TY - JOUR
AU1 - Sakama, Chiaki
AU2 - Inoue, Katsumi
AU3 - Sato, Taisuke
AB - 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.
TI - Logic programming in tensor spaces
JF - Annals of Mathematics and Artificial Intelligence
DO - 10.1007/s10472-021-09767-x
DA - 2021-12-01
UR - https://www.deepdyve.com/lp/springer-journals/logic-programming-in-tensor-spaces-JoJhMeaLsM
SP - 1133
EP - 1153
VL - 89
IS - 12
DP - DeepDyve
ER -