transitivelike

Transitivelike is not a standard term in mathematics or logic. In scholarly and semi-formal writing, it is used as an umbrella label for relations or systems that resemble transitivity without necessarily satisfying its precise definition. The idea appears across disciplines such as mathematics, computer science, linguistics, and social science, where researchers encounter situations in which a relation propagates or aggregates information in a way that is similar to transitivity but not strictly identical to it.

Because no universal definition exists, transitivelike is defined differently by different authors. Common interpretations include approximate transitivity, where aRb and bRc imply aRc up to a permitted tolerance; and graded or fuzzy transitivity, where relations carry degrees of truth and the degree of aRc is bounded below by a combination (for example, a t-norm) of the degrees of aRb and bRc. Probabilistic or statistical versions model the propagation of relations through likelihoods, stating that high probabilities for aRb and bRc tend to yield a high probability for aRc, possibly with some loss factor. In graph-theoretic or data contexts, transitivelike may describe near-transitive closure properties that hold in practice but fail under strict formalization.

Because the term is not standardized, authors should specify the precise meaning and any conditions when using transitivelike in a given work. It is most useful as a descriptive notion guiding models of propagation, inference, or similarity that feel transitive in effect but do not meet the strict criteria of transitivity. Related concepts include transitive relation, transitive closure, and fuzzy or probabilistic transitivity.