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Generalized to stochastic versions (stochastic transitivity), the study of transitivity finds applications of in decision theory, psychometrics and utility models. [19] A quasitransitive relation is another generalization; [5] it is required to be transitive only on its non-symmetric part. Such relations are used in social choice theory or ...
In propositional logic, hypothetical syllogism is the name of a valid rule of inference (often abbreviated HS and sometimes also called the chain argument, chain rule, or the principle of transitivity of implication). The rule may be stated:
The four axioms of VNM-rationality are completeness, transitivity, continuity, and independence. These axioms, apart from continuity, are often justified using the Dutch book theorems (whereas continuity is used to set aside lexicographic or infinitesimal utilities). Completeness assumes that an individual has well defined preferences:
The mathematical notion of quasitransitivity is a weakened version of transitivity that is used in social choice theory and microeconomics. Informally, a relation is quasitransitive if it is symmetric for some values and transitive elsewhere. The concept was introduced by Sen (1969) to study the consequences of Arrow's theorem.
This shows how Transitivity is used. Finally, note that line (), , is a theorem, as indicated by the hint to its right. Hence, by inference rule Equanimity, we conclude that line () is also a theorem. And () is what we wanted to prove. [2]
Transitivity is a linguistics property that relates to whether a verb, participle, or gerund denotes a transitive object. It is closely related to valency , which considers other arguments in addition to transitive objects.
Given a set of functional dependencies , an Armstrong relation is a relation which satisfies all the functional dependencies in the closure + and only those dependencies. . Unfortunately, the minimum-size Armstrong relation for a given set of dependencies can have a size which is an exponential function of the number of attributes in the dependencies conside
Transitivity (grammar), a property regarding whether a lexical item denotes a transitive object; Transitive verb, a verb which takes an object; Transitive case, a grammatical case to mark arguments of a transitive verb