Logic Programming in Tensor Spaces
Chiaki Sakama, Katsumi Inoue, and Taisuke Sato
Annals of Mathematics and Artificial Intelligence, vol.89(12), pages 1133-1153,
This paper introduces a novel approach to computing logic programming semantics.
First, a propositional Herbrand base is represented in a vector space and if-then rules in a program are encoded
in a matrix. Then the least fixpoint of a definite logic program is computed by matrix-vector products
with a non-linear operation. Second, disjunctive logic programs are represented in third-order tensors
and their minimal models are computed by algebraic manipulation of tensors.
Third, normal logic programs are represented by matrices and third-order tensors, and their stable models are computed.
The result of this paper exploits a new connection between linear algebraic computation and symbolic computation,
which has the potential to realize logical inference in huge scale of knowledge bases.