Transitiivisuus

Transitiivisuus, or transitivity, is a fundamental concept used in several disciplines, most prominently in logic, mathematics, and linguistics. In a broad sense it describes a rule about how a relation or predicate propagates through a chain of connections. A transitive relation allows a direct connection to be inferred from two consecutive connections.

In logic and mathematics, a relation R on a set A is transitive if, for all elements a, b, and c in A, whenever a is related to b (aRb) and b is related to c (bRc), then a is related to c (aRc). For example, the relation “is an ancestor of” is transitive: if A is an ancestor of B and B is an ancestor of C, then A is an ancestor of C. Not all relations are transitive; a relation such as “is the parent of” is not transitive, since if A is a parent of B and B is a parent of C, A is not necessarily a parent of C.

In linguistics, transitivity refers to whether a verb can take a direct object. Transitive verbs require a direct object (for example, “eat an apple”), while intransitive verbs do not (for example, “sleep”). Some verbs are ambitransitive, functioning as either transitive or intransitive depending on the context. Transitivity interacts with syntactic structure, argument marking, and voice in many languages, and it can influence how sentences are formed and interpreted.

Additional concepts related to transitivity include transitive closure, which describes the smallest transitive relation containing a given relation, and various classifications such as monotransitive and ditransitive, used to describe the number of object arguments a verb can take.