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.

Integer Linear Programming (ILP) provides a viable mechanism to encode explicit and controllable assumptions about explainable multi-hop inference with natural language. However, an ILP formulation is non-differentiable and cannot be integrated into broader deep learning architectures. Recently, Thayaparan et al. (2021a) proposed a novel methodology to integrate ILP with Transformers to achieve end-to-end differentiability for complex multi-hop inference. While this hybrid framework has been demonstrated to deliver better answer and explanation selection than transformer-based and existing ILP solvers, the neuro-symbolic integration still relies on a convex relaxation of the ILP formulation, which can produce sub-optimal solutions. To improve these limitations, we propose Diff-Comb Explainer, a novel neuro-symbolic architecture based on Differentiable BlackBox Combinatorial solvers (DBCS) (Pogan\v{c}i\'c et al., 2019). Unlike existing differentiable solvers, the presented model does not require the transformation and relaxation of the explicit semantic constraints, allowing for direct and more efficient integration of ILP formulations. Diff-Comb Explainer demonstrates improved accuracy and explainability over non-differentiable solvers, Transformers and existing differentiable constraint-based multi-hop inference frameworks.

We propose a novel approach for answering and explaining multiple-choice science questions by reasoning on grounding and abstract inference chains. This paper frames question answering as an abductive reasoning problem, constructing plausible explanations for each choice and then selecting the candidate with the best explanation as the final answer. Our system, ExplanationLP, elicits explanations by constructing a weighted graph of relevant facts for each candidate answer and extracting the facts that satisfy certain structural and semantic constraints. To extract the explanations, we employ a linear programming formalism designed to select the optimal subgraph. The graphs' weighting function is composed of a set of parameters, which we fine-tune to optimize answer selection performance. We carry out our experiments on the WorldTree and ARC-Challenge corpus to empirically demonstrate the following conclusions: (1) Grounding-Abstract inference chains provides the semantic control to perform explainable abductive reasoning (2) Efficiency and robustness in learning with a fewer number of parameters by outperforming contemporary explainable and transformer-based approaches in a similar setting (3) Generalisability by outperforming SOTA explainable approaches on general science question sets.