different jurisdictions > United States. The patent applications on the inventions were refused by the USPTO, which held that only natural persons can be named as inventors in a patent application. Thaler first fought this result by filing a complaint under Administrative Procedure Act (APA) allegin... | Wikipedia - DABUS - History in different jurisdictions > United States | 227 | 1,048 | null |
Article: Deep Learning Anti-Aliasing. Deep Learning Anti-Aliasing (DLAA) is a form of spatial anti-aliasing developed by Nvidia. DLAA depends on and requires Tensor Cores available in Nvidia RTX cards. DLAA is similar to Deep Learning Super Sampling (DLSS) in its anti-aliasing method, with one important differentiation... | Wikipedia - Deep Learning Anti-Aliasing - Summary | 180 | 801 | null |
Section: History. The first game that added support for DLAA was The Elder Scrolls Online, which implemented the feature in 2021. By June 2022, DLAA was only available in six games. This number rose to 17 by February 2023. In June 2023, TechPowerUp reported that "DLAA is seeing sluggish adoption among game developers",... | Wikipedia - Deep Learning Anti-Aliasing - History | 153 | 635 | null |
Section: Differences between TAA and DLAA. TAA is used in many modern video games and game engines; however, all previous implementations have used some form of manually written heuristics to prevent temporal artifacts such as ghosting and flickering. One example of this is neighborhood clamping which forcefully preven... | Wikipedia - Deep Learning Anti-Aliasing - Differences between TAA and DLAA | 183 | 949 | null |
Section: Reception. TechPowerUp found that "[c]ompared to TAA and DLSS, DLAA is clearly producing the best image quality, especially at lower resolutions", arguing that, while "DLSS was already doing a better job than TAA at reconstructing small objects", "DLAA does an even better job". In a Cyberpunk 2077 performance ... | Wikipedia - Deep Learning Anti-Aliasing - Reception | 181 | 764 | null |
Article: 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 ... | Wikipedia - Description logic - Summary | 205 | 1,090 | null |
Section: Nomenclature > Naming convention > 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 conc... | Wikipedia - Description logic - Nomenclature > Naming convention > Examples | 345 | 1,201 | null |
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 ) {\displa... | Wikipedia - Description logic - Nomenclature > Naming convention > Examples | 167 | 455 | null |
Section: History > 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-base... | Wikipedia - Description logic - History > Knowledge representation | 294 | 1,324 | null |
Section: History > 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... | Wikipedia - Description logic - History > Semantic web | 332 | 1,189 | null |
Section: 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 hierarch... | Wikipedia - Description logic - Modeling > TBox vs Abox | 227 | 978 | null |
Section: Modeling > 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 infe... | Wikipedia - Description logic - Modeling > Motivation for having Tbox and Abox | 332 | 1,610 | null |
Section: Formal description > Syntax > The description logic ALC. The prototypical DL Attributive Concept Language with Complements ( A L C {\displaystyle {\mathcal {ALC}}} ) was introduced by Manfred Schmidt-Schauß and Gert Smolka in 1991, and is the basis of many more expressive DLs. The following definitions follow ... | Wikipedia - Description logic - Formal description > Syntax > The description logic ALC | 208 | 721 | null |
Section: Formal description > Syntax > The description logic ALC > Concepts. The set of A L C {\displaystyle {\mathcal {ALC}}} concepts is the smallest set such that: The following are concepts: ⊤ {\displaystyle \top } (top is a concept) ⊥ {\displaystyle \bot } (bottom is a concept) Every A ∈ N C {\displaystyle A\in N_... | Wikipedia - Description logic - Formal description > Syntax > The description logic ALC > Concepts | 268 | 916 | null |
