#  blossomRedPInKS: Preconditioned Commonsense Inference with Minimal
Supervision

Ehsan Qasemi∗ Piyush Khanna∗ Qiang Ning† Muhao Chen∗
$*$Department of Computer Science, University of Southern California
$\dagger$Amazon Inc.
<EMAIL_ADDRESS><EMAIL_ADDRESS>

###### Abstract

Reasoning with preconditions such as “glass can be used for drinking water
unless the glass is shattered” remains an open-problem for language models.
The main challenge lies in the scarcity of preconditions data and model’s lack
of support for such reasoning. We present PInKS , Preconditioned Commonsense
Inference with WeaK Supervision, an improved model for reasoning with
preconditions through minimum supervision. We show, both empirically and
theoretically, that PInKS improves the results on benchmarks focused on
reasoning with the preconditions of commonsense knowledge (up to $40\%$
Macro-F1 scores). We further investigate PInKS through PAC-Bayesian
informativeness analysis, precision measures and ablation study.

##  1 Introduction

Inferring the effect of a situation or precondition on a subsequent action or
state (illustrated in Figure 1) is an open part of commonsense reasoning. It
requires an agent to possess and understand different dimensions of
commonsense knowledge Woodward (2011), e.g. physical, causal, social, etc.
This ability can improve many knowledge-driven tasks such as question
answering Wang et al. (2019); Talmor et al. (2019), machine reading
comprehension Sakaguchi et al. (2020), and narrative prediction Mostafazadeh
et al. (2016). It also seeks to benefit a wide range of real-world intelligent
applications such as legal document processing Hage (2005), claim verification
Nie et al. (2019) and debate processing Widmoser et al. (2021).

Figure 1: Examples on Preconditioned Inference and the NLI format they can be
represented in.

Multiple recent studies have taken the effort on reasoning with preconditions
of commonsense knowledge Rudinger et al. (2020); Qasemi et al. (2022);
Mostafazadeh et al. (2020); Hwang et al. (2020). These studies show that
preconditioned reasoning represents an unresolved challenge to state-of-the-
art (SOTA) language model (LM) based reasoners. Generally speaking, the
problem of reasoning with preconditions has been formulated as variations of
the natural language inference (NLI) task where, given a precondition/update,
the model has to decide its effect on common sense statement or chain of
statements. For example, PaCo Qasemi et al. (2022) approaches the task from
the causal (hard reasoning) perspective in term of _enabling_ and _disabling_
preconditions of commonsense knowledge, and evaluate reasoners with
crowdsourced commonsense statements about the two polarities of preconditions
of statements in ConceptNet Speer et al. (2017). Similarly, $\delta-$NLI
Rudinger et al. (2020) formulates the problem from the perspective of soft
assumptions, i.e., _weakeners_ and _strengtheners_ , and justify whether they
_update_ sentences to _weakens_ or _strengthens_ the textual entailment in
sentence pairs from sources such as SNLI Bowman et al. (2015). Obviously, both
tasks capture the same phenomena of reasoning with preconditions and the
slight difference in format does not hinder their usefulness Gardner et al.
(2019). As both works conclude, SOTA models generally fall short of tackling
these tasks.

We identify two reasons for such shortcomings of LMs on reasoning with
preconditions: 1) relying on expensive direct supervision and 2) the need of
improved LMs to reason with such knowledge. First, current resources for
preconditions of common sense are manually annotated. Although this yields
high-quality direct supervision, it is costly and not scalable. Second, off-
the-shelf LMs are trained on free-text corpora with no direct guidance on
specific tasks. Although such models can be further fine-tuned to achieve
impressive performance on a wide range of tasks, they are far from perfect in
reasoning on preconditions due to their complexity of need for deep
commonsense understanding and lack of large scale training data.

In this work, we present PInKS (see Figure 2), a minimally supervised approach
for reasoning with the precondition of commonsense knowledge in LMs. The main
contributions are 3 points. First, to enhance training of the reasoning model
(Section 3), we propose two strategies of retrieving rich amount of cheap
supervision signals (Figure 1). In the first strategy (Section 3.1), we use
common linguistic patterns (e.g. “[action] unless [precondition]”) to gather
sentences describing preconditions and actions associated with them from
massive free-text corpora (e.g. OMCS Havasi et al. (2010)). The second
strategy (Section 3.2) then uses generative data augmentation methods on top
of the extracted sentences to induce even more training instances. As the
second contribution (Section 3.3), we improve LMs with more targeted
preconditioned commonsense inference. We modify the masked language model
(MLM) learning objective to biased masking, which puts more emphasis on
preconditions, hence improving the LMs capability to reason with
preconditions. Finally, for third contribution, we go beyond empirical
analysis of PInKS and investigate the performance and robustness through
theoretical guarantees of PAC-Bayesian analysis He et al. (2021).

Through extensive evaluation on five representative datasets (ATOMIC2020 Hwang
et al. (2020), WINOVENTI Do and Pavlick (2021), ANION Jiang et al. (2021),
PaCo Qasemi et al. (2022) and DNLI Rudinger et al. (2020), we show that PInKS
improves the performance of NLI models, up to $5\%$ Macro-F1 without seeing
any task-specific training data and up to $40\%$ Macro-F1 after being
incorporated into them (Section 4.1). In addition to the empirical results,
using theoretical guarantees of informativeness measure in PABI He et al.
(2021), we show that the minimally supervised data of PInKS is as informative
as fully supervised datasets (Section 4.2). Finally, to investigate the
robustness of PInKS and effect of each component, we focus on the weak
supervision part (Section 5). We perform ablation study of PInKS w.r.t. the
linguistic patterns themselves, the recall value associated with linguistic
patterns, and finally contribution of each section to overall quality and the
final performance.

Figure 2: Overview of the three minimally supervised methods in PInKS.

