# Are LLMs classical or nonmonotonic reasoners? Lessons from generics

Alina Leidinger
ILLC
University of Amsterdam
<EMAIL_ADDRESS>
Robert van Rooij
ILLC
University of Amsterdam
<EMAIL_ADDRESS>
Ekaterina Shutova
ILLC
University of Amsterdam
<EMAIL_ADDRESS>
###### Abstract

Recent scholarship on reasoning in LLMs has supplied evidence of impressive
performance and flexible adaptation to machine generated or human feedback.
Nonmonotonic reasoning, crucial to human cognition for navigating the real
world, remains a challenging, yet understudied task. In this work, we study
nonmonotonic reasoning capabilities of seven state-of-the-art LLMs in one
abstract and one commonsense reasoning task featuring generics, such as ‘Birds
fly’, and exceptions, ‘Penguins don’t fly’ (see Fig. 1). While LLMs exhibit
reasoning patterns in accordance with human nonmonotonic reasoning abilities,
they fail to maintain stable beliefs on truth conditions of generics at the
addition of supporting examples (‘Owls fly’) or unrelated information (‘Lions
have manes’). Our findings highlight pitfalls in attributing human reasoning
behaviours to LLMs, as well as assessing general capabilities, while
consistent reasoning remains elusive.111Resources available at:
https://github.com/aleidinger/nonmonotonic_reasoning_generics

Are LLMs classical or nonmonotonic reasoners? Lessons from generics

Alina Leidinger ILLC University of Amsterdam<EMAIL_ADDRESS>Robert van
Rooij ILLC University of Amsterdam<EMAIL_ADDRESS>Ekaterina Shutova
ILLC University of Amsterdam<EMAIL_ADDRESS>

##  1 Introduction

Generics are unquantified statements such as ‘Birds fly’ or ‘Tigers are
striped’ (Carlson and Pelletier, 1995; Mari et al., 2013). They are
generalisations about kinds even if exceptions are known (‘Penguins don’t
fly’; Fig. 1). Humans typically accept generics even if the property in
question is rare among the kind (‘Ticks carry the lime disease’; Brandone et
al., 2012; Cimpian et al., 2010). Generics play a crucial role in human
beliefs on whether an example of a kind has a given property (Pelletier and
Asher, 1997). Human children master generics before they are able to reason
about quantified statements (Hollander et al., 2002; Leslie and Gelman, 2012).

In defeasible or nonmonotonic reasoning (Sloman and Lagnado, 2005; Ginsberg,
1987; Koons, 2005), a hypothesis follows defeasibly from a premise, if the
hypothesis is true in most normal cases in which the premise holds. Generics
make for a rich test bed for testing nonmonotonic reasoning capabilities
(Pelletier and Asher, 1997; Asher and Morreau, 1995). For example, given the
generic ‘Birds fly’ the inference ‘Tweety, the bird, can fly’ is defeasibly
valid (McCarthy, 1986; Reiter, 1988, i.a.), i.e., it is reasonable to assume
‘Tweety can fly’ even if exceptions are possible (‘Tweety is a penguin’)
(Lascarides and Asher, 1991). A classical reasoner however would reject the
generic ‘Birds fly’ upon learning that ‘Penguins don’t fly’.

Nonmonotonic reasoning is an integral part of human cognition (Russell, 2001),
that helps us to navigate the real-world, e.g., by planning (Stenning and Van
Lambalgen, 2012, Ch.5), a task that LLMs still struggle with (Valmeekam et
al., 2023; Stechly et al., 2024). Nonmonotonic reasoning poses a greater
challenge for LLMs than other reasoning tasks (Han et al., 2024) and hasn’t
been featured prominently among natural language inference (NLI) (Gubelmann et
al., 2023) or reasoning benchmarks (see §2).

Figure 1: Reasoning about generics and exceptions

The question of whether LLMs reason nonmonotonically or classically about
generics and exceptions is intricately linked to desiderata of LLMs as
reasoners. LLMs are heralded for their ability to adapt to human or machine
generated feedback (Shinn et al., 2023; Paul et al., 2023; Madaan et al.,
2024; Pan et al., 2024, i.a.). At the same time, it is desired that they
reason reliably when presented with invalid counterarguments, irrelevant
information or user viewpoints. Sycophancy (Perez et al., 2023) of LLMs, i.e.,
susceptibility to be swayed by user belief, is a case in point that has been
investigated in recent studies (Ranaldi and Pucci, 2023; Laban et al., 2023,
i.a.).