A terminological interpretation I = ( Δ I , ⋅ I ) {\displaystyle {\mathcal {I}}=(\Delta ^{\mathcal {I}},\cdot ^{\mathcal {I}})} over a signature ( N C , N R , N O ) {\displaystyle (N_{C},N_{R},N_{O})} consists of a non-empty set Δ I {\displaystyle \Delta ^{\mathcal {I}}} called the domain a interpretation function ⋅ I ... | Wikipedia - Description logic - Formal description > Semantics > The description logic ALC | 341 | 866 | null |
{I}}=C^{\mathcal {I}}\cup D^{\mathcal {I}}} (union means disjunction) ( C ⊓ D ) I = C I ∩ D I {\displaystyle (C\sqcap D)^{\mathcal {I}}=C^{\mathcal {I}}\cap D^{\mathcal {I}}} (intersection means conjunction) ( ¬ C ) I = Δ I ∖ C I {\displaystyle (\neg C)^{\mathcal {I}}=\Delta ^{\mathcal {I}}\setminus C^{\mathcal {I}}} (... | Wikipedia - Description logic - Formal description > Semantics > The description logic ALC | 299 | 606 | null |
C ) I = { x ∈ Δ I | for every y , ( x , y ) ∈ R I implies y ∈ C I } {\displaystyle (\forall R.C)^{\mathcal {I}}=\{x\in \Delta ^{\mathcal {I}}|{\text{for}}\;{\text{every}}\;y,(x,y)\in R^{\mathcal {I}}\;{\text{implies}}\;y\in C^{\mathcal {I}}\}} ( ∃ R . C ) I = { x ∈ Δ I | there exists y , ( x , y ) ∈ R I and y ∈ C I } {... | Wikipedia - Description logic - Formal description > Semantics > The description logic ALC | 291 | 572 | null |
Section: Formal description > Semantics > The description logic ALC > TBox. I ⊨ C ⊑ D {\displaystyle {\mathcal {I}}\models C\sqsubseteq D} if and only if C I ⊆ D I {\displaystyle C^{\mathcal {I}}\subseteq D^{\mathcal {I}}} I ⊨ T {\displaystyle {\mathcal {I}}\models {\mathcal {T}}} if and only if I ⊨ Φ {\displaystyle {\... | Wikipedia - Description logic - Formal description > Semantics > The description logic ALC > TBox | 154 | 402 | null |
Section: Formal description > Semantics > The description logic ALC > ABox. I ⊨ a : C {\displaystyle {\mathcal {I}}\models a:C} if and only if a I ∈ C I {\displaystyle a^{\mathcal {I}}\in C^{\mathcal {I}}} I ⊨ ( a , b ) : R {\displaystyle {\mathcal {I}}\models (a,b):R} if and only if ( a I , b I ) ∈ R I {\displaystyle ... | Wikipedia - Description logic - Formal description > Semantics > The description logic ALC > ABox | 232 | 556 | null |
Section: Inference > Decision problems. In addition to the ability to describe concepts formally, one also would like to employ the description of a set of concepts to ask questions about the concepts and instances described. The most common decision problems are basic database-query-like questions like instance checki... | Wikipedia - Description logic - Inference > Decision problems | 191 | 991 | null |
Article: Data Science and Predictive Analytics. The first edition of the textbook Data Science and Predictive Analytics: Biomedical and Health Applications using R, authored by Ivo D. Dinov, was published in August 2018 by Springer. The second edition of the book was printed in 2023. This textbook covers some of the co... | Wikipedia - Data Science and Predictive Analytics - Summary | 151 | 796 | null |
Section: Structure > Second edition table of contents. The significantly reorganized revised edition of the book (2023) expands and modernizes the presented mathematical principles, computational methods, data science techniques, model-based machine learning and model-free artificial intelligence algorithms. The 14 cha... | Wikipedia - Data Science and Predictive Analytics - Structure > Second edition table of contents | 165 | 1,059 | null |
Section: Reception. The materials in the Data Science and Predictive Analytics (DSPA) textbook have been peer-reviewed in the Journal of the American Statistical Association, International Statistical Institute’s ISI Review Journal, and the Journal of the American Library Association. Many scholarly publications refere... | Wikipedia - Data Science and Predictive Analytics - Reception | 152 | 780 | null |
Article: Dynamic epistemic logic. Dynamic epistemic logic (DEL) is a logical framework dealing with knowledge and information change. Typically, DEL focuses on situations involving multiple agents and studies how their knowledge changes when events occur. These events can change factual properties of the actual world (... | Wikipedia - Dynamic epistemic logic - Summary | 344 | 1,733 | null |