##  2 Problem Definition

Common sense statements describe well-known information about concepts, and,
as such, they are acceptable by people without need for debate Sap et al.
(2019); Davis and Marcus (2015). The preconditions of common sense knowledge
are eventualities that affect happening of a common sense statement Hobbs
(2005). Here, we only distinguish between the possibility that a statement is
true given preconditions and the general possibility for it to be true without
depending on extra information. These preconditions can either allow or
prevent the common sense statement in different degrees Rudinger et al.
(2020); Qasemi et al. (2022). For example, Qasemi et al. (2022) model the
preconditions as _enabling_ and _disabling_ (hard preconditions), whereas
Rudinger et al. (2020) model them as _strengthening_ and _weakening_(soft
preconditions).

Beyond the definition of preconditions, the task of inference with
preconditions is also defined differently among the literature. Some task
definitions have strict constraints on the format of statement, e.g. two
sentence format Rudinger et al. (2020) or being human-related Sap et al.
(2019), whereas others do not Do and Pavlick (2021); Qasemi et al. (2022).

To unify the definitions in available literature, we define the preconditioned
inference task as below:

###### Definition 1

Preconditioned Inference: given a common sense statement and an update
sentence that serves as precondition, is the statement still allowed or
prevented?

This definition is consistent with definitions in the literature (for more
details see appendix G). First, similar to the definition by Rudinger et al.
(2020), the update can have different levels of effect on the statement (no
degree constraint), from causal connection (hard) to material implication
(soft). Second, similar to the one Qasemi et al. (2022), the statement can
have any format (no format constraint).

##  3 Preconditioned Inference with Minimal Supervision

In PInKS, to overcome the challenges associated with inference with
preconditions, we propose two sources of weak supervision to enhance the
training of a reasoner: linguistic patterns to gather rich (but allowably
noisy) preconditions (Section 3.1), and generative augmentation of the
preconditions data (Section 3.2). The main hypothesis in using weak-
supervision methods is that pretraining models on large amount of weak-
supervised labeled data could improve model’s performance on similar
downstream tasks Ratner et al. (2017). In weak supervision terminology for
heuristics, the experts design a set of heuristic labeling functions (LFs)
that serves as the generators of the noisy label Ratner et al. (2017). These
labeling functions can produce overlapping or conflicting labels for a single
instance of data that will need to be resolved either with simple methods such
as ensemble inference or more sophisticated probabilistic methods such as data
programming Ratner et al. (2016), or generative Bach et al. (2017). Here, the
expert still needs to design the heuristics to query the knowledge and convert
the results to appropriate labels for the task. In addition, we propose the
modified language modeling objective that uses biased masking to improve the
precondition-reasoning capabilities of LMs (Section 3.3).

###  3.1 Weak Supervision with Linguistic Patterns

We curate a large-scale automatically labeled dataset for, both type of,
preconditions of commonsense statements by defining a set of linguistic
patterns and searching through raw corpora. Finally, we have a post-processing
filtering step to ensure the quality of the extracted preconditions.

#### Raw Text Corpora:

In our experiments, we acquire weak supervision from two corpora: Open Mind
Common Sense (OMCS) Singh et al. (2002) and ASCENT Nguyen et al. (2021a). OMCS
is a large commonsense statement corpus that contains over 1M sentences from
over 15,000 contributors. ASCENT has consolidated over 8.9M commonsense
statements from the Web.

First, we use sentence tokenization in NLTK Bird et al. (2009) to separate
individual sentences in the raw text. Each sentence is then considered as an
individual statement to be fed into the labeling functions. We further filter
out the data instances based on the conjunctions used in the common sense
statements after processing the labeling functions (discussed in Post-
Processing paragraph).

Text | Label |  Action | Precondition
---|---|---|---
A drum makes noise  only if you beat it. | Allow |  A drum makes noise | you beat it.
Your feet might come into contact with something  if it is on the floor. | Allow |  Your feet might come into contact with something | it is on the floor.
Pears will rot  if not refrigerated | Prevent |  Pears will rot | refrigerated
Swimming pools have cold water in the winter  unless they are heated. | Prevent |  Swimming pools have cold water in the winter | they are heated.
Table 1: Examples from the collected dataset through linguistic patterns in
Section 3.1.

#### Labeling Functions (LF):

We design the LFs required for weak-supervision with a focus on the presence
of a linguistic pattern in the sentences based on a conjunction (see Table 1
for examples). In this setup, each LF labels the training data as _Allowing_ ,
_Preventing_ or _Abstaining_ (no label assigned) depending on the linguistic
pattern it is based on. For example, as shown in Table 1 the presence of
conjunctions only if and if, with a specific pattern, suggests that the
precondition _Allows_ the action. Similarly, the presence of the conjunction
unless indicates a _Preventing_ precondition. We designed 20 such LFs based on
individual conjunctions through manual inspection of the collected data in
several iterations, for which details are described in section A.1.

#### Extracting Action-Precondition Pairs

Once the sentence have an assigned label, we extract the action-precondition
pairs using the same linguistic patterns. This extraction can be achieved by
leveraging the fact that a conjunction divides a sentence into action and
precondition in the following pattern “precondition conjunction action”, as
shown in Table 1.

However, there could be sentences that contain multiple conjunctions. For
instance, the sentence “Trees continue to grow for all their lives except in
winter if they are not evergreen.” includes two conjunctions “except” and
“if”. Such co-occurring conjunctions in a sentence leads to ambiguity in the
extraction process. To overcome this challenge, we further make selection on
the patterns by measuring their precisions 111how many of the labeled
instances (non-abstaining) for each labeling function are relevant. To do so,
we sample $20$ random sentences from each conjunction ($400$ total) and label
them manually on whether they are relevant to our task or not by two expert
annotators. If a sentence is relevant to the task, it is labeled as $1$;
otherwise, $0$. We then average the scores of two annotators for each
pattern/conjunction to get its precision score. This precision score serves as
an indicator of the quality of preconditions extracted by the
pattern/conjunction in the context of our problem statement. Hence, priority
is given to a conjunction with a higher precision in case of ambiguity.
Further, we also set a minimum precision threshold (=$0.7$) to filter out the
conjunctions having a low precision score (8 LFs), indicating low relevance to
the task of reasoning with preconditions (see Section A.1 for list of
precision values).