As studies on reasoning patterns with generics remain scarce (Ralethe and
Buys, 2022; Lin et al., 2020) and do not examine nonmonotonic reasoning, we
address this gap by investigating the following research questions: 1) Do LLMs
reason nonmonotonically or classically about generics? 2) Are LLMs sensitive
to counter-evidence in the form of exceptions? 3) Do LLMs reason consistently
and reliably by maintaining their response given supporting or unrelated
examples? We test seven state-of-the-art LLMs for their reasoning capabilities
about generics in the presence of exceptions (‘Penguins don’t fly’), as well
as supporting (‘Owls fly’) and irrelevant exemplars (‘Lions have manes’).
Across two datasets featuring both abstract and commonsense generics, we find
that LLM behaviour mirrors human nonmonotonic reasoning patterns in the
presence of exceptions (§5.1). However, most LLMs are not able to consistently
maintain their agreement with generics given unrelated, or even supportive
exemplars (§5.2). Our study highlights challenges in comparing LLM behaviour
to human reasoning patterns as well as assessing reasoning capabilities more
broadly, while consistent reasoning cannot be guaranteed. In Section 7, we
present recommendations for a more holistic evaluation practice encompassing
logical consistency measures.

##  2 Related Work

###  2.1 Generics in NLP

To date most works on generics focus on injecting commonsense knowledge or
generics into LLMs (Gajbhiye et al., 2022; Liu et al., 2023a, i.a.), or
training LLMs for knowledge/generic generation (Bhagavatula et al., 2023).
(See AlKhamissi et al. (2022) for a review.) Bhakthavatsalam et al. (2020)
construct GenericsKG, a large knowledge base of generics as an asset for
downstream tasks such as Question Answering or explanation generation.
Bhagavatula et al. (2023) design a pipeline for synthetic generation of
generics using samples from GenericsKB as seeds. Allaway et al. (2023) in turn
complement the data with exceptions and instantiations for each generic, but
do not investigate nonmonotonic reasoning capabilities.

Most closely related to our work, Lin et al. (2020) find that LMs struggle to
predict numerical knowledge in generics such as ‘Birds have two legs’. Ralethe
and Buys (2022) find that pre-trained masked LMs falsely overgeneralise
(Leslie et al., 2011) from generics (‘Ducks lay eggs’) to universally
quantified statements (‘All ducks lay eggs’).

###  2.2 Nonmonotonic reasoning in NLP

Han et al. (2024) test nonmonotonic reasoning among other inductive reasoning
tasks and find that only GPT-4 performs adequately. LLMs struggle to reason
with contradictory information (Kazemi et al., 2024). Rudinger et al. (2020);
Brahman et al. (2021); Bhagavatula et al. (2019) develop NLI tasks to test
defeasible or abductive reasoning in pragmatics, while Pyatkin et al. (2023);
Ziems et al. (2023); Rao et al. (2023) focus on defeasible reasoning and
social norms. Parmar et al. (2024) introduce non-monotonic reasoning tasks
inspired by Lifschitz (1989) as part of their LogicBench.

###  2.3 Consistency in reasoning

Most recent studies on reliability and consistency in reasoning examine
sycophancy (Perez et al., 2023; Laban et al., 2023; Ranaldi and Pucci, 2023),
consistency within multi-step reasoning or across sessions and users (Chen et
al., 2023a; Wang et al., 2022). (See Liu et al. (2023b) for a review.)

Orthogonal to this, our work connects to studies of reasoning in the presence
of unrelated or conflicting information. Shi et al. (2023) find that LLMs are
easily confounded by irrelevant information in arithmetic reasoning. Across a
variety of reasoning tasks, Wang et al. (2023a) find that OpenAI models
struggle to maintain stable responses given irrelevant objections. Xie et al.
(2023) find mixed evidence of LLMs being sensitive to information that
contradicts prior knowledge, yet showing a form of ‘confirmation bias’ when
presented with diverse viewpoints.

##  3 Tasks and datasets

We test nonmonotonic reasoning with generics using two datasets, featuring
commonsense and abstract generics. Both datasets contain generics (‘Birds
fly’) accompanied by statements where the generic holds (‘Owls fly’) or
doesn’t (‘Penguins don’t fly’). We refer to such examples as instantiations or
exceptions respectively, and to both collectively as as exemplars.

