This document introduces the syntax of BLOG, a probabilistic programming language, for describing random variables and their probabilistic dependencies. BLOG defines probabilistic generative models over first-order structures. For example, all Bayesian networks can be easily described by BLOG. BLOG has the following features: (a) it employs open-universe semantics; (b) it can describe relational uncertainty; (c) it can handle identity uncertainty; and (d) it is empowered by first-order logic. The syntax as described in this document corresponds to BLOG version 0.6. The current version represents a significant redesign and extension to previous versions of BLOG, based on the principles of usability and implementation efficiency.