What makes a presupposition of an utterance -- information taken for granted
by its speaker -- different from other pragmatic inferences such as an
entailment is projectivity (e.g., the negative sentence the boy did not stop
shedding tears presupposes the boy had shed tears before). The projectivity may
vary depending on the combination of presupposition triggers and environments.
However, prior natural language understanding studies fail to take it into
account as they either use no human baseline or include only negation as an
entailment-canceling environment to evaluate models' performance. The current
study attempts to reconcile these issues. We introduce a new dataset,
projectivity of presupposition (PROPRES, which includes 12k premise-hypothesis
pairs crossing six triggers involving some lexical variety with five
environments. Our human evaluation reveals that humans exhibit variable
projectivity in some cases. However, the model evaluation shows that the
best-performed model, DeBERTa, does not fully capture it. Our findings suggest
that probing studies on pragmatic inferences should take extra care of the
human judgment variability and the combination of linguistic items.

项目性等词设想和词语公推等范围应该在言语理解研究中得到充分考虑。

PROPRES: 探索各种触发器和环境中的预设语的项目性

PROPRES: Investigating the Projectivity of Presupposition with Various  Triggers and Environments

The behaviour of statistical relational representations across differently
sized domains has become a focal area of research from both a modelling and a
complexity viewpoint.Recently, projectivity of a family of distributions
emerged as a key property, ensuring that marginal probabilities are independent
of the domain size. However, the formalisation used currently assumes that the
domain is characterised only by its size. This contribution extends the notion
of projectivity from families of distributions indexed by domain size to
functors taking extensional data from a database. This makes projectivity
available for the large range of applications taking structured input. We
transfer key known results on projective families of distributions to the new
setting. This includes a characterisation of projective fragments in different
statistical relational formalisms as well as a general representation theorem
for projective families of distributions. Furthermore, we prove a
correspondence between projectivity and distributions on countably infinite
domains, which we use to unify and generalise earlier work on statistical
relational representations in infinite domains. Finally, we use the extended
notion of projectivity to define a further strengthening, which we call
$\sigma$-projectivity, and which allows the use of the same representation in
different modes while retaining projectivity.

本文研究统计关系表示在不同规模域中的行为，并通过将域的概念从仅大小表示扩展到从数据库中获取的外延数据的函子，为更广泛的应用提供了 projectivity。将关于 projective families 的关键结果转移到了新的设置中，从而证明了 projectivity 和无限域上的分布之间的对应关系，并使用扩展后的 projectivity 定义了更强大的 sigma-projectivity。

工程性重新审视

Projectivity revisited

Markov Logic Networks (MLNs) define a probability distribution on relational
structures over varying domain sizes. Many works have noticed that MLNs, like
many other relational models, do not admit consistent marginal inference over
varying domain sizes. Furthermore, MLNs learnt on a certain domain do not
generalize to new domains of varied sizes. In recent works, connections have
emerged between domain size dependence, lifted inference and learning from
sub-sampled domains. The central idea to these works is the notion of
projectivity. The probability distributions ascribed by projective models
render the marginal probabilities of sub-structures independent of the domain
cardinality. Hence, projective models admit efficient marginal inference,
removing any dependence on the domain size. Furthermore, projective models
potentially allow efficient and consistent parameter learning from sub-sampled
domains. In this paper, we characterize the necessary and sufficient conditions
for a two-variable MLN to be projective. We then isolate a special model in
this class of MLNs, namely Relational Block Model (RBM). We show that, in terms
of data likelihood maximization, RBM is the best possible projective MLN in the
two-variable fragment. Finally, we show that RBMs also admit consistent
parameter learning over sub-sampled domains.

该论文研究了马尔可夫逻辑网络及其特征，提出了一种基于 projectivity 的模型 ——relational block model (RBM), 并证明了它是在二元片段中最佳 projective MLN，并且可以对采样数据进行一致的参数学习。

关于马尔科夫逻辑网络中的可投影性

On Projectivity in Markov Logic Networks

A subtle difference between propositional and relational data is that in many
relational models, marginal probabilities depend on the population or domain
size. This paper connects the dependence on population size to the classic
notion of projectivity from statistical theory: Projectivity implies that
relational predictions are robust with respect to changes in domain size. We
discuss projectivity for a number of common SRL systems, and identify syntactic
fragments that are guaranteed to yield projective models. The syntactic
conditions are restrictive, which suggests that projectivity is difficult to
achieve in SRL, and care must be taken when working with different domain
sizes.

本文研究了命题数据和关系数据之间微妙差别，指出在许多关系模型中，边缘概率取决于人口或领域的大小，将此与统计理论中的经典概率密度函数基本概念建立联系：Projectivity 意味着关系预测对领域大小的变化具有鲁棒性，讨论了许多常见 SRL 系统的 projectivity，找出了保证产生 projective 模型的语法片段，但语法条件是限制性的，这表明在 SRL 中难以实现 projectivity，应注意区分不同领域大小。