=Paper=
{{Paper
|id=Vol-3432/paper1
|storemode=property
|title=A Roadmap for Neuro-argumentative Learning
|pdfUrl=https://ceur-ws.org/Vol-3432/paper1.pdf
|volume=Vol-3432
|authors=Maurizio Proietti,Francesca Toni
|dblpUrl=https://dblp.org/rec/conf/nesy/ProiettiT23
}}
==A Roadmap for Neuro-argumentative Learning==
https://ceur-ws.org/Vol-3432/paper1.pdf
A Roadmap for Neuro-argumentative Learning
Maurizio Proietti1,* , Francesca Toni2,*
1
IASI-CNR, Rome, Italy
2
Department of Computing, Imperial College London, UK
Abstract
Computational argumentation (CA) has emerged, in recent decades, as a powerful formalism for knowl-
edge representation and reasoning in the presence of conflicting information, notably when reasoning
non-monotonically with rules and exceptions. Much existing work in CA has focused, to date, on rea-
soning with given argumentation frameworks (AFs) or, more recently, on using AFs, possibly automat-
ically drawn from other systems, for supporting forms of XAI. In this short paper we focus instead
on the problem of learning AFs from data, with a focus on neuro-symbolic approaches. Specifically,
we overview existing forms of neuro-argumentative (machine) learning, resulting from a combination
of neural machine learning mechanisms and argumentative (symbolic) reasoning. We include in our
overview neuro-symbolic paradigms that integrate reasoners with a natural understanding in argumen-
tative terms, notably those capturing forms of non-monotonic reasoning in logic programming. We also
outline avenues and challenges for future work in this spectrum.
Keywords
Computational argumentation, Artificial neural networks, Non-monotonic reasoning
1. Introduction
Computational argumentation (CA) has emerged, since the nineties, as a powerful formalism for
knowledge representation and reasoning in the presence of conflicting information (see [1, 2]
for recent overviews). It has been shown to capture and generalise, in particular, several forms
of non-monotonic reasoning [3, 4], notably required when operating with rules and exceptions
naturally giving rise to conflicts (e.g. both the rule “birds fly” and the exception ”penguins do
not fly” apply to the same individual tweety – a penguin and thus a bird). Also, it is being widely
deployed to support forms of explainable AI (XAI) (e.g. see overview in [5]), given the appeal of
argumentation in explanations amongst humans, e.g. as in [6], within the broad view that XAI
should take findings from the social sciences into account [7].
To date, the bulk of work in CA amounts to defining so-called argumentation frameworks
(AFs), which are symbolic representations equipped with semantics/tools for reasoning towards
the resolution of conflicts and drawing (argumentatively acceptable) conclusions. In addition,
increasingly more attention has been given over the years to combining CA and machine
NeSy’23: 17TH INTERNATIONAL WORKSHOP ON NEURAL-SYMBOLIC LEARNING AND REASONING, Certosa di
Pontignano, Siena, Italy, 3–5 July 2023
*
Corresponding author.
" maurizio.proietti@iasi.cnr.it (M. Proietti); ft@ic.ac.uk (F. Toni)
~ http://www.iasi.cnr.it/~proietti/ (M. Proietti); https://www.doc.ic.ac.uk/~ft/ (F. Toni)
0000-0003-3835-4931 (M. Proietti); 0000-0001-8194-1459 (F. Toni)
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
learning (e.g. as overviewed in [8]). Here, we focus specifically on methods combining CA
and machine learning with artificial neural networks (NNs)1 , focusing on what we term neuro-
argumentative (machine) learning (NAL), resulting from a combination of neural (machine
learning) mechanisms and (symbolic) argumentative reasoning using methods in CA. Specifically,
in Section 2 we overview existing forms of NAL, including neuro-symbolic paradigms integrating
forms of logic programming with a natural understanding in CA terms (see below). Finally, in
Section 3 we outline avenues and challenges for future work in the broad spectrum of NAL.