As commonsense generics, we use the synthetic dataset of generics and
exemplars released by Allaway et al. (2023) (henceforth referred to as GEN-
comm). The dataset consists of $\sim 650$ generics and $\sim 19.000$ exemplars
(E.g., ‘Hoes are used to plow fields or clear snow’; ‘Hoes can be used to cut
grass’).222See App. B for additional information on preprocessing. Secondly,
we construct an abstract reasoning dataset featuring generics (GEN-abs).
Inspired by Han et al. (2024), we use categories (‘birds’) and examples
(‘eagles’) from De Deyne et al. (2008) to construct generics of the form
‘Birds have property P’ and exemplars of the form ‘Eagles do (not) have
property P’. The dataset contains 260 tuples of a generic paired with an
exemplar.333The dataset is available at:
https://github.com/aleidinger/nonmonotonic_reasoning_generics/blob/main/data/abstract_generics.csv

For both datasets, our goal is to prompt LLMs for their agreement with a
generic in the presence of exemplars which confirm or contradict the generic.
We use the following prompt template, including model-specific special
tokens444See Appendix A or
https://huggingface.co/docs/transformers/main/en/chat_templating for details.
to signal a chat history between an assistant and a user.555We also experiment
with an alternative prompting template and Chain-of-Thought prompting. Since
results are similar, they are included in Appendix F.

Example: [INST] Is the following statement true: “Birds fly.” \nPlease answer
yes or no. [/INST]
yes
[INST] Penguins don’t fly.\nIs the following statement true: “Birds
fly.”\nPlease answer yes or no. [/INST]

As a control study, we also replace the exception in the prompt (‘Penguins
don’t fly’) with an instantiation (‘Owls fly’) or a random exemplar (‘Hoes can
be used to cut grass’). Since generics in GEN-abs are abstract in nature, and
to enable a consistent set-up across both datasets, we retain generics in GEN-
comm that LLMs accepts when prompted with the first part of the above
template, e.g., [INST] Is the following statement true: “Birds fly.” \nPlease
answer yes or no. [/INST].666See App. B for details and results on discarded
generics.

##  4 Method

###  4.1 Models

We conduct our experiments on medium-sized open-weight models selected from
the top of AlpacaEval777https://tatsu-lab.github.io/alpaca_eval/ and
LMSys888https://chat.lmsys.org/?leaderboard leaderboards, namely Llama-2-13b
(Touvron et al., 2023), Mistral-7b-Instruct-v0.2 (Jiang et al., 2023),
Mixtral-8x7B-Instruct-v0.1 (Jiang et al., 2024), Zephyr-7b-beta (Tunstall et
al., 2023), WizardLM-13B-V1.2 (Xu et al., 2023), Starling-LM-7B-alpha (Zhu et
al., 2023a), and OpenHermes-2.5-Mistral-7B (NousResearch, 2023).999See App. C
for checkpoints and additional information.

###  4.2 Prompting set-up

Since LLM behaviour can vary considerably with the phrasing of an instruction
(Webson and Pavlick, 2022; Leidinger et al., 2023), we formulate three
different instructions to test if an LLM agrees with a given generic: ‘Is the
following statement true’, ‘Do you believe the following statement to be
true’, ‘Do you believe that the following statement is accurate’. Since the
optimal model reply is short and succinct, we follow the convention of HELM
(Liang et al., 2023, p.161) in setting temperature to $0$ for reproducibility
across runs. We format every prompt using the chat template appropriate for
each model, with no system prompt.44footnotemark: 4 To map LLM responses to
labels disagree vs. agree, we use pattern matching and record whether a
response starts with yes or no (Röttger et al., 2023). We aggregate responses
for the three instructions via majority voting.

###  4.3 Statistical tests

To assess whether behaviour of LLMs is significantly different in the absence
vs. presence of exemplars we resort to non-parametric statistical testing.
Since our samples are paired, we use the Wilcoxon signed-rank test (Wilcoxon,
1992).

Figure 2: LLM agreement with generics in the presence of exemplars on GEN-comm
(top) and GEN-abs (bottom). Missing columns indicate agreement rates of $0\%$.

##  5 Results

We present our main results in Figure 2. Additional, accordant results are
described in Appendix F.

###  5.1 Do LLMs reason nonmonotonically?

Since humans maintain their beliefs about truth conditions of generics (‘Birds
fly’) in the presence of exceptions (‘Penguins do not fly’), we examine
whether challenging LLMs with an exception decreases their agreement to
generics significantly. We find this to be the case for all models on both
datasets ($p=0.01$; see App. E for statistical test results). Notably,
agreement rates drop to 0 for Llama-2, Mixtral, Starling and WizardLM on GEN-
abs.

