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 \cite{Lin04} 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. As our approach is purely numerical and only contains vector/matrix operations, acceleration by parallel technologies such as many-cores and GPUs is expected.
We propose a method for generating explainable rule sets from tree-ensemble learners using Answer Set Programming (ASP). To this end, we adopt a decompositional approach where the split structures of the base decision trees are exploited in the construction of rules, which in turn are assessed using pattern mining methods encoded in ASP to extract interesting rules. We show how user-defined constraints and preferences can be represented declaratively in ASP to allow for transparent and flexible rule set generation, and how rules can be used as explanations to help the user better understand the models. Experimental evaluation with real-world datasets and popular tree-ensemble algorithms demonstrates that our approach is applicable to a wide range of classification tasks.