nLab locally confluent relation

Definition

Let $(X,\rightarrow)$ be an abstract rewriting system, i.e., a set equipped with a binary relation $\rightarrow$. Write $\rightarrow^{*}$ for the reflexive-transitive closure of $\rightarrow$. We say that $\rightarrow$ is locally confluent iff for every $a,b,c \in X$ such that $a \rightarrow b$ and $a \rightarrow c$, there exists $d \in X$ such that $b \rightarrow^{*} d$ and $c \rightarrow^{*} d$.

Related concepts

• confluent relation

References

• Franz Baader, Tobias Nipkow: Term Rewriting and All That, Cambridge University Press (1998) [doi:10.1017/CBO9781139172752]