#### Post-Processing

On manual inspection of sentences matched by the patterns, we observed a few
instances from random samples that were not relevant to the context of
commonsense reasoning tasks, for example: How do I know if he is sick? or,
Pianos are large but entertaining. We accordingly filter out sentences that
are likely to be irrelevant instances. Specifically, those include 1)
questions which are identified based on presence of question mark and
interrogative words (List of interrogative words in Section A.4), or 2) do not
have a verb in their precondition. Through this process we end up with a total
of 113,395 labeled action-precondition pairs with 102,474 _Allow_ and 10,921
_Prevent_ assertions.

###  3.2 Generative Data Augmentation

To further augment and diversify training data, we leverage another technique
of retrieving weak supervision signals by probing LMs for generative data
augmentation. To do so, we mask the nouns and adjectives (pivot-words) from
the text and let the generative language model fill in the masks with
appropriate alternatives.

After masking the pivot-word and filling in the mask using the LM, we filter
out the augmentations that change the POS tag of the pivot-word and then keep
the top 3 predictions for each mask. In addition, to keep the diversity of the
augmented data, we do not use more than 20 augmented sentences for each
original statement (picked randomly). For example, in the statement “Dogs are
pets unless they are wild”, the pivot-words are “dogs”, “pets” and “wild”.
Upon masking “dogs”, using RoBERTa (large) language model, we get valid
augmentations such as “Cats are pets unless they are wild”. Using this
generative data augmentation, we end up with $7M$ labeled action-precondition
pair with $11\%$ _prevent_ preconditions.

###  3.3 Precondition-Aware Biased Masking

To increase the LM’s attention on preconditions, we used biased masking on
conjunctions as the closest proxies to preconditions’ reasoning. Based on this
observation, we devised a biased masked language modeling loss that solely
focuses on masking conjunctions in the sentences instead of random tokens.
Similar to Dai et al. (2019), we mask the whole conjunction word in the
sentence and ask the LM to fulfill the mask. The goal here is to start from a
pretrained language model and, through this additional fine-tuning step,
improve its ability to reason with preconditions. To use such fine-tuned LM in
a NLI module, we further fine-tune the “LM+classification head” on subset of
MNLI Williams et al. (2018) dataset. For full list of conjunctions and
implementation details check Section A.3.

##  4 Experiments

This section first showcases improvements of PInKS on five representative
tasks for preconditioned inference (Section 4.1). We then theoretically
justify the improvements by measuring the informativeness of weak supervision
by PInKS using PABI He et al. (2021) score and then experiment on the effect
of precision (discussed in section 3.1) on PInKS using PABI score (Section
4.2). Additional analysis on various training strategies of PInKS is also
provided in Appendix C.

###  4.1 Main Results

Comparing the capability for models to reason with preconditions across
different tasks requires canonicalizing the inputs and outputs in such tasks
be in the same format. We used natural language inference (NLI) as such a
canonical format. PaCo Qasemi et al. (2022) and $\delta$-NLI Rudinger et al.
(2020) are already formulated as NLI and others can be converted easily using
the groundwork laid by Qasemi et al. (2022). In NLI, given a sentence pair
with a _hypothesis_ and a _premise_ , one predicts whether the hypothesis is
true (entailment), false (contradiction), or undetermined (neutral) given the
premise Williams et al. (2018). Each task is preserved with equivalence before
and after any format conversion at here, hence conversion does not seek to
affect the task performance, inasmuch as it is discussed by Gardner et al.
(2019). More details on this conversion process are in Appendix B, and
examples from the original target datasets are given in Table 8.

#### Setup

To implement and execute labeling functions, and resolve labeling conflict, we
use Snorkel Ratner et al. (2017), one of the SOTA frameworks for algorithmic
labeling on raw data that provides ease-of-use APIs.222Other alternatives such
as skweak Lison et al. (2021) can also be used for this process. For more
details on Snorkel and its setup details, please see Appendix A.2.

For each target task, we start from a pretrained NLI model (RoBERTa-Large-MNLI
Liu et al. (2019)), fine-tune it according to PInKS (as discussed in Section
3) and evaluate its performance on the test portion of the target dataset in
two setups: zero-shot transfer learning without using the training data for
the target task (labeled as _PInKS_ column) and fine-tuned on the training
portion of the target task (labeled as _Orig.+PInKS_). To facilitate
comparison, we also provide the results for fully fine-tuning on the training
portion of the target task and evaluating on its testing portion (labeled as
_Orig._ column; PInKS is not used here). To create the test set, if the
original data does not provide a split (e.g. ATOMIC and Winoventi), following
Qasemi et al. (2022), we use unified random sampling with the
$[0.45,0.15,0.40]$ ratio for train/dev/test. For all the tasks, we used the
pretrained model from _huggingface_ Wolf et al. (2020), and utilized PyTorch
Lightning Falcon and The PyTorch Lightning team (2019) library to manage the
fine-tuning process. We evaluate each performance by aggregating the
_Macro-F1_ score (implemented in Pedregosa et al. (2011)) on the ground-truth
labels and report the results on the unseen test split of the data.

#### Discussion

Target Task | Orig. | PInKS | Orig+PInKS
---|---|---|---
$\delta$-NLI | 83.4 | 60.3 | 84.1
PaCo | 77.1 | 69.5 | 68.0
ANION | 81.1 | 52.9 | 81.2
ATOMIC | 43.2 | 48.0 | 88.6
Winoventi | 51.1 | 52.4 | 51.3
Table 2: Macro-F1 (%) results of PInKS on the target datasets: no PInKS
(_Orig._), with PInKS in zero-shot transfer learning setup (_PInKS_) and PInKS
in addition to original task’s data (_Orig.+PInKS_). Bold values are cases
where PInKS is improving supervised results.

Table 2 presents the evaluation results of this section. As illustrated, on
ATOMIC Hwang et al. (2020) and Winoventi Do and Pavlick (2021), PInKS exceeds
the supervised results even without seeing any examples from the target data
(zero-shot transfer learning setup). On $\delta$-NLI Rudinger et al. (2020),
ANION Jiang et al. (2021) and ATOMIC Hwang et al. (2020), combination of PInKS
and train subset of target task (PInKS in low-resource setup) outperforms the
target task results. This shows PInKS can also utilize additional data from
target task to achieve better performance consistently across different
aspects of preconditioned inference. However, on PaCo Qasemi et al. (2022),
PInKS is not able to outperform original target task results in none of the
setups. This can be attributed to nature of data in PaCo, on the contrary to
other tasks, focuses on hard preconditions instead of soft ones Qasemi et al.
(2022). This result is also consistent with Qasemi et al. (2022) results on
transfer learning from soft to hard preconditioned reasoning.