###  5.2 Do LLMs reason consistently?

In the presence of supporting evidence (instantiation) to a generic (‘Owls
fly’), we expect LLM agreement to remain at $100\%$, but this is not the case.
While agreement rates remain high in numbers, they drop significantly for all
models. On GEN-abs, only Mistral, OpenHermes, and WizardLM maintain agreement
rates of $>90\%$, while agreement drops to $<10\%$ for Mixtral.

Similarly, most LLMs are not able to disregard irrelevant random exemplars
(exception/instantiation (shuffled)). Agreement rates decline steeply below
$50\%$ for Llama-2, Mistral, Mixtral and Zephyr on GEN-comm and to below
$20\%$ for Llama-2, Mixtral, Starling, WizardLM and Zephyr on GEN-abs.
OpenHermes stands out as the only model that maintains agreement rates above
$85\%$ on both datasets. Notably, OpenHermes is the only model which has been
trained on additional code data which has been shown to also help reasoning in
natural language (Liang et al., 2023; Yang et al., 2024; Ma et al., 2023).
Nevertheless, observed differences are statistically significant for all
models on both datasets (App. E).

Figure 3: LLM agreement with bare plural (BP) and indefinite singular (IS)
generics in the presence of exemplars on GEN-comm.

##  6 Analysis

###  6.1 How do LLMs reason about different types of generics?

GEN-comm contains both bare plural (BP) generics as well as indefinite
singular (IS) generics (Leslie et al., 2009). (For example, ‘Sea snails have a
hard shell, which protects them from predators’ (BP) and ‘A deciduous tree can
be identified by its leaves’ (IS)). We did not find notable differences
between LLM agreement to BP or IS generics in the presence of exemplars (see
Figure 3). Aforementioned consistency failures persist for both types of
generics.

###  6.2 Qualitative analysis

Generics in GEN-comm which are accepted in isolation, but are rejected in the
presence of exceptions or instantiations include ‘Stimulants can be used to
treat ADHD’ (Llama-2, Starling, Mixtral) or ‘A bobsleigh is driven by a single
driver’ (Starling, Mistral, Mixtral, OpenHermes, WizardLM). Generics which are
accepted no matter the exemplar presented in context include ‘Inflammatory
diseases may be caused by an imbalance of the immune system’ (Llama-2,
Starling, Mistral, OpenHermes), ‘A processor should be able to run a program’
(Starling, Mixtral, OpenHermes, WizardLM), ‘Experimental evidence is used to
support or refute theories’, ‘An adventure has a beginning, middle, end’
(Starling, OpenHermes, WizardLM), and ‘Coincidence is part of the human
condition’ (Starling, Mistral, OpenHermes).

For GEN-abs, OpenHermes is the only LLM which maintains its agreement to a
generic (‘Birds have property P’, ‘Mammals have property P’) in the presence
of any instantiation or unrelated exemplar, but flips its decision and outputs
disagreement in the presence of an exception. No LLM accepts any of the
generics regardless of the exemplar it is paired with.

##  7 Discussion

With the advent of LLMs and reports of impressive performance, including on
reasoning tasks (Wei et al., 2022; Kojima et al., 2022), recent investigations
into failure modes in reasoning have focused, e.g., on prompt attacks (Zhu et
al., 2023b; Wang et al., 2023b, i.a.), sycophancy (Perez et al., 2023; Laban
et al., 2023; Ranaldi and Pucci, 2023, i.a.) or adaptability to critique or
feedback (Madaan et al., 2024; Chen et al., 2023b; Huang et al., 2023; Pan et
al., 2024). Such research trends might be seen as emblematic of a view of LLMs
as artificial natural artifacts (Kambhampati, 2022). Results in this study
demonstrate the difficulties of making claims about reasoning capabilities of
LLMs or comparing them to human reasoners (Han et al., 2024; Ralethe and Buys,
2022; Lin et al., 2020), while consistent reasoning remains elusive even for
state-of-the-art LLMs. Research that predates the paradigm shift to few-shot
prompting, has advocated for arguably simpler, systematic diagnostic tests
(Ribeiro et al., 2020; Ettinger, 2020; Kassner and Schütze, 2020). We argue
that such behavioural tests merit a revival, so that performance metrics for
reasoning are complemented with measures of logical consistency and
robustness.

##  8 Conclusion

The present study focuses on nonmonotonic reasoning capabilities of LLMs in
the context of generics. We evaluate seven state-of-the-art LLMs on two
datasets featuring both abstract and commonsense generic statements. While LLM
behaviour on generics paired with exceptions is in line with nonmonotonic
reasoning patterns, LLMs fail to reason consistently and robustly when adding
supporting or unrelated exemplars.

