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Transitivity And Valency
Transitivity or transitive may refer to: Grammar * Transitivity (grammar), a property of verbs that relates to whether a verb can take direct objects * Transitive verb, a verb which takes an object * Transitive case, a grammatical case to mark arguments of a transitive verb Logic and mathematics * Transitive group action * Transitive relation, a binary relation in which if ''A'' is related to ''B'' and ''B'' is related to ''C'', then ''A'' is related to ''C'' * Syllogism, a related notion in propositional logic * Intransitivity, properties of binary relations in mathematics * Arc-transitive graph, a graph whose automorphism group acts transitively upon ordered pairs of adjacent vertices * Edge-transitive graph, a graph whose automorphism group acts transitively upon its edges * Vertex-transitive graph, a graph whose automorphism group acts transitively upon its vertices * Transitive set a set ''A'' such that whenever ''x'' ∈ ''A'', and ''y'' ∈ ''x'', then ''y'' ∈ ''A'' * Top ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitivity (grammar)
In linguistics, transitivity is a property of verbs that relates to whether a verb can take objects and how many such objects a verb can take. It is closely related to valency, which considers other verb arguments in addition to direct objects. The obligatory noun phrases and prepositional phrases determine how many arguments a predicate has. Obligatory elements are considered arguments while optional ones are never counted in the list of arguments. Traditional grammar makes a binary distinction between intransitive verbs, which cannot take a direct object (such as ''fall'' or ''sit'' in English), and transitive verbs, which take a direct object (such as ''throw'', ''injure'', or ''kiss'' in English). In practice, many languages (including English) also have verbs that have two objects (ditransitive verbs) or even verbs that can be used as both a transitive verb and an intransitive verb (ambitransitive verbs, for example ''She walked the dog'' and ''She walked with a dog''). I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Verb
A transitive verb is a verb that accepts one or more objects, for example, 'cleaned' in ''Donald cleaned the window''. This contrasts with intransitive verbs, which do not have objects, for example, 'panicked' in ''Donald panicked''. Transitivity is traditionally thought of as a global property of a clause, by which activity is transferred from an agent to a patient. Transitive verbs can be classified by the number of objects they require. Verbs that accept only two arguments, a subject and a single direct object, are monotransitive. Verbs that accept two objects, a direct object and an indirect object, are ''ditransitive'', or less commonly ''bitransitive''. An example of a ditransitive verb in English is the verb ''to give'', which may feature a subject, an indirect object, and a direct object: ''John gave Mary the book''. Verbs that take three objects are ''tritransitive''. In English a tritransitive verb features an indirect object, a direct object, and a prepositional ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Case
In linguistic typology, transitive alignment is a type of morphosyntactic alignment used in a small number of languages in which a single grammatical case is used to mark both arguments of a transitive verb, but not with the single argument of an intransitive verb. Such a situation, which is quite rare among the world's languages, has also been called a ''double- oblique'' clause structure. Rushani, an Iranian dialect, has this alignment in the past tense. That is, in the past tense (or perhaps perfective aspect), the agent and object of a transitive verb are marked with the same case ending, while the subject of an intransitive verb is not marked. In the present tense, the object of the transitive verb is marked, the other two roles are not – that is, a typical nominative–accusative alignment.J.R. Payne, 'Language Universals and Language Types', in Collinge, ed. 1990. ''An Encyclopedia of Language''. Routledge. From Payne, 1980. Intransitive: no case marking : :'I went ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Group Action
In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group ''acts'' on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it. For example, it acts on the set of all triangles. Similarly, the group of symmetries of a polyhedron acts on the vertices, the edges, and the faces of the polyhedron. A group action on a vector space is called a representation of the group. In the case of a finite-dimensional vector space, it allows one to identify many groups with subgroups of , the group of the invertible matrices of dimension over a field . The symmetric group acts on any set with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Relation
In mathematics, a relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Each partial order as well as each equivalence relation needs to be transitive. Definition A homogeneous relation on the set is a ''transitive relation'' if, :for all , if and , then . Or in terms of first-order logic: :\forall a,b,c \in X: (aRb \wedge bRc) \Rightarrow aRc, where is the infix notation for . Examples As a non-mathematical example, the relation "is an ancestor of" is transitive. For example, if Amy is an ancestor of Becky, and Becky is an ancestor of Carrie, then Amy, too, is an ancestor of Carrie. On the other hand, "is the birth parent of" is not a transitive relation, because if Alice is the birth parent of Brenda, and Brenda is the birth parent of Claire, then this does not imply that Alice is the birth parent of Claire. What is more, it is antitransitive: Alice can ''never'' be the birth parent of Claire. "Is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syllogism
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defined by Aristotle in his 350 BCE book '' Prior Analytics''), a syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise) and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism. From the Middle Ages onwards, ''categorical syllogism'' and ''syllogism'' were usually used interchangeably. This a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intransitivity
