Please see the Appendix of Ref. 1 for a formal proof.

We present a hierarchy of natural language understanding abilities and argue for the importance of moving beyond assessments of understanding at the lexical and sentence levels to the discourse level. We propose the task of anaphora accessibility as a diagnostic for assessing discourse understanding, and to this end, present an evaluation dataset inspired by theoretical research in dynamic semantics. We evaluate human and LLM performance on our dataset and find that LLMs and humans align on some tasks and diverge on others. Such divergence can be explained by LLMs' reliance on specific lexical items during language comprehension, in contrast to human sensitivity to structural abstractions.

This article presents a technique for proving problems hard for classes of the polynomial hierarchy or for PSPACE. The rationale of this technique is that some problem restrictions are able to simulate existential or universal quantifiers. If this is the case, reductions from Quantified Boolean Formulae (QBF) to these restrictions can be transformed into reductions from QBFs having one more quantifier in the front. This means that a proof of hardness of a problem at level n in the polynomial hierarchy can be split into n separate proofs, which may be simpler than a proof directly showing a reduction from a class of QBFs to the considered problem.

The problem we consider in this paper is that of discovering formal rules which will enable us to decide when a question posed in English can be answered on the basis of one or more declarative English sentences. To illustrate how this may be done in very simple cases we give rules which translate certain declarative sentences and questions involving the quantifiers'some', 'every', 'any', and'no' into a modified first-order predicate calculus, and answer the questions by comparing their translated forms with those of the declaratives. We suggest that in order to capture the meanings of more complex sentences it will be necessary to go beyond the first-order predicate calculus, to a notation in which the scope of words other than quantifiers and negations is clearly indicated. We conclude by describing a notational form for connected sentences, which seems to be a natural extension of Chomsky's'deep structures'.