  We introduce a new logic programming language T-PRISM based on tensor
embeddings. Our embedding scheme is a modification of the distribution
semantics in PRISM, one of the state-of-the-art probabilistic logic programming
languages, by replacing distribution functions with multidimensional arrays,
i.e., tensors. T-PRISM consists of two parts: logic programming part and
numerical computation part. The former provides flexible and interpretable
modeling at the level of first order logic, and the latter part provides
scalable computation utilizing parallelization and hardware acceleration with
GPUs. Combing these two parts provides a remarkably wide range of high-level
declarative modeling from symbolic reasoning to deep learning. To embody this
programming language, we also introduce a new semantics, termed tensorized
semantics, which combines the traditional least model semantics in logic
programming with the embeddings of tensors. In T-PRISM, we first derive a set
of equations related to tensors from a given program using logical inference,
i.e., Prolog execution in a symbolic space and then solve the derived equations
in a continuous space by TensorFlow. Using our preliminary implementation of
T-PRISM, we have successfully dealt with a wide range of modeling. We have
succeeded in dealing with real large-scale data in the declarative modeling.
This paper presents a DistMult model for knowledge graphs using the FB15k and
WN18 datasets.