###  4.2 Informativeness Evaluation

He et al. (2021) proposed a unified PAC-Bayesian motivated informativeness
measure, namely PABI, that correlates with the improvement provided by the
incidental signals to indicate their effectiveness on a target task. The
incidental signal can include an inductive signal, e.g. partial/noisy labeled
data, or a transductive signal, e.g. cross-domain signal in transfer learning.

In this experiment, we go beyond the empirical results and use the PABI
measure to explain how improvements from PInKS are theoretically justified.
Here, we use the PABI score for cross-domain signal assuming the weak
supervised data portion of PInKS (Section 3.1 and Section 3.2) as a indirect
signal for a given target task. We use PABI measurements from two perspective.
First, we examine how useful is the weak supervised data portion of PInKS for
target tasks in comparison with fully-supervised data. And second, we examine
how the precision of the linguistic patterns (discussed in Section 3.1)
affects this usefulness.

#### Setup

We carry over the setup on models and tasks from Section 4.1. For details on
the PABI itself and the measurement details associated with it, please see
Appendix E. For the aforementioned first perspective, we only consider PaCo
and $\delta$-NLI as target tasks. We measure the PABI of the weak supervised
data portion of PInKS on the two target tasks, and compare it with the PABI of
the fully-supervised data from Section 4.1. For the second perspective, we
only focus on PInKS and consider PaCo as target task. We create different
versions of the weak supervised data portion of PInKS with different levels of
precision threshold (e.g. $0.0$, $0.5$) and compare their informativeness on
PaCo. To limit the computation time, we only use $100K$ samples from the weak
supervised data portion of PInKS in each threshold value, which is especially
important in lower thresholds due to huge size of extracted patterns with low
precision threshold.

#### Informativeness in Comparison with Direct Supervision:

Table 3 summarizes the PABI informativeness measure in comparison with other
datasets with respect to PaCo Qasemi et al. (2022) and $\delta$-NLI Rudinger
et al. (2020). To facilitate the comparison of PABI scores in Table 3, we have
also reported the minimum achievable (Zero Rate classifier) and maximum
achievable PABI scores. To clarify, to compute the maximum achievable PABI
score, the training subset of the target task is considered as an indirect
signal for the test subset, and we assume that the training subset is in
practice the most informative indirect signal available. Our results show that
although, PInKS is not the top informative incidental signal on the both
target dataset, its PABI numbers are still significant considering that its
the only weak-supervision data which is automatically acquired, while others
are acquired based on human annotations.

| PABI on
---|---
Indir. Task | PaCo |  $\delta$-NLI | ATOMIC
PInKS | 37 | 67 | 78
$\delta$-NLI | 52 | 86 | 68
PaCo | 52 | 31 | 78
ANION | 34 | 14 | 18
ATOMIC | 21 | 17 | 12
Winoventi | 36 | 53 | 65
Zero Rate | 26 | 2 | 7
Table 3: PABI informativeness measures (x100) of PInKS and other target tasks
w.r.t PaCo and $\delta$-NLI. Bold values represent the maximum achievable PABI
Score (per target task) by considering train subset as an _indirect_ signal
for test subset of respective data. The highest PABI score, excluding the max
achievable (per target task), is indicated in italic.

#### Effect of Precision on Informativeness:

Figure 3 presents the PABI informativeness estimation on weak supervision data
under different threshold levels of precision values, and compare them with
the “zero rate” classifier (always predicting majority class). As illustrated,
the informativeness show a significant drop in lower precision showcasing the
importance of using high precision templates in our weak-supervision task. For
higher thresholds ($0.95$) the data will mostly consist of _allow_ patterns,
the model drops to near zero rate informativeness baseline again. This
susceptibility on pattern precision can be mitigated with having more fine-
grained patterns on larger corpora. We leave further analysis on precision of
patterns to future work.

Figure 3: PABI informativeness measures of PInKS with different precision
thresholds on PaCo.

##  5 Analysis on Weak Supervision

In this section, we shift focus from external evaluation of PInKS on target
tasks to analyze distinct technical component of PInKS. Here, through an
ablation study, we try to answer four main questions to get more insight on
the weak supervision provided by those components. First (Q1), how each
labeling function (LF; Section 3.1) is contributing to the extracted
preconditions? Second (Q2), what is the quality of the weak supervision data
obtained from different ways of data acquisition? Third (Q3), how does
generative data augmentation (Section 3.2) contribute to PInKS? And finally
(Q4), how much does the precondition-aware masking (Section 3.3) affect the
overall performance of PInKS?

#### (Q1) LF Analysis:

To address the first question, we use statistics of the 6 top performing LFs
(see Appendix F for detailed results). These 6 top performing LFs generate
more than 80% of data (Coverage) with the highest one generating 59% of data
and lowest one generating 1%. Our results show that, in 0.14% of instances we
have conflict among competing LFs with different labels and in 0.12% we have
overlap among LFs with similar labels, which showcases the level of
independence each LF has on individual samples333convectional inner-annotator
agreement (IAA) methods hence are not applicable.

#### (Q2) Quality Control:

To assess the quality of collected data, we used an expert annotator. The
expert annotator is given a subset of the collected preconditions
(preconditions-statement-label triplet) and asked to assign a binary label
based on whether each the precondition is valid to its statement w.r.t the
associated label. We then report the average quality score as a proxy for
precision of data. We sampled 100 preconditions-statement-label triplets from
three checkpoint in the pipeline: 1) extracted through linguistic patterns
discussed in Section 3.1, 2) outcome of the generative augmentations discussed
in Section 3.2, and 3) final data used in Section 3.3. Table Table 4 contains
the average precision of the collected data, that shows the data has
acceptable quality with minor variance in quality for different weak
supervised steps in PInKS.