##  9 Limitations

We acknowledge that our experiments exclusively feature generics and exemplars
in English. Future research might profit from including additional languages
to examine nonmonotonic reasoning capabilities in other languages, drawing on
cross-linguistic research on generics (Mari et al., 2013). Such work might
also highlight differences in consistency failures between different
languages. In this work, we do not experiment with generics pertaining to
demographic groups or nationalities because of concerns around social bias.
Future work might examine LLM behaviour on generic statements for larger LLMs
or closed-source models. We restrict ourselves to medium-sized open-weight
LLMs, due to their widespread use and availability, as well as restrictions on
our computational budget.

## Acknowledgements

We thank our anonymous reviewers for their insightful comments. The work for
this publication is financially supported by the project, ‘From Learning to
Meaning: A new approach to Generic Sentences and Implicit Biases’ (project
number 406.18.TW.007) of the research programme SGW Open Competition, which is
(partly) financed by the Dutch Research Council (NWO).

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##  Appendix A Example input

Example input formatted using our prompt template and the chat
template101010https://huggingface.co/blog/chat-templates, e.g., for
Mistral-7B-Instruct:

Prompt: [INST] Do you believe that the following statement is accurate: ‘Birds
fly.’
Please answer yes or no. [/INST]
yes
[INST] Penguins do not fly.
Do you believe that the following statement is accurate: ‘Birds fly.’
Please answer yes or no. [/INST]

##  Appendix B Additional information on data preprocessing

For GEN-comm, we conduct additional processing to obtain high quality generics
and ensure a parallel experimental setup between GEN-comm and GEN-abs. We
retain only generics that were annotated as ‘valid’ by human annotators. We
filter generics for which both an exception and an instantiation exists. Since
generics are unquantified statements, we remove any quantifiers such as
‘generally’, ‘usually’ and ‘typically’ at the beginning of each generic. To
enable consistent evaluation on GEN-abs and GEN-comm, we evaluate each LLM on
generics contained in GEN-comm which it accepts a priori. In an initial
experiment, we prompt LLMs using the first part of our template (above; App.
A). An example input for GEN-comm would be, e.g., ‘[INST] Do you believe that
the following statement is accurate: ‘Birds have property P.’ Please answer
yes or no[/INST]’. Generics for which an LLM does not generate yes as a
response are discarded. We retain $>1200$ samples for each model (See Table 1
for details).

Model | # samples
---|---
Mistral-7B-Instruct | 2093
Llama-2-13b | 1245
Zephyr-7b-beta | 1536
WizardLM-13B-V1.2 | 2225
OpenHermes-2.5-Mistral-7B | 2153
Starling-LM-7B-alpha | 2244
Mixtral-8x7B-Instruct-v0.1 | 1959
Table 1: # retained samples in GEN-comm

Results on the resultant dataset are presented in the main body of the paper
(Section 5). For the reader’s interest, we include here also LLM responses to
generics contained in GEN-comm which are rejected by LLMs, i.e., a given LLM
generates the response no to the prompt above (See Figure 4). As expected
agreement rates soar for almost all models when adding an instantiation which
confirms the previously rejected generic. Nevertheless, agreement rates also
increase, albeit less, when adding exceptions or unrelated random examplars,
particularly for Llama-2 and WizardLM. OpenHermes and Starling show the least
inconsistencies.

Figure 4: Results on generics contained in GEN-comm that are rejected a
priori. Missing bars for ‘no exemplar’ indicate agreement rates of zero.

##  Appendix C Additional information on LLMs

In this section we provide additional details on the models used in this study
which are listed in Section 4.1. The specific checkpoints we use can be seen
in Table 2 and are all available through the HuggingFace Hub. All models we
use are trained for chat interaction.

LLM Checkpoints
---
meta-llama/Llama-2-13b-chat-hf
mistralai/Mistral-7B-Instruct-v0.2
mistralai/Mixtral-8x7B-Instruct-v0.1
HuggingFaceH4/zephyr-7b-beta
berkeley-nest/Starling-LM-7B-alpha
WizardLM/WizardLM-13B-V1.2
teknium/OpenHermes-2.5-Mistral-7B
Table 2: LLM checkpoints used in this study.

