Weighted arithmetic mean

averageaverage ratingweighted average
Summary statistics. Weight function. Weighted average cost of capital. Weighted geometric mean. Weighted harmonic mean. Weighted least squares. Weighted median. Weighting.

Statistical theory

statisticalstatistical theoriesmathematical statistics
Statistical theory provides a basis for good data collection and the structuring of investigations in the topics of: The task of summarising statistical data in conventional forms (also known as descriptive statistics) is considered in theoretical statistics as a problem of defining what aspects of statistical samples need to be described and how well they can be described from a typically limited sample of data.


Descriptive statistics. Quartile. Q–Q plot. Quantile function. Quantile normalization. Quantile regression. Quantization. Summary statistics. Tolerance interval ("confidence intervals for the pth quantile" ).

Statistical inference

inferenceinferential statisticsinferences
In minimizing description length (or descriptive complexity), MDL estimation is similar to maximum likelihood estimation and maximum a posteriori estimation (using maximum-entropy Bayesian priors). However, MDL avoids assuming that the underlying probability model is known; the MDL principle can also be applied without assumptions that e.g. the data arose from independent sampling. The MDL principle has been applied in communication-coding theory in information theory, in linear regression, and in data mining. The evaluation of MDL-based inferential procedures often uses techniques or criteria from computational complexity theory.

Complexity class

complexity classescomputational complexityclasses
Many complexity classes can be characterized in terms of the mathematical logic needed to express them; see descriptive complexity. The most commonly used problems are decision problems. However, complexity classes can be defined based on function problems (an example is FP), counting problems (e.g. #P), optimization problems, promise problems, etc. The most common model of computation is the deterministic Turing machine, but many complexity classes are based on nondeterministic Turing machines, boolean circuits, quantum Turing machines, monotone circuits, etc.

Finite model theory

finite modelsfinite model
Thus the main application areas of FMT are: descriptive complexity theory, database theory and formal language theory. FMT is mainly about discrimination of structures. The usual motivating question is whether a given class of structures can be described (up to isomorphism) in a given language. For instance, can all cyclic graphs be discriminated (from the non-cyclic ones) by a sentence of the first-order logic of graphs? This can also be phrased as: is the property "cyclic" FO expressible?.

Nonparametric statistics

non-parametricnonparametricnon-parametric statistics
Nonparametric statistics includes both descriptive statistics and statistical inference. The term "nonparametric statistics" has been imprecisely defined in the following two ways, among others. Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels of measurement, non-parametric methods result in ordinal data. As non-parametric methods make fewer assumptions, their applicability is much wider than the corresponding parametric methods.

Artificial intelligence

AIartificially intelligentA.I.
The semantics of these are captured as description logic concepts, roles, and individuals, and typically implemented as classes, properties, and individuals in the Web Ontology Language. The most general ontologies are called upper ontologies, which attempt to provide a foundation for all other knowledge by acting as mediators between domain ontologies that cover specific knowledge about a particular knowledge domain (field of interest or area of concern).

Web Ontology Language

OWLWeb Ontology Language (OWL)OWL2
Description logics are a family of logics that are decidable fragments of first-order logic with attractive and well-understood computational properties. OWL DL and OWL Lite semantics are based on DLs. They combine a syntax for describing and exchanging ontologies, and formal semantics that gives them meaning. For example, OWL DL corresponds to the description logic, while OWL 2 corresponds to the logic. Sound, complete, terminating reasoners (i.e. systems which are guaranteed to derive every consequence of the knowledge in an ontology) exist for these DLs.

Semantic Web

It involves publishing in languages specifically designed for data: Resource Description Framework (RDF), Web Ontology Language (OWL), and Extensible Markup Language (XML). HTML describes documents and the links between them. RDF, OWL, and XML, by contrast, can describe arbitrary things such as people, meetings, or airplane parts. These technologies are combined in order to provide descriptions that supplement or replace the content of Web documents.

Query (complexity)

In descriptive complexity, a query is a mapping from structures of one signature to structures of another vocabulary. Neil Immerman, in his book Descriptive Complexity, "use[s] the concept of query as the fundamental paradigm of computation" (p. 17). Given signatures \sigma and \tau, we define the set of structures on each language, and. A query is then any mapping Computational complexity theory can then be phrased in terms of the power of the mathematical logic necessary to express a given query. A query is order-independent if the ordering of objects in the structure does not affect the results of the query.

Fagin's theorem

Fagin 1974
Fagin's theorem is a result in descriptive complexity theory that states that the set of all properties expressible in existential second-order logic is precisely the complexity class NP. It is remarkable since it is a characterization of the class NP that does not invoke a model of computation such as a Turing machine. It was proven by Ronald Fagin in 1973 in his doctoral thesis. The arity required by the second-order formula was improved (in one direction) in Lynch's theorem, and several results of Grandjean have provided tighter bounds on nondeterministic random-access machines. Immerman 1999 provides a detailed proof of the theorem.