Checkpoint Name Precision. % Linguistic Patterns from Section 3.1 78
Generative Augmentation from Section 3.2 76 Final Data used in Section 3.3 76

Table 4: Precision of the sampled preconditions-statement-label triplets from
three checkpoints in pipeline.

#### (Q3) Effectiveness of Generative Augmentation:

The main effect of generative data augmentation (Section 3.2) is, among
others, to acquire PInKS additional training samples labeled as _prevent_ from
pretrained LMs. When considering PaCo as target task, the PInKS that does not
use this technique (no-augment-PInKS) sees a $4.14\%$ absolute drop in
Macro-F1 score. Upon further analysis of the two configurations, we observed
that the no-augment-PInKS leans more toward the zero rate classifier (only
predicting _allow_ as the majority class) in comparison to the PInKS.

#### (Q4) Effectiveness of Biased Masking:

We focus on PaCo as the target task and compare the results of PInKS with an
alternative setup with no biased masking. In the alternative setup, we only
use the weak-supervision data obtained through PInKS to fine-tune the RoBERTa-
Large-MNLI model and compare the results. Our results show that the Macro-F1
score for zero-shot transfer learning setup drops to $68.4\%$ (from $69.5\%$)
without biased masking process.

##  6 Related Work

#### Reasoning with Preconditions

Collecting preconditions of common sense and reasoning with them has been
studied in multiple works. Rudinger et al. (2020) uses the notion of
“defeasible inference” Pollock (1987); Levesque (1990) in term of how an
_update_ sentence weakens or strengthens a common sense hypothesis-premise
pair. For example, given the premise “Two men and a dog are standing among
rolling green hills.”, the _update_ “The men are studying a tour map” weakens
the hypothesis that “they are farmers”, whereas “The dog is a sheep dog”
strengthens it. Similarly, PaCo Qasemi et al. (2022) uses the notion of
“causal complex” from Hobbs (2005), and defines preconditions as eventualities
that either allow or prevent (allow negation Fikes and Nilsson (1971) of) a
common sense statement to happen. For example, for the knowledge “the glass is
shattered” prevents the statement “A glass is used for drinking water”,
whereas "there is gravity" allows it. In PaCo, based on Shoham (1990) and
Hobbs (2005), authors distinguish between two type of preconditions, causal
connections (_hard_), and material implication (tends to cause; _soft_). Our
definition covers these definitions and is consistent with both.

Hwang et al. (2020), Sap et al. (2019), Heindorf et al. (2020), and Speer et
al. (2017), provided representations for preconditions of statements in term
of relation types, e.g. _xNeed_ in ATOMIC2020 Hwang et al. (2020). However,
the focus in none of these works is on evaluating SOTA models on such data.
The closest study of preconditions to our work are Rudinger et al. (2020),
Qasemi et al. (2022), Do and Pavlick (2021) and Jiang et al. (2021). In these
works, direct human supervision (crowdsourcing) is used to gather
preconditions of commonsense knowledge. They all show the shortcomings of SOTA
models on dealing with such knowledge. Our work differs as we rely on
combination of distant-supervision and targeted fine-tuning instead of direct
supervision to achieve on-par performance. Similarly, Mostafazadeh et al.
(2020), and Kwon et al. (2020) also study the problem of reasoning with
preconditions. However they do not explore _preventing_ preconditions.

#### Weak Supervision

In weak-supervision, the objective is similar to supervised learning. However
instead of using human/expert resource to directly annotate unlabeled data,
one can use the experts to design user-defined patterns to infer “noisy” or
“imperfect” labels Rekatsinas et al. (2017); Zhang et al. (2017); Dehghani et
al. (2017), e.g. using heuristic rules. In addition, other methods such as re-
purposing of external knowledge Alfonseca et al. (2012); Bunescu and Mooney
(2007); Mintz et al. (2009) or other types of domain knowledge Stewart and
Ermon (2017) also lie in the same category. Weak supervision has been used
extensively in NLU. For instance, Zhou et al. (2020) utilize weak-supervision
to extract temporal commonsense data from raw text, Brahman et al. (2020) use
it to generate reasoning rationale, Dehghani et al. (2017) use it for improved
neural ranking models, and Hedderich et al. (2020) use it to improve
translation in African languages. Similar to our work, ASER Zhang et al.
(2020) and ASCENT Nguyen et al. (2021b) use weak supervision to extract
relations from unstructured text. However, do not explore preconditions and
cannot express _preventing_ preconditions. As they do focus on reasoning
evaluation, the extent in which their contextual edges express _allowing_
preconditions is unclear.

#### Generative Data Augmentation

Language models can be viewed as knowledge bases that implicitly store vast
knowledge on the world. Hence querying them as a source of weak-supervision is
a viable approach. Similar to our work, Wang et al. (2021) use LM-based
augmentation for saliency of data in tables, Meng et al. (2021) use it as a
source of weak-supervision in named entity recognition, and Dai et al. (2021)
use masked LMs for weak supervision in entity typing.

##  7 Conclusion

In this work we presented PInKS , as an improved method for preconditioned
commonsense reasoning which involves two techniques of weak supervision. To
maximize the effect of the weak supervision data, we modified the masked
language modeling loss function using biased masking method to put more
emphasis on conjunctions as closest proxy to preconditions. Through empirical
and theoretical analysis of PInKS, we show it significantly improves the
results across the benchmarks on reasoning with the preconditions of
commonsense knowledge. In addition, we show the results are robust in
different precision values using the PABI informativeness measure and
extensive ablation study.

Future work can consider improving the robustness of preconditioned inference
models using methods such as virtual adversarial training Miyato et al.
(2018); Li and Qiu (2020). With advent of visual-language models such as Li et
al. (2019), preconditioned inference should also expand beyond language and
include different modalities (such as image or audio). To integrate in down-
steam tasks, one direction is to include such models in aiding inference in
the neuro-symbolic reasoners Lin et al. (2019); Verga et al. (2020).

## Ethical Consideration

We started from openly available data that is both crowdsource-contributed and
neutralized, however they still may reflect human biases. For example in case
of PaCo Qasemi et al. (2022) they use ConceptNet as source of commonsense
statements which multiple studies have shown its bias and ethical issues, e.g.
Mehrabi et al. (2021).

