Partial Evaluation of Logic Programs in Vector Spaces

TL;DR

This paper presents a novel approach to encode propositional logic programs in vector spaces, enabling efficient computation through partial evaluation and linear algebra techniques, which could scale to large programs.

Contribution

It introduces a method for partial evaluation of logic programs in vector spaces using matrix multiplication, enhancing computational efficiency.

Findings

Partial evaluation reduces computation time.

Vector space encoding allows scalable logic program processing.

Experimental results show potential for large-scale applications.

Abstract

In this paper, we introduce methods of encoding propositional logic programs in vector spaces. Interpretations are represented by vectors and programs are represented by matrices. The least model of a definite program is computed by multiplying an interpretation vector and a program matrix. To optimize computation in vector spaces, we provide a method of partial evaluation of programs using linear algebra. Partial evaluation is done by unfolding rules in a program, and it is realized in a vector space by multiplying program matrices. We perform experiments using randomly generated programs and show that partial evaluation has potential for realizing efficient computation in huge scale of programs.