There have been attempts to connect machine learning and symbolic reasoning, providing interfaces between them. This work focuses on our original approach to integrate machine learning and symbolic reasoning, in the context of algebraic approaches to logic programming. We here realize logical reasoning using algebraic methods, in which algebraic data structures such as matrices and tensors are used to represent logical formulas. These reasoning methods are robust against noise, while allowing for high parallelism and scalable computation. Algebraic logic programming has been applied to fixpoint computation, abduction, answer set programming and inductive logic programming.