Section: Epistemic Logic. Epistemic logic is a modal logic dealing with the notions of knowledge and belief. As a logic, it is concerned with understanding the process of reasoning about knowledge and belief: which principles relating the notions of knowledge and belief are intuitively plausible? Like epistemology, it ... | Wikipedia - Dynamic epistemic logic - Epistemic Logic | 343 | 1,433 | null |
For example, the interaction axioms K p → B p {\displaystyle Kp\rightarrow Bp} and B p → K B p {\displaystyle Bp\rightarrow KBp} are often considered to be intuitive principles: if an agent Knows p {\displaystyle p} then (s)he also Believes p {\displaystyle p} , or if an agent Believes p {\displaystyle p} , then (s)he ... | Wikipedia - Dynamic epistemic logic - Epistemic Logic | 179 | 752 | null |
Formally, the epistemic language L EL C {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}} is defined inductively by the following grammar in BNF: L EL C : ϕ ::= p ∣ ¬ ϕ ∣ ( ϕ ∧ ϕ ) ∣ K j ϕ ∣ C A ϕ ∣ D A ϕ {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}:\phi ~~::=~~p~\mid ~\neg \phi ~\mid ~(\phi \land \phi )~\mid ~K_{j... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Syntax | 290 | 700 | null |
The basic epistemic language L E L {\displaystyle {\mathcal {L}}_{EL}} is the language L E L C {\displaystyle {\mathcal {L}}_{EL}^{C}} without the common knowledge and distributed knowledge operators. The formula ⊥ {\displaystyle \bot } is an abbreviation for ¬ p ∧ p {\displaystyle \neg p\land p} (for a given p ∈ P R O... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Syntax | 342 | 1,187 | null |
General knowledge. General knowledge of ϕ {\displaystyle \phi } means that everybody in the group of agents A G T S {\displaystyle {AGTS}} knows that ϕ {\displaystyle \phi } . Formally, this corresponds to the following formula: E ϕ := ⋀ j ∈ A G T S K j ϕ . {\displaystyle E\phi :={\underset {j\in {AGTS}}{\bigwedge }}K_... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Syntax | 329 | 1,297 | null |
Lewis wanted to know what kind of knowledge is needed so that the statement p {\displaystyle p} : “every driver must drive on the right” be a convention among a group of agents. In other words, he wanted to know what kind of knowledge is needed so that everybody feels safe to drive on the right. Suppose there are only ... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Syntax | 286 | 1,125 | null |
This is again not enough to ensure that everybody feels safe to drive on the right. Indeed, it might still be possible that agent i {\displaystyle i} considers possible that agent j {\displaystyle j} considers possible that agent i {\displaystyle i} does not know p {\displaystyle p} (formally ¬ K i K j K i p {\displays... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Syntax | 329 | 1,131 | null |
Section: Epistemic Logic > Semantics. Epistemic logic is a modal logic. So, what we call an epistemic model M = ( W , R 1 , … , R n , I ) {\displaystyle {\mathcal {M}}=(W,R_{1},\ldots ,R_{n},I)} is just a Kripke model as defined in modal logic. The set W {\displaystyle W} is a non-empty set whose elements are called po... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Semantics | 245 | 814 | null |
The accessibility relations R j ⊆ W × W {\displaystyle R_{j}\subseteq W\times W} are binary relations for each agent j ∈ A G T S {\displaystyle j\in AGTS} ; they are intended to capture the uncertainty of each agent (about the actual world and about the other agents' uncertainty). Intuitively, we have ( w , v ) ∈ R j {... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Semantics | 282 | 870 | null |
We abusively write w ∈ M {\displaystyle w\in {\mathcal {M}}} for w ∈ W {\displaystyle w\in W} and R j ( w ) {\displaystyle R_{j}(w)} denotes the set of worlds { v ∈ W ; ( w , v ) ∈ R j } {\displaystyle \{v\in W;(w,v)\in R_{j}\}} . Intuitively, a pointed epistemic model ( M , w ) {\displaystyle ({\mathcal {M}},w)} , whe... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Semantics | 191 | 509 | null |