During design of labeling functions we did not collect any sensitive
information and the corpora we used were both publicly available, however they
may contain various types of bias. The labeling functions in PInKS are only
limited to English language patterns, which may additional cultural bias to
the data. However, our expert annotators did not notice any offensive language
in data or the extracted preconditions. Given the urgency of addressing
climate change we have reported the detailed model sizes and runtime
associated with all the experiments in Appendix D.

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##  Appendix A Details on PInKS Method

In this section, we discuss some of the extra details related to PInKS and its
implementation.

###  A.1 Linguistic Patterns for PInKS

We use a set of conjunctions to extract sentences that follow the action-
precondition sentence structure. Initially, we started with two simple
conjunctions-if and unless, for extracting assertions containing _Allowing_
and _Preventing_ preconditions, respectively. To further include similar
sentences, we expanded our vocabulary by considering the synonyms of our
initial conjunctions. Adding the synonyms of unless we got the following set
of new conjunctions for _Preventing_ preconditions-{but, except, except for,
if not, lest, unless}, similarly we expanded the conjunctions for Enabling
preconditions using the synonyms of if-{contingent upon, in case, in the case
that, in the event, on condition, on the assumption, supposing}. Moreover, on
manual inspection of the OMCS and ASCENT datasets, we found the following
conjunctions that follow the Enabling precondition sentence pattern-{makes
possible, statement is true, to understand event}. Table 5, summarizes the
final patterns used in PInKS, coupled with their precision value and their
associated conjunction.

Conjunctions Precision Pattern but 0.17 {action} but {negative_precondition}
contingent upon 0.6 {action} contingent upon {precondition} except 0.7
{action} except {precondition} except for 0.57 {action} except for
{precondition} if 0.52 {action} if {precondition} if not 0.97 {action} if not
{precondition} in case 0.75 {action} in case {precondition} in the case that
0.30 {action} in the case that {precondition} in the event 0.3 {action} in the
event {precondition} lest 0.06 {action} lest {precondition} makes possible
0.81 {precondition} makes {action} possible. on condition 0.6 {action} on
condition {precondition} on the assumption 0.44 {action} on the assumption
{precondition} statement is true 1.0 The statement "{event}" is true because
{precondition}. supposing 0.07 {action} supposing {precondition} to understand
event 0.87 To understand the event "{event}", it is important to know that
{precondition}. unless 1.0 {action} unless {precondition} with the proviso -
{action} with the proviso {precondition} on these terms - {action} on these
terms {precondition} only if - {action} only if {precondition} make possible -
{precondition} makes {action} possible. without - {action} without
{precondition} excepting that - {action} excepting that {precondition}

Table 5: Linguistic patterns in PInKS and their recall value. For patterns
with not enough match in the corpora have empty recall values.

###  A.2 Details of Snorkel Setup

Beyond a simple API to handle implementing patterns and applying them to the
data, Snorkel’s main purpose is to model and integrate noisy signals
contributed by the labeling functions modeled as noisy, independent voters,
which commit mistakes uncorrelated with other LFs.

To improve the predictive performance of the model, Snorkel additionally
models statistical relationships between LFs. For instance, the model takes
into account similar heuristics expressed by two LFs to avoid "double
counting" of voters. Snorkel, further, models the generative learner as a
factor graph. A labeling matrix $\Lambda$ is constructed by applying the LFs
to unlabeled data points. Here, $\Lambda_{i,j}$ indicates the label assigned
by the $j^{th}$ LF for the $i^{th}$ data point. Using this information, the
generative model is fed signals via three factor types, representing the
labeling propensity, accuracy, and pairwise correlations of LFs.

$\phi^{Lab}_{i,j}(\Lambda)=\mathds{1}\\{\Lambda_{i,j}\neq\emptyset\\}$

$\phi^{Acc}_{i,j}(\Lambda)=\mathds{1}\\{\Lambda_{i,j}=y_{i}\\}$

$\phi^{Corr}_{i,j,k}(\Lambda)=\mathds{1}\\{\Lambda_{i,j}=\Lambda_{i,k}\\}$

The above three factors are concatenated along with the potential correlations
existing between the LFs and are further fed to a generative model which
minimizes the negative log marginal likelihood given the observed label matrix
$\Lambda$.

###  A.3 Modified Masked Language Modeling

Table 6 summarizes the list of _Allowing_ and _Preventing_ conjunctions which
the modified language modeling loss function is acting upon.

Type |  Conjunctions
---|---
Allowing |  only if, subject to, in case, contingent upon, given, if, in the case that, in case, in the case that, in the event, on condition, on the assumption, only if, so, hence, consequently, on these terms, subject to, supposing, with the proviso, so, thus, accordingly, therefore, as a result, because of that, as a consequence, as a result
Preventing |  but, except, except for, excepting that, if not, lest, saving, without, unless
Table 6: List of conjunctions used in modified masked loss function in section 3.3 Conjunction |  Pattern
---|---
to understand event |  To understand the event “{event}", it is important to know that {precondition}.
in case |  {action} in case {precondition}
statement is true |  The statement “{event}" is true because {precondition}.
except |  {action} except {precondition}
unless |  {action} unless {precondition}
if not |  {action} if not {precondition}
Table 7: Filtered Labeling Functions Patterns and their associated polarity.

###  A.4 Interrogative Words

On manual inspection of the dataset, we observed some sentences that were not
relevant to the common sense reasoning task. Many of such instances were
interrogative statements. We filter out such cases based on the presence of
interrogative words in the beginning of a sentence. These interrogative words
are listed below.

Interrogative words: ["Who", "What", "When", "Where", "Why", "How", "Is",
"Can", "Does", "Do"]

##  Appendix B Details on Target Data Experiments

For converting Rudinger et al. (2020), similar to Qasemi et al. (2022), we
concatenate the “Hypothesis” and “Premise” and consider then as NLI’s
hypothesis. We then use the “Update” sentence as NLI’s premise. The labels are
directly traslated based on _Update_ sentences’s label, _weakener_ to
_prevent_ and the _strengthener_ to _allow_.

