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Mutually Exclusive
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both. In the coin-tossing example, both outcomes are, in theory, collectively exhaustive, which means that at least one of the outcomes must happen, so these two possibilities together exhaust all the possibilities. However, not all mutually exclusive events are collectively exhaustive. For example, the outcomes 1 and 4 of a single roll of a six-sided die are mutually exclusive (both cannot happen at the same time) but not collectively exhaustive (there are other possible outcomes; 2,3,5,6). Logic In logic, two mutually exclusive propositions are propositions that logically cannot be true in the same sense at the same time. To say that more than two propositions are mutually exclusive, depending on the context, means that one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Regression
In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear function (calculus), linear combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) is estimation theory, estimating the parameters of a logistic model (the coefficients in the linear combination). Formally, in binary logistic regression there is a single binary variable, binary dependent variable, coded by an indicator variable, where the two values are labeled "0" and "1", while the independent variables can each be a binary variable (two classes, coded by an indicator variable) or a continuous variable (any real value). The corresponding probability of the value labeled "1" can vary between 0 (certainly the value "0") and 1 (certainly the value "1"), hence the labeling; the function that converts log-odds to probability is the logistic function, h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Mathematics
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. History The origin of mathematics is subject to arguments and disagreements. Whether the birth of mathematics was a random happening or induced by necessity during the development of other subjects, like physics, is still a matter of prolific debates. Many thinkers have contributed their ideas concerning the nature of mathematics. Today, some philosophers of mathematics aim to give accounts of this form of inquiry and its products as they stand, while others emphasize a role for themselves that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synchronicity
Synchronicity (german: Synchronizität) is a concept first introduced by analytical psychologist Carl G. Jung "to describe circumstances that appear meaningfully related yet lack a causal connection." In contemporary research, synchronicity experiences refer to one's subjective experience that coincidences between events in one's mind and the outside world may be causally unrelated to each other yet have some other unknown connection. Jung held that this was a healthy, even necessary, function of the human mind that can become harmful within psychosis. Jung developed the theory of synchronicity as a hypothetical noncausal principle serving as the intersubjective or philosophically objective connection between these seemingly meaningful coincidences. Mainstream science generally regards that any such hypothetical principle either does not exist or falls outside the bounds of science. After first coining the term in the late 1920s or early 30s, Jung further developed the conc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxymoron
An oxymoron (usual plural oxymorons, more rarely oxymora) is a figure of speech that juxtaposes concepts with opposing meanings within a word or phrase that creates an ostensible self-contradiction. An oxymoron can be used as a rhetorical device to illustrate a rhetorical point or to reveal a paradox. A more general meaning of "contradiction in terms" (not necessarily for rhetoric effect) is recorded by the ''OED'' for 1902. The term is first recorded as Latinized Greek ', in Maurus Servius Honoratus (c. AD 400); it is derived from the Greek word ' "sharp, keen, pointed" Retrieved 2013-02-26. and "dull, stupid, foolish"; as it were, "sharp-dull", "keenly stupid", or "pointedly foolish".. Retrieved 2013-02-26. "Pointedly foolish: a witty saying, the more pointed from being paradoxical or seemingly absurd." The word ''oxymoron'' is autological, i.e. it is itself an example of an oxymoron. The Greek compound word ', which would correspond to the Latin formation, does not seem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Event Structure
In mathematics and computer science, an event structure represents a set of events, some of which can only be performed after another (there is a ''dependency'' between the events) and some of which might not be performed together (there is a ''conflict'' between the events). Formal definition An event structure (E,\leq,\#) consists of * a set E of events * a partial order relation on E called causal dependency, * an irreflexive symmetric relation \# called incompatibility (or conflict) such that * ''finite causes'': for every event e \in E, the set = \ of predecessors of e in E is finite * ''hereditary conflict'': for every events d,e,f \in E, if d \leq e and d \# f then e \# f. See also * Binary relation * Mathematical structure In mathematics, a structure is a set endowed with some additional features on the set (e.g. an operation, relation, metric, or topology). Often, the additional features are attached or related to the set, so as to provide it with some additional ... ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Bind
A double bind is a dilemma in communication in which an individual (or group) receives two or more reciprocally conflicting messages. In some scenarios (e.g. within families or romantic relationships) this can be emotionally distressing, creating a situation in which a successful response to one message results in a failed response to the other (and vice versa), such that the person responding will automatically be perceived as in the wrong, no matter how they respond. This double bind prevents the person from either resolving the underlying dilemma or opting out of the situation. Double bind theory was first described by Gregory Bateson and his colleagues in the 1950s,Bateson, G., Jackson, D. D., Haley, J. & Weakland, J., 1956, Toward a theory of schizophrenia.''Behavioral Science'', Vol. 1, 251–264. in a theory on the origins of schizophrenia and post-traumatic stress disorder. Double binds are often utilized as a form of control without open coercion—the use of confusion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disjoint Sets
In mathematics, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set.. For example, and are ''disjoint sets,'' while and are not disjoint. A collection of two or more sets is called disjoint if any two distinct sets of the collection are disjoint. Generalizations This definition of disjoint sets can be extended to a family of sets \left(A_i\right)_: the family is pairwise disjoint, or mutually disjoint if A_i \cap A_j = \varnothing whenever i \neq j. Alternatively, some authors use the term disjoint to refer to this notion as well. For families the notion of pairwise disjoint or mutually disjoint is sometimes defined in a subtly different manner, in that repeated identical members are allowed: the family is pairwise disjoint if A_i \cap A_j = \varnothing whenever A_i \neq A_j (every two ''distinct'' sets in the family are disjoint).. For example, the collection of sets is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dichotomy
A dichotomy is a partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be * jointly exhaustive: everything must belong to one part or the other, and * mutually exclusive: nothing can belong simultaneously to both parts. If there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A. Such a partition is also frequently called a bipartition. The two parts thus formed are complements. In logic, the partitions are opposites if there exists a proposition such that it holds over one and not the other. Treating continuous variables or multi categorical variables as binary variables is called dichotomization. The discretization error inherent in dichotomization is temporarily ignored for modeling purposes. Etymology The term '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multinomial Logit
In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.). Multinomial logistic regression is known by a variety of other names, including polytomous LR, multiclass LR, softmax regression, multinomial logit (mlogit), the maximum entropy (MaxEnt) classifier, and the conditional maximum entropy model. Background Multinomial logistic regression is used when the dependent variable in question is nominal (equivalently ''categorical'', meaning that it falls into any one of a set of categories that cannot be ordered in any meaningful way) and for which there are more than two categories. Some examples ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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