For every epistemic model M {\displaystyle {\mathcal {M}}} , every w ∈ M {\displaystyle w\in {\mathcal {M}}} and every ϕ ∈ L EL {\displaystyle \phi \in {\mathcal {L}}_{\textsf {EL}}} , we define M , w ⊨ ϕ {\displaystyle {\mathcal {M}},w\models \phi } inductively by the following truth conditions: where ( ⋃ j ∈ A R j ) ... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Semantics | 348 | 808 | null |
w_{0}=w,w_{m}=v} and for all i ∈ { 1 , … , m } {\displaystyle i\in \{1,\ldots ,m\}} , w i − 1 R j i w i {\displaystyle w_{i-1}R_{j_{i}}w_{i}} . Despite the fact that the notion of common belief has to be introduced as a primitive in the language, we can notice that the definition of epistemic models does not have to be... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Semantics | 265 | 895 | null |
This example is depicted in the pointed epistemic model ( M , w ) {\displaystyle ({\mathcal {M}},w)} represented below. In this example, A G T S := { A , B , C } {\displaystyle AGTS:=\{A,B,C\}} and P R O P := { A , B , C , B , C , A , C , A , B } {\displaystyle PROP:=\{{\color {red}{A}},{\color {green}{B}},{\color {blu... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Semantics | 319 | 803 | null |
There is an arrow indexed by agent j ∈ { A , B , C } {\displaystyle j\in \{A,B,C\}} from a possible world u {\displaystyle u} to a possible world v {\displaystyle v} when ( u , v ) ∈ R j {\displaystyle (u,v)\in R_{j}} . Reflexive arrows are omitted, which means that for all j ∈ { A , B , C } {\displaystyle j\in \{A,B,C... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Semantics | 275 | 723 | null |
A {\displaystyle {\color {red}{A}}} stands for : " A {\displaystyle A} has the red card'' C {\displaystyle {\color {blue}{C}}} stand for: " C {\displaystyle C} has the blue card'' B {\displaystyle {\color {green}{B}}} stands for: " B {\displaystyle B} has the green card'' and so on... When accessibility relations are e... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Semantics | 334 | 1,027 | null |
So, for example, A {\textstyle A} cannot distinguish the actual world w {\displaystyle w} from the possible world where B {\displaystyle B} has the blue card ( B {\displaystyle {\color {blue}{B}}} ), C {\displaystyle C} has the green card ( C {\displaystyle {\color {green}{C}}} ) and A {\displaystyle A} still has the r... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Semantics | 275 | 715 | null |
In particular, the following statements hold: M , w ⊨ ( A ∧ K A A ) ∧ ( C ∧ K C C ) ∧ ( B ∧ K B B ) {\displaystyle {\mathcal {M}},w\models ({\color {red}{A}}\land K_{A}{\color {red}{A}})\land ({\color {blue}{C}}\land K_{C}{\color {blue}{C}})\land ({\color {green}{B}}\land K_{B}{\color {green}{B}})} 'All the agents know... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Semantics | 297 | 689 | null |
M , w ⊨ K A ( B ∨ B ) ∧ K A ( C ∨ C ) {\displaystyle {\mathcal {M}},w\models K_{A}({\color {blue}{B}}\vee {\color {green}{B}})\land K_{A}({\color {blue}{C}}\vee {\color {green}{C}})} ' A {\displaystyle A} knows that B {\displaystyle B} has either the blue or the green card and that C {\displaystyle C} has either the bl... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Semantics | 291 | 699 | null |
Section: Epistemic Logic > Knowledge versus Belief. We use the same notation K j {\displaystyle K_{j}} for both knowledge and belief. Hence, depending on the context, K j ϕ {\displaystyle K_{j}\phi } will either read ‘the agent j {\displaystyle j} Knows that ϕ {\displaystyle \phi } holds’ or ‘the agent j {\displaystyle... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Knowledge versus Belief | 320 | 1,218 | null |
These constraints might affect the nature of the accessibility relations R j {\displaystyle R_{j}} which may then comply to some extra properties. So, we are now going to define some particular classes of epistemic models that all add some extra constraints on the accessibility relations R j {\displaystyle R_{j}} . The... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Knowledge versus Belief | 348 | 1,432 | null |
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