Mixtral-8x7B-Instruct-v0.1 (MistralAI, 2023) is a sparse mixture of expert
model based on 8 Mistral 7B models that has been further trained using
supervised finetuning and Direct Preference Optimisation. It ranks highest
among its weight class on AlpacaEval111111https://tatsu-
lab.github.io/alpaca_eval/ and
chat.lmsys121212https://chat.lmsys.org/?leaderboard leaderboards (as of Feb 6
2024). At its release it surpasses GPT-3.5 and LLaMA-2-70b.

StarlingLM-13B-V1.2 (Zhu et al., 2023a) has been trained via Reinforcement
Learning from AI Feedback (RLAIF) on the Nectar dataset. In its weight class,
it is the second best performing model on chat.lmsys and 4th on AlpacaEval (as
of Feb 6 2024).

Amidst mounting evidence that training on code enhances reasoning abilities
also for natural language (Liang et al., 2023; Yang et al., 2024; Ma et al.,
2023), we also use OpenHermes-2.5-Mistral-7B NousResearch (2023) which ranks
third in its weight class on chat.lmsys. It is Mistral-based model that has
been finetuned on additional code datasets. Notably, the developers detail
that this results in improvements on non-code
tasks.131313https://huggingface.co/teknium/OpenHermes-2.5-Mistral-7B

WizardLM-13B-V1.2 (Xu et al., 2023) is a finetuned version of Llama-2 13b and
is ranked 8th in its weight-class on both chat.lmsys and AlpacaEval.

Zephyr-7b-beta (Tunstall et al., 2023) is a finetuned version of
Mistral-7B-v0.1. It is ranked 9th on chat.lmsys and 11th on AlpacaEval.

##  Appendix D Average runtime

Generating LLM responses for one LLM and all generics across all settings took
less than $0.5$ GPU hours. All experiments were conducted on one NVIDIA A100
GPU.

##  Appendix E Statistical test results

Responses in the presence of exemplars are significantly different from
results obtained without examplars (see Tables 3, 4, 5), for all types of
exemplars and all models (significance level $0.01$; sole exception is Llama-2
with CoT prompting as can be seen in Table 5 rows 1-2).

Figure 5: Results on GEN-comm. Alternative prompt template described in
Section F Figure 6: Results on GEN-abs. Alternative prompt template described
in Section F. Figure 7: Results on generics of GEN-comm that are rejected by
LLMs a priori. Alternative prompt template described in Section F. Missing
bars indicate that agreement for ‘no exemplar’ is zero.

##  Appendix F Additional experimental results

We demonstrate additional experimental results based on an alternative
prompting set-up in Figures 5 and 6.

To this end, we prompt LLMs using the following template where [INST] is an
example of a model-specific special token used in chat templating. For
example:

Prompt [INST] Do you believe that the following statement is accurate: ‘Birds
fly’
Please answer yes or no. [/INST]

For GEN-comm, we retain all generics to which an LLM responds yes to the
prompt above. We then prompt LLMs anew supplying an exception, instantiation
or random exemplar together with a generic for both datasets. For example:

Prompt [INST] Penguins do not fly.
Do you believe that the following statement is accurate: ‘Birds fly’
Please answer yes or no. [/INST]

We find that results differ significantly between the two conditions (no
exemplar vs. with an exemplar) (see Table 4 for statistical test results). On
GEN-comm (Figure 5) agreement rates drop considerably in the presence of
exceptions which mirrors nonmonotonic reasoning patterns. Agreement is higher,
yet still drops significantly in the presence of instantiations. No LLM
maintains perfectly consistent responses at the addition of random
instantiations or exceptions. When prompting with random exemplars
surprisingly agreement drops, most notably for Llama-2 and Zephyr.

For the reader’s interest, we also include results on the portion of generics
in GEN-comm which is rejected by LLMs a priori (Table 7). As expected,
agreement increases from zero at the addition of an instantiation to the
prompt, most notably for OpenHermes and Starling. However, LLMs should
maintain a response of no at the addition of an exception or random exemplar
to the prompt. This is visibly not the case with agreement rates increasing
significantly for all models.

On GEN-abs, agreement drops considerably at the addition of an exception for
all models except OpenHermes (Figure 6). Notably OpenHermes and Starling-LM
appear to yield consistent responses in the presence of our controls, the
random exemplars, while Llama-2 and Zephyr perform worst in that regard.

###  F.1 Chain-of-thought prompting

Additionally, we ran experiments using zero-shot Chain-of-Thought (CoT)
prompting in the style of (Kojima et al., 2022) by appending ‘Let’s think step
by step’ to our prompts. We present results on GEN-comm in Figure 8 and
results on GEN-abs in Figure 9.

