Towards end-to-end ASP computation
Taisuke Sato, Akihiro Takemura, Katsumi Inoue
TL;DR
This work addresses computing stable models for propositional normal logic programs in an end-to-end vector-space framework. It derives a full pipeline that matricizes programs, evaluates rules via linear algebra, and minimizes a nonnegative cost function whose zero implies a valid stable model, incorporating Lin-Zhao loop formulas and optional constraints. To manage combinatorial hardness, it introduces strategic precomputation to shrink the search space and selective loop-formula heuristics, demonstrated on 3-coloring and Hamiltonian cycle problems with notable speedups and solution diversity. The results indicate the approach is feasible for small-scale ASP tasks and has potential for parallelization and integration with neural components, suggesting a path toward scalable neuro-symbolic reasoning.
Abstract
We propose an end-to-end approach for Answer Set Programming (ASP) and linear algebraically compute stable models satisfying given constraints. The idea is to implement Lin-Zhao's theorem together with constraints directly in vector spaces as numerical minimization of a cost function constructed from a matricized normal logic program, loop formulas in Lin-Zhao's theorem and constraints, thereby no use of symbolic ASP or SAT solvers involved in our approach. We also propose precomputation that shrinks the program size and heuristics for loop formulas to reduce computational difficulty. We empirically test our approach with programming examples including the 3-coloring and Hamiltonian cycle problems.