We present an implementation of a probabilistic first-order logic called
TensorLog, in which classes of logical queries are compiled into differentiable
functions in a neural-network infrastructure such as Tensorflow or Theano. This
leads to a close integration of probabilistic logical reasoning with
deep-learning infrastructure: in particular, it enables high-performance deep
learning frameworks to be used for tuning the parameters of a probabilistic
logic. Experimental results show that TensorLog scales to problems involving
hundreds of thousands of knowledge-base triples and tens of thousands of
examples.

本研究提出了一种基于神经网络基础设施（如 Tensorflow 或 Theano）的概率一阶逻辑 TensorLog 的实现，在其中，逻辑查询的类别被编译成可微分函数，从而实现概率逻辑推理与深度学习基础设施的紧密集成，并且实验结果表明 TensorLog 可以扩展到涉及数十万个知识库三元组和数万个示例的问题。

TensorLog: 深度学习与概率数据库的结合

TensorLog: Deep Learning Meets Probabilistic DBs

Large knowledge bases (KBs) are useful in many tasks, but it is unclear how
to integrate this sort of knowledge into "deep" gradient-based learning
systems. To address this problem, we describe a probabilistic deductive
database, called TensorLog, in which reasoning uses a differentiable process.
In TensorLog, each clause in a logical theory is first converted into certain
type of factor graph. Then, for each type of query to the factor graph, the
message-passing steps required to perform belief propagation (BP) are
"unrolled" into a function, which is differentiable. We show that these
functions can be composed recursively to perform inference in non-trivial
logical theories containing multiple interrelated clauses and predicates. Both
compilation and inference in TensorLog are efficient: compilation is linear in
theory size and proof depth, and inference is linear in database size and the
number of message-passing steps used in BP. We also present experimental
results with TensorLog and discuss its relationship to other first-order
probabilistic logics.

介绍一种基于 TensorLog 的可微分概率演绎数据库，可在包含多个相互关联子句和谓词的非平凡逻辑理论中执行推理。