Linear Algebraic Characterization of Logic Programs
Chiaki Sakama, Katsumi Inoue and Taisuke Sato
in: Proceedings of the 10th International Conference on Knowledge Science, Engineering and Management (KSEM 2017)
This paper introduces a novel approach for computing
logic programming semantics based on multilinear algebra.
First, a propositional Herbrand base is represented in a vector space and
if-then rules in a program are encoded in a matrix.
Then we provide methods of computing the least model of a Horn logic program,
minimal models of a disjunctive logic program, and stable models of a normal logic program
by algebraic manipulation of higher-order tensors.
The result of this paper exploits a new connection between
linear algebraic computation and symbolic computation, which
has potential to realize logical inference in huge scale of knowledge bases.
Full Paper (PDF 146K)