To convert the ATOMIC2020 Hwang et al. (2020), similar to Qasemi et al.
(2022), we focused on three relations _HinderedBy_ , _Causes_ , and _xNeed_.
From these relations, edges with _HinderedBy_ are converted as _prevent_ and
the rest are converted as _allow_.

Winoventi Do and Pavlick (2021), proposes Winograd-style ENTAILMENT schemas
focusing on negation in common sense. To convert it to NLI style, we first
separate the two sentences in the masked_prompt of each instance to form
_hypothesis_ and _premise_. We get two versions of _premise_ by replacing the
MASK token in _premise_ with their _target_ or _incorrect_ tokens. For the
labels the version with _target_ token is considered as _allow_ and the
version with _incorrect_ token as _prevent_.

ANION Jiang et al. (2021), focuses on CONTRADICTION in general. We focus on
their commonsense dCONTRADICTION subset as it is clean of lexical hints. Then
we convert their crowdsourced _original head_ or _CONTRADICTION head_ as
hypothesis, and the lexicalized predicate and tail as the premise (e.g.
_xIntent_ to _PersonX intends to_). Finally the label depends on head is
_allow_ for _original head_ and _prevent_ for _CONTRADICTION head_. We also
replace “PersonX” and “PersonY” with random human names (e.g. “ALice”, “Bob”).

Finally, for the PaCo Qasemi et al. (2022), we used their proposed P-NLI task
as a NLI-style task derived from their preconditions dataset. We converted
their _Disabling_ and _Enabling_ labels to _prevent_ and _allow_ respectively.

Table 8 summarizes the conversion process through examples from the original
data and the NLI task derived from each.

Name Original Data Derived NLI Winoventi Do and Pavlick (2021) masked_prompt:
a Margaret smelled her bottle of maple syrup and it was sweet. The syrup is
{MASK}. Hypothesis: a Margaret smelled her bottle of maple syrup and it was
sweet. target: edible Premise: The syrup is edible/malodorous incorrect:
malodorous Label: ENTAILMENT/ CONTRADICTION ANION Jiang et al. (2021)
Orig_Head: PersonX expresses PersonX’s delight. Hypothesis: Alice expresses
Alice’s delight/anger. Relation: xEffect Premise: feel happy. Tail: Alice feel
happy Label: ENTAILMENT/ CONTRADICTION Neg_Head: PersonX expresses PersonX’s
anger. ATOMIC2020 Hwang et al. (2020) Head: PersonX takes a long walk.
Hypothesis: PersonX takes a long walk. Relation: HinderedBy Premise: It is 10
degrees outside.. Tail: It is 10 degrees outside. Label: CONTRADICTION
$\delta$-NLI Rudinger et al. (2020) Hypothesis: PersonX takes a long walk.
Hypothesis: PersonX takes a long walk. Premise: HinderedBy Premise: It is 10
degrees outside.. Update: It is 10 degrees outside. Label: CONTRADICTION
Label: Weakener PaCo Qasemi et al. (2022) Statement: A net is used for
catching fish. Hypothesis: A net is used for catching fish. Precondition: You
are in a desert. Premise: You are in a desert. Label: Disabling Label:
CONTRADICTION

Table 8: Examples from target tasks in NLI format

To run all the experiments, we fine-tune the models on tuning data for maximum
of 5 epochs with option for early stopping available upon 5 evaluation cycles
with less than $1e-3$ change on validation data. For optimizer, we use AdamW
Loshchilov and Hutter (2017) with learning rate of 3e-6 and default
hyperparamter for the rest.

##  Appendix C Curriculum vs. Multitask Learning

For results of Section 4.1, we considered the target task and PInKS as
separate datasets, and fine-tuned model sequentially on them (curriculum
learning;Pentina et al., 2015). We chose _curriculum_ learning setup due to
its simplicity in implementation, ease of fine-tuning process monitoring and
hyperparameter setup. It would also allow us to monitor each task separately
that increases interpretability of results.

However, in an alternative fine-tuning setup, one can merge the two datasets
into one and fine-tune the model on the aggregate dataset (multi-task
learning;Caruana, 1997). Here, we investigate such alternative and its effect
on the results of Section 4.1.

#### Setup

We use the same setup as Section 4.1 for fine-tuning the model on
_Orig.+PInKS_. Here instead of first creating PInKS and then fine-tuning it on
the target task, we merge the weak-supervision data of PInKS with the training
subset of the target task and then do fine-tuning on the aggregate dataset. To
manage length of this section, we only consider PaCo, $\delta$-NLI and
Winoventi as the target dataset.

Target Data | Orig+PInKS (Multi-Task) | Diff.
---|---|---
$\delta$-NLI | 72.1 | -11.00
PaCo | 77.3 | +9.3
Winoventi | 51.7 | +0.7
Table 9: Macro-F1 (x100) results of PInKS on the target datasets using _multi-
task_ fine-tuning strategy and its difference with _curriculum_ strategy.

#### Discussion

Table 9 summarizes the results for _multi-task_ learning setup and its
difference w.r.t to the results of the _curriculum_ learning setup in Table 2.
Using _multi-task_ learning does not show the consistent result across tasks.
We see significant performance loss on $\delta$-NLI on one hand and major
performance improvements on PaCo on the other. The Winoventi, however appears
to not change as much in the new setup. We leave further analysis of
_curriculum learning_ to future work.

##  Appendix D Model Sizes and Run-times

All the experiments are conducted on a commodity workstation with an Intel
Xeon Gold 5217 CPU and an NVIDIA RTX 8000 GPU. For all the fine-tuning results
in Table 2, Table 3 we used “RoBERTa-Large-MNLI” with 356M tuneable
parameters. The mean run-time on target datasets is 1hr 55mins.

For the augmentation in PInKS dataset, we used “BERT” language model with
$234M$ tuneable parameters. The mean run-time on the extracted sentences is
49hr.

##  Appendix E Details on PABI Measurement

PABI provides an Informativeness measure that quantifies the reduction in
uncertainty provided by incidental supervision signals. We use the PABI
measure to study the impact of transductive cross-domain signals obtained from
our weak-supervision approach.