In mathematics, intransitivity (sometimes called nontransitivity) is a property of binary relations that are not transitive relations. This may include any relation that is not transitive, or the Mathematical jargon#stronger, stronger property of antitransitivity, which describes a relation that is never transitive. Intransitivity A relation is transitive if, whenever it relates some A to some B, and that B to some C, it also relates that A to that C. Some authors call a relation if it is not transitive, that is, (if the relation in question is named R) \lnot\left(\forall a, b, c: a R b \land b R c \implies a R c\right). This statement is equivalent to \exists a,b,c : a R b \land b R c \land \lnot(a R c). For instance, in the food chain, wolves feed on deer, and deer feed on grass, but wolves do not feed on grass. Thus, the relation among life forms is intransitive, in this sense. Another example that does not involve preference loops arises in freemasonry: in some instance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arc-transitive Graph
In the mathematical field of graph theory, a graph is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices and of , there is an automorphism :f : V(G) \rightarrow V(G) such that :f(u_1) = u_2 and f(v_1) = v_2. In other words, a graph is symmetric if its automorphism group acts transitively on ordered pairs of adjacent vertices (that is, upon edges considered as having a direction). Such a graph is sometimes also called -transitive or flag-transitive. By definition (ignoring and ), a symmetric graph without isolated vertices must also be vertex-transitive. Since the definition above maps one edge to another, a symmetric graph must also be edge-transitive. However, an edge-transitive graph need not be symmetric, since might map to , but not to . Star graphs are a simple example of being edge-transitive without being vertex-transitive or symmetric. As a further example, semi-symmetric graphs are edge-transitive and regular, but not vertex-transit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge-transitive Graph
In the mathematical field of graph theory, an edge-transitive graph is a graph such that, given any two edges and of , there is an automorphism of that maps to . In other words, a graph is edge-transitive if its automorphism group acts transitively on its edges. Examples and properties The number of connected simple edge-transitive graphs on n vertices is 1, 1, 2, 3, 4, 6, 5, 8, 9, 13, 7, 19, 10, 16, 25, 26, 12, 28 ... Edge-transitive graphs include all symmetric graph, such as the vertices and edges of the cube. Symmetric graphs are also vertex-transitive (if they are connected), but in general edge-transitive graphs need not be vertex-transitive. Every connected edge-transitive graph that is not vertex-transitive must be bipartite, (and hence can be colored with only two colors), and either semi-symmetric or biregular.. Examples of edge but not vertex transitive graphs include the complete bipartite graphs K_ where m ≠ n, which includes the star graphs K_. For ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertex-transitive Graph
In the mathematical field of graph theory, a vertex-transitive graph is a graph in which, given any two vertices and of , there is some automorphism :f : G \to G\ such that :f(v_1) = v_2.\ In other words, a graph is vertex-transitive if its automorphism group acts transitively on its vertices.. A graph is vertex-transitive if and only if its graph complement is, since the group actions are identical. Every symmetric graph without isolated vertices is vertex-transitive, and every vertex-transitive graph is regular. However, not all vertex-transitive graphs are symmetric (for example, the edges of the truncated tetrahedron), and not all regular graphs are vertex-transitive (for example, the Frucht graph and Tietze's graph). Finite examples Finite vertex-transitive graphs include the symmetric graphs (such as the Petersen graph, the Heawood graph and the vertices and edges of the Platonic solids). The finite Cayley graphs (such as cube-connected cycles) are also ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Set
In set theory, a branch of mathematics, a set A is called transitive if either of the following equivalent conditions hold: * whenever x \in A, and y \in x, then y \in A. * whenever x \in A, and x is not an urelement, then x is a subset of A. Similarly, a class M is transitive if every element of M is a subset of M. Examples Using the definition of ordinal numbers suggested by John von Neumann, ordinal numbers are defined as hereditarily transitive sets: an ordinal number is a transitive set whose members are also transitive (and thus ordinals). The class of all ordinals is a transitive class. Any of the stages V_\alpha and L_\alpha leading to the construction of the von Neumann universe V and Gödel's constructible universe L are transitive sets. The universes V and L themselves are transitive classes. This is a complete list of all finite transitive sets with up to 20 brackets: * \, * \, * \, * \, * \, * \, * \, * \, * \, * \, * \, * \, * \, * \, * \, * \, * \, * \, * \, * \, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Transitivity
In mathematics, mixing is an abstract concept originating from physics: the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: mixing paint, mixing drinks, industrial mixing, ''etc''. The concept appears in ergodic theory—the study of stochastic processes and measure-preserving dynamical systems. Several different definitions for mixing exist, including ''strong mixing'', ''weak mixing'' and ''topological mixing'', with the last not requiring a measure to be defined. Some of the different definitions of mixing can be arranged in a hierarchical order; thus, strong mixing implies weak mixing. Furthermore, weak mixing (and thus also strong mixing) implies ergodicity: that is, every system that is weakly mixing is also ergodic (and so one says that mixing is a "stronger" notion than ergodicity). Informal explanation The mathematical definition of mixing aims to capture the ordinary every-day process of mixing, such as mixing paints, drinks, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