Ontology Inference Layer

OIL is based on concepts developed in Description Logic (DL) and frame-based systems and is compatible with RDFS. OIL was developed by Dieter Fensel, Frank van Harmelen (Vrije Universiteit, Amsterdam) and Ian Horrocks (University of Manchester) as part of the IST OntoKnowledge project. Much of the work in OIL was subsequently incorporated into DAML+OIL and the Web Ontology Language (OWL). de:Ontology Inference Layer DARPA Agent Markup Language (DAML). DAML+OIL. Ontology.


Rushing averageReceiving averagemean
The mode, the median, and the mid-range are often used in addition to the mean as estimates of central tendency in descriptive statistics. These can all be seen as minimizing variation by some measure; see. The most frequently occurring number in a list is called the mode. For example, the mode of the list (1, 2, 2, 3, 3, 3, 4) is 3. It may happen that there are two or more numbers which occur equally often and more often than any other number. In this case there is no agreed definition of mode. Some authors say they are all modes and some say there is no mode. The median is the middle number of the group when they are ranked in order.

FO (complexity)

Neil Immerman's descriptive complexity page, including a diagram. Complexity zoo about FO, see also the following classes.

PH (complexity)

PHpolynomial hierarchy PHpolynomial hierarchy
In computational complexity theory, the complexity class PH is the union of all complexity classes in the polynomial hierarchy:

Neil Immerman

He is one of the key developers of descriptive complexity, an approach he is currently applying to research in model checking, database theory, and computational complexity theory. Professor Immerman is an editor of the SIAM Journal on Computing and of Logical Methods in Computer Science. He received B.S. and M.S. degrees from Yale University in 1974 and his Ph.D. from Cornell University in 1980 under the supervision of Juris Hartmanis, a Turing award winner at Cornell. His book "Descriptive Complexity" appeared in 1999.


The interpretation of these triplets is (implicitly) based on the semantics of a simple Description logic (DL). E.g., the triplet Common Cold – causative agent – Virus, corresponds to the first-order expression or the more intuitive DL expression In the Common cold example the concept description is "primitive", which means that necessary criteria are given that must be met for each instance, without being sufficient for classifying a disorder as an instance of Common Cold .

Quantitative research

quantitativequantitative methodsquantitative data
In natural sciences and social sciences, quantitative research is the systematic empirical investigation of observable phenomena via statistical, mathematical, or computational techniques. The objective of quantitative research is to develop and employ mathematical models, theories, and hypotheses pertaining to phenomena. The process of measurement is central to quantitative research because it provides the fundamental connection between empirical observation and mathematical expression of quantitative relationships.

Unique name assumption

The unique name assumption is a simplifying assumption made in some ontology languages and description logics. In logics with the unique name assumption, different names always refer to different entities in the world. It was included in Ray_Reiter's discussion of the Closed-world_assumption often tacitly included in Database Management Systems (e.g. SQL) in his 1984 article "Towards a logical reconstruction of relational database theory (in M.L. Brodie, J. Mylopoulos, J. W. Schmidt (Hrsg.), Data modelling in Artificial Intelligence, Database and Programming Languages, Springer 1984, S. 191–233).

Computational complexity theory

computational complexitycomplexity theorycomplexity
Descriptive complexity theory. Game complexity. List of complexity classes. List of computability and complexity topics. List of important publications in theoretical computer science. List of unsolved problems in computer science. Parameterized complexity. Proof complexity. Quantum complexity theory. Structural complexity theory. Transcomputational problem.


statisticalstatistical analysisstatistician
Descriptive statistics can be used to summarize the population data. Numerical descriptors include mean and standard deviation for continuous data types (like income), while frequency and percentage are more useful in terms of describing categorical data (like race). When a census is not feasible, a chosen subset of the population called a sample is studied. Once a sample that is representative of the population is determined, data is collected for the sample members in an observational or experimental setting. Again, descriptive statistics can be used to summarize the sample data.

Ontology (information science)

Gruber introduced the term as a specification of a conceptualization: An ontology is a description (like a formal specification of a program) of the concepts and relationships that can formally exist for an agent or a community of agents. This definition is consistent with the usage of ontology as set of concept definitions, but more general. And it is a different sense of the word than its use in philosophy.

Frame language

Description logic. Deductive classifier. First-order logic. Knowledge base. Knowledge-based system. Ontology language. Semantic Networks. Marvin Minsky, A Framework for Representing Knowledge, MIT-AI Laboratory Memo 306, June, 1974. Daniel G. Bobrow, Terry Winograd, An Overview of KRL, A Knowledge Representation Language, Stanford Artificial Intelligence Laboratory Memo AIM 293, 1976. R. Bruce Roberts and Ira P. Goldstein, The FRL Primer, 1977. R. Bruce Roberts and Ira P. Goldstein, The FRL Manual, 1977. Peter Clark & Bruce Porter: KM - The Knowledge Machine 2.0: Users Manual, http://www.cs.utexas.edu/users/mfkb/RKF/km.html. Peter D.

Ronald J. Brachman

Ron Brachman
He is considered by some to be the godfather of Description Logic, the logic-based knowledge representation formalism underlying the Web Ontology Language OWL.] He is the co-author with Hector Levesque of a popular book on knowledge representation and reasoning and many scientific papers. * External biography