# Transitiveness

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## Transitiveness

a property of some logical relations between objects or quantities.

The relation a*b is said to be transitive if a*c follows from a*b and b*c. For example, the relation “a is equal to b” (a = b) is transitive because a = c follows from a = b and b = c. Similarly, the relation “a is greater than b” (a > b) is transitive. The relation “a is not equal to b” (ab) is not transitive because ac does not necessarily follow from ab and bc.

In geometry, the relation of parallelism between two lines is transitive: if α is parallel to β and β is parallel to γ, then α is parallel to γ. By contrast, the relation of perpendicularity between lines is not transitive.

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For example, he produces in his introduction a structure in which 'Nonrationalism and Work' is opposed to 'Rationalism and Labour', and under these general headings are further opposed, inter alia, 'Homo faber' and 'Homo economicus', the realm of freedom and the realm of maximizing or the realm of necessity, idealism and materialism, moralism and pragmatism, form and reform, finality and conditionality, totality and variability, withdrawal and concession, intransitiveness and transitiveness, 'a priori' and 'a posteriori', and so on (p.
by transculturation as a form of narrative transitiveness between
The following ontology components are included in WEBODE's knowledge model: concepts and their attributes (both instance and class attributes); concept groups, which represent sets of disjoint concepts; concept taxonomies and disjoint and exhaustive class decompositions; ad hoc binary relations between concepts, which can be characterized by relation properties (symmetry, transitiveness, and so on); constants; formal axioms, expressed in first-order logic; rules; and instances of concepts and relations.

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