An emerging line of research in Explainable NLP is the creation of datasets enriched with human-annotated explanations and rationales, used to build and evaluate models with step-wise inference and explanation generation capabilities. While human-annotated explanations are used as ground-truth for the inference, there is a lack of systematic assessment of their consistency and rigour. In an attempt to provide a critical quality assessment of Explanation Gold Standards (XGSs) for NLI, we propose a systematic annotation methodology, named Explanation Entailment Verification (EEV), to quantify the logical validity of human-annotated explanations. The application of EEV on three mainstream datasets reveals the surprising conclusion that a majority of the explanations, while appearing coherent on the surface, represent logically invalid arguments, ranging from being incomplete to containing clearly identifiable logical errors. This conclusion confirms that the inferential properties of explanations are still poorly formalised and understood, and that additional work on this line of research is necessary to improve the way Explanation Gold Standards are constructed.

The relational syllogistic is an extension of the language of Classical syllogisms in which predicates are allowed to feature transitive verbs with quantified objects. It is known that the relational syllogistic does not admit a finite set of syllogism-like rules whose associated (direct) derivation relation is sound and complete. We present a modest extension of this language which does.