  Integer Linear Programming (ILP) has been proposed as a formalism for
encoding precise structural and semantic constraints for Natural Language
Inference (NLI). However, traditional ILP frameworks are non-differentiable,
posing critical challenges for the integration of continuous language
representations based on deep learning. In this paper, we introduce a novel
approach, named Diff-Comb Explainer, a neuro-symbolic architecture for
explanation-based NLI based on Differentiable BlackBox Combinatorial Solvers
(DBCS). Differently from existing neuro-symbolic solvers, Diff-Comb Explainer
does not necessitate a continuous relaxation of the semantic constraints,
enabling a direct, more precise, and efficient incorporation of neural
representations into the ILP formulation. Our experiments demonstrate that
Diff-Comb Explainer achieves superior performance when compared to conventional
ILP solvers, neuro-symbolic black-box solvers, and Transformer-based encoders.
Moreover, a deeper analysis reveals that Diff-Comb Explainer can significantly
improve the precision, consistency, and faithfulness of the constructed
explanations, opening new opportunities for research on neuro-symbolic
architectures for explainable and transparent NLI in complex domains.