On GEN-comm, agreement rates drop significantly for all models at the addition
of exceptions, instantiations or shuffled exemplars (with the exception of
Llama-2 when we include instantiations; see Table 5 for significance results).
Agreement rates drop more given exceptions in comparison to instantiations or
unrelated examplars for Mistral, Mixtral, OpenHermes and Starling. For Llama-2
and Zephyr agreement rates fall below $10\%$ at the addition of unrelated
exemplars.

On GEN-abs, agreement rates fall drastically given exceptions and equal $0\%$
for Llama-2, Mixtral, Starling and Zephyr. The same is true for shuffled
instantiations. OpenHermes is the only model to maintain agreement rates above
$90\%$ when presented with instantiations or shuffled exceptions.

Figure 8: Results on GEN-comm using zero-shot CoT prompting. Figure 9: Results on GEN-abs using zero-shot CoT prompting. Missing bars indicate agreement rate of $0\%$. Model | prompt setting | p-value
---|---|---
Llama-2-13b-chat-hf | exception | 1.2444035588550786e-84
Llama-2-13b-chat-hf | instantiation | 1.3944889010907487e-28
Llama-2-13b-chat-hf | exception (shuffled) | 1.3664041679452567e-86
Llama-2-13b-chat-hf | instantiation (shuffled) | 3.7504271121760947e-128
OpenHermes-2.5-Mistral-7B | exception | 2.0884875837625446e-45
OpenHermes-2.5-Mistral-7B | instantiation | 7.237829871739995e-08
OpenHermes-2.5-Mistral-7B | exception (shuffled) | 1.733880104231141e-27
OpenHermes-2.5-Mistral-7B | instantiation (shuffled) | 9.799073841979368e-26
Starling-LM-7B-alpha | exception | 1.0691632340127197e-102
Starling-LM-7B-alpha | instantiation | 7.247101964362887e-14
Starling-LM-7B-alpha | exception (shuffled) | 3.14927364689666e-77
Starling-LM-7B-alpha | instantiation (shuffled) | 5.588400099286033e-62
Mixtral-8x7B-Instruct-v0.1 | exception | 5.599059901868063e-84
Mixtral-8x7B-Instruct-v0.1 | instantiation | 4.84145282763492e-53
Mixtral-8x7B-Instruct-v0.1 | exception (shuffled) | 1.8855259265259482e-119
Mixtral-8x7B-Instruct-v0.1 | instantiation (shuffled) | 3.312378211336223e-151
WizardLM-13B-V1.2 | exception | 3.169934685227252e-109
WizardLM-13B-V1.2 | instantiation | 1.244192114854348e-15
WizardLM-13B-V1.2 | exception (shuffled) | 6.7440576522393956e-49
WizardLM-13B-V1.2 | instantiation (shuffled) | 3.312389179997469e-50
zephyr-7b-beta | exception | 3.2434215158679907e-99
zephyr-7b-beta | instantiation | 2.68778179464934e-25
zephyr-7b-beta | exception (shuffled) | 2.7464111838608292e-137
zephyr-7b-beta | instantiation (shuffled) | 2.671546422248841e-187
Mistral-7B-Instruct-v0.2 | exception | 6.521923113646968e-71
Mistral-7B-Instruct-v0.2 | instantiation | 2.0670658180782593e-15
Mistral-7B-Instruct-v0.2 | exception (shuffled) | 6.923699393684986e-120
Mistral-7B-Instruct-v0.2 | instantiation (shuffled) | 4.9982887921763924e-139
Table 3: Results of Wilcoxon signed ranked test for paired samples. We compare agreement of LLMs to generics with and without an exemplar (one of exception, instantiation, exception (shuffled), instantiation (shuffled). Results are obtained using the original prompt template described in section 5 and correspond to the main results in the paper in Figure 2. Model | prompt setting | p-value
---|---|---
Llama-2-13b-chat-hf | exception | 1.2402659787920488e-62
Llama-2-13b-chat-hf | instantiation | 1.8577351435735865e-29
Llama-2-13b-chat-hf | exception (shuffled) | 6.558556037957885e-98
Llama-2-13b-chat-hf | instantiation (shuffled) | 9.990918651724453e-148
OpenHermes-2.5-Mistral-7B | exception | 9.041178413936276e-31
OpenHermes-2.5-Mistral-7B | instantiation | 0.025347318677468252
OpenHermes-2.5-Mistral-7B | exception (shuffled) | 9.236596617174027e-13