Following He et al. (2021), in order to calculate PABI
$\hat{S}(\pi_{0},\tilde{\pi}_{0})$, we first find out $\eta$, the difference
between a perfect system and a gold system in the target domain $\mathcal{D}$
that uses a label set $\mathcal{L}$ for a task, using Eq.1.

$\begin{split}\eta&=\mathbb{E}_{x\sim
P_{\mathcal{D}(x)}}1(c(x)\neq\tilde{c}(x))\\\
&=\frac{(\lvert\mathcal{L}\rvert-1)(\eta_{1}-\eta_{2})}{1-\lvert\mathcal{L}\rvert(1-\eta_{1})}\end{split}$
(1)

Indir. Task | $|L|$ | $\eta_{1}$ | $\eta_{2}^{ATMC}$ | $\eta_{2}^{\textit{PaCo}}$ | $\eta_{2}^{\delta-NLI}$ | $\eta^{ATMC}$ | $\eta^{\textit{PaCo}}$ | $\eta^{\delta-NLI}$ | $\textit{PABI}^{ATMC}$ | $\textit{PABI}^{\textit{PaCo}}$ | $\textit{PABI}^{\delta-NLI}$
---|---|---|---|---|---|---|---|---|---|---|---
PInKS | 2 | 0.04 | 0.11 | 0.31 | 0.16 | 0.076 | 0.288 | 0.129 | 0.782 | 0.366 | 0.667
$\delta$-NLI | 2 | 0.13 | 0.22 | 0.28 | 0.16 | 0.122 | 0.203 | 0.046 | 0.683 | 0.522 | 0.855
PaCo | 2 | 0.03 | 0.10 | 0.22 | 0.33 | 0.074 | 0.202 | 0.318 | 0.786 | 0.523 | 0.313
ATOMIC | 2 | 0.01 | 0.57 | 0.62 | 0.60 | 0.608 | 0.622 | 0.602 | 0.184 | 0.209 | 0.174
ANION | 2 | 0.16 | 0.57 | 0.36 | 0.44 | 0.571 | 0.302 | 0.418 | 0.122 | 0.341 | 0.139
Winoventi | 2 | 0.19 | 0.10 | 0.37 | 0.31 | 0.139 | 0.289 | 0.196 | 0.647 | 0.364 | 0.534
Table 10: Details of PABI metric computations in Section 4.2 according to
Equation 1

Here, $P_{\mathcal{D}(x)}$ indicates the marginal distribution of $x$ under
$\mathcal{D}$, $c(x)$ refers to gold system on gold signals, $\tilde{c}(x)$ is
a perfect system on incidental signals, $\eta_{1}$ refers to the difference
between the silver system and the perfect system in the source domain,
$\acute{\eta_{1}}$ indicates difference between the silver system and the
perfect system in the target domain, and $\eta_{2}$ is the difference between
the silver system and the gold system in the target domain.

Using Eq.1, the informative measure supplied by the transductive signals
$\hat{S}(\pi_{0},\tilde{\pi}_{0})$ can be calculated as follows:

$\sqrt{1-\frac{\eta\ln(\lvert\mathcal{L}\rvert-1)-\eta\ln\eta-(1-\eta)\ln(1-\eta))}{\ln\lvert\mathcal{L}\rvert}}$

Table 10 contains the details associated computation of PABI score as reported
in Section 4.2.

##  Appendix F Details on LFs in PInKS

Table 11 shows Coverage (fraction of instances assigned the non-abstain label
by the labeling function), Overlaps (fraction of instances with at least two
non-abstain labels), and Conflicts (fraction of instances with conflicting and
non-abstain labels) on top performing LFs in PInKS.

LF name Cov. % Over. % Conf. % to understand 59.03 0.03 0.03 statement is
10.58 0.03 0.03 except 4.84 0.02 0.01 unless 4.79 0.04 0.04 in case 1.46 0.01
0.00 if not 1.00 0.01 0.01 Overall 81.69 0.14 0.12

Table 11: Coverage (fraction of raw corpus instances assigned the non-abstain
label by the labeling function), Overlaps (fraction of raw corpus instances
with at least two non-abstain labels), and Conflicts (fraction of the raw
corpus instances with conflicting (non-abstain) labels) on top performing LFs.
Green and  red color respectively represent LFs that assign _allow_ and
_prevent_ labels.

##  Appendix G Details on Preconditioned Inference in the Literature

As mentioned in section 2, existing literature does not have a consistent
(unified) definitions from to aspects: 1) the definition of the preconditions,
and 2) the definition of preconditioned inference.

First, existing literature define preconditions of common sense statements in
different degrees of impact on the statement. For example, Qasemi et al.
(2022) follows the notion of “causal complex” from Hobbs (2005), where for a
common sense statement $s$ preconditions of the statement $P_{f}(s)$ are
defined as collection of eventualities (events or states) that results in $s$
to happen. According to Qasemi et al. (2022), such eventualities can either
enable ($p_{f}^{+}\in P_{f}$) or disable ($p_{f}^{-}\in P_{f}$) the statement
to happen. Also, Qasemi et al. (2022) uses Fikes and Nilsson (1971) to define
disable as enabling the negation of the statement. On other hand, Rudinger et
al. (2020) defines strengthener as updates that a human would find them to
increase likelihood of a hypothesis, and the weakener as the one that humans
would find them to decrease it. Here, the focus on human’s opinion is stemmed
from definition of common sense. In this work, given the focus on noisy labels
derived from weak-supervision, we adopted the more relaxed definition from
Rudinger et al. (2020) for preconditions of common sense statements.

Second, there is also inconsistencies in the definition of reasoning with the
preconditions or preconditioned inference. Rudinger et al. (2020) has a strict
structure. It defines the task w.r.t to effect of precondition on the relation
of two sentences: hypothesis and premise; where a model has to find the type
of the precondition based on whether it strengthens or weakens the relation
between the two sentences. Differently, Qasemi et al. (2022) has a relaxed
definition in which the model is to decide if the precondition either enables
or disables the statement. Here the statement can have any format. Do and
Pavlick (2021), Hwang et al. (2020), and Jiang et al. (2021), on the other
hand, define only a generative task to evaluate the models. In this work,
again we adopted the more relaxed definition from Qasemi et al. (2022) that
imposes less constraint on weak-supervised data.