OpenHermes-2.5-Mistral-7B | instantiation (shuffled) | 1.2052982584446398e-13
Starling-LM-7B-alpha | exception | 4.84145282763492e-53
Starling-LM-7B-alpha | instantiation | 0.0009111188771537128
Starling-LM-7B-alpha | exception (shuffled) | 9.89884333064868e-40
Starling-LM-7B-alpha | instantiation (shuffled) | 6.7440576522393956e-49
Mixtral-8x7B-Instruct-v0.1 | exception | 2.6891242658680216e-51
Mixtral-8x7B-Instruct-v0.1 | instantiation | 2.8706760140807313e-27
Mixtral-8x7B-Instruct-v0.1 | exception (shuffled) | 7.287679729162835e-32
Mixtral-8x7B-Instruct-v0.1 | instantiation (shuffled) | 1.8712872006902566e-36
WizardLM-13B-V1.2 | exception | 5.8780179991539864e-33
WizardLM-13B-V1.2 | instantiation | 9.633570086430965e-07
WizardLM-13B-V1.2 | exception (shuffled) | 7.74421643104407e-06
WizardLM-13B-V1.2 | instantiation (shuffled) | 2.5802843041604163e-08
zephyr-7b-beta | exception | 3.525239394844374e-74
zephyr-7b-beta | instantiation | 2.476062658812572e-30
zephyr-7b-beta | exception (shuffled) | 3.7238080067294776e-86
zephyr-7b-beta | instantiation (shuffled) | 9.415767818703249e-116
Mistral-7B-Instruct-v0.2 | exception | 3.9328331793483447e-54
Mistral-7B-Instruct-v0.2 | instantiation | 2.0670658180782593e-15
Mistral-7B-Instruct-v0.2 | exception (shuffled) | 3.699479889932592e-64
Mistral-7B-Instruct-v0.2 | instantiation (shuffled) | 2.6476609044572044e-100
Table 4: Results of Wilcoxon signed ranked test for paired samples. We compare agreement of LLMs to generics with and without an exemplar (one of exception, instantiation, exception (shuffled), instantiation (shuffled)). These results correspond to the alternative prompting style and results described in section F. Model | prompt setting | p-value
---|---|---
Llama-2-13b-chat-hf | exception | 0.025347318677468252
Llama-2-13b-chat-hf | instantiation | 0.31731050786291415
Llama-2-13b-chat-hf | exception (shuffled) | 0.0009111188771537128
Llama-2-13b-chat-hf | instantiation (shuffled) | 3.737981840170154e-05
Starling-LM-7B-alpha | exception | 4.320463057827488e-08
Starling-LM-7B-alpha | instantiation | 5.733031437583866e-07
Starling-LM-7B-alpha | exception (shuffled) | 1.5417257900279904e-08
Starling-LM-7B-alpha | instantiation (shuffled) | 1.1825298845719069e-11
OpenHermes-2.5-Mistral-7B | exception | 2.3159484001346495e-35
OpenHermes-2.5-Mistral-7B | instantiation | 3.552964224155306e-33
OpenHermes-2.5-Mistral-7B | exception (shuffled) | 4.4044942248007814e-32
OpenHermes-2.5-Mistral-7B | instantiation (shuffled) | 1.773177466197228e-41
Mixtral-8x7B-Instruct-v0.1 | exception | 2.9303133449994263e-53
Mixtral-8x7B-Instruct-v0.1 | instantiation | 4.474661339129513e-39
Mixtral-8x7B-Instruct-v0.1 | exception (shuffled) | 6.758775639492622e-37
Mixtral-8x7B-Instruct-v0.1 | instantiation (shuffled) | 5.058648827940248e-40
zephyr-7b-beta | exception | 3.6136286243610392e-96
zephyr-7b-beta | instantiation | 8.956226067732092e-94
zephyr-7b-beta | exception (shuffled) | 1.2813208444193637e-111
zephyr-7b-beta | instantiation (shuffled) | 2.0076004412348868e-151
Mistral-7B-Instruct-v0.2 | exception | 3.294362383314041e-67
Mistral-7B-Instruct-v0.2 | instantiation | 6.210993425425191e-19
Mistral-7B-Instruct-v0.2 | exception (shuffled) | 2.380470154600155e-54
Mistral-7B-Instruct-v0.2 | instantiation (shuffled) | 1.2444035588550786e-84
Table 5: Results of Wilcoxon signed ranked test for paired samples. We compare
agreement of LLMs to generics with and without an exemplar (one of exception,
instantiation, exception (shuffled), instantiation (shuffled)). These results
correspond to Chain-of-Thought prompting results described in section F.