Background on CA. The simplest form of AFs is given by abstract AFs (AAFs) [3], which
boil down to directed graphs whose nodes are arguments (e.g. “tweety flies as it is a bird” and
“tweety does not fly as it is a penguin”) and whose edges are attacks between them (e.g., the latter
argument for tweety attacks the former). They are equipped, e.g., with the semantics of stable
extensions, which are conflict-free sets of arguments attacking every argument they do not
contain (leading to accepting the second argument for tweety and inferring that it does not fly).
Several other forms of CA have been proposed and play a role in existing works in NAL, notably
bipolar AFs (BAFs) [9], i.e. directed graphs with two types of edges: attacks as in AAFs and
supports (e.g. between “tweety has wings” and the earlier “tweety flies as it is a bird”), variations
of AAFs and BAFs such as quantified BAFs (where arguments are equipped with base scores and
dialectical strengths obtained using gradual semantics [10]), weighted (quantified) BAFs (where
edges are weighted, e.g. see [11]), and forms of structured CA [12], where arguments and attacks
are drawn from logical formalisms. For example, in Assumption-Based AFs (ABAFs) [4, 13, 14, 15],
arguments are drawn from “rules” and are supported by “assumptions”, and attacks are targeted
at the assumptions, by arguments for their “contraries”.
CA and non-monotonic reasoning. CA is naturally non-monotonic and indeed there are
some close connections between (forms of) CA and several formalisms for non-monotonic
reasoning [3, 4], including normal logic programs (LPs in short) with negation as fail-
ure (NAF) and answer set programs (ASPs in short). In particular, ABAFs admit LPs/ASPs
as instances. For illustration, consider the LP/ASP 𝑃 ∪ 𝐹 with rules 𝑃 = {flies(𝑋) ←
bird(𝑋), 𝑛𝑜𝑡 ¬flies(𝑋), ¬flies(𝑋) ← penguin(𝑋)} (with ¬ interpreted syntactically, and 𝑛𝑜𝑡
denoting NAF) and facts 𝐹 = {penguin(tweety), bird(tweety)}. This LP/ASP corresponds to an
ABAF with
∙ rules 𝑃 ∪ 𝐹 ,
∙ all NAF literals in the vocabulary of the LP as assumptions,
∙ contraries of assumptions 𝑛𝑜𝑡 𝑙 given by 𝑙.
Note that, in particular, assumptions include 𝑛𝑜𝑡 ¬flies(tweety), with contrary ¬flies(tweety)).
The semantics of the original LP/ASP is exactly captured by the semantics of the ABAF [4]. For
example, stable extensions of ABAFs correspond exactly to stable models of LPs/ASPs [16].
1
We will refer to several standard NN architectures, notably multi-layer perceptrons (MLPs), convolutional neural
networks (CNNs), Long-Short-Term-Memory NNs (LSTMs), and AutoEncoders (AEs).
2. Overview of existing work in NAL
Here, we focus on works at the intersection of CA and NNs positioned as NAL, while ignoring
works combining CA and NNs for supporting CA itself, e.g.: NNs performing argumentative
reasoning, as in [17, 18, 19]; works on argument mining, using NNs to extract arguments and/or
AFs, as in [20]; methods using NNs for computing semantics of AFs, such as [21, 22, 23]; works
on the correspondence between AFs of various types and NNs, as in [24, 25].
We summarise existing works on NAL in Table 1 and related works in neuro-symbolic
learning with LP/ASP in Table 2, and describe their main characteristics for our purposes below.
Translation of NNs to AFs. A line of work includes methods that take a trained NN as an
input and translate it into an AF of some kind. Amongst these methods, DAX [26] envisages
generic mappings into generalised AFs, with any number of dialectical relations. Several
concrete instantiations of this approach focus on mapping NNs (e.g. MLPs or CNNs) into
BAFs [27, 28]. Further, SpArX [29] relies upon a provable one-to-one-correspondence between
MLPs and weighted BAFs [11] to translate MLPs into sparse weighted BAFs, where hidden
neurons are clustered, for the purpose of rendering the MLP sparser and more interpretable.
These methods aim at using the AFs resulting from the translation for explaining the NNs.
Pipeline methods. Some other methods use NNs to extract AFs, and then apply symbolic,
argumentative reasoning on the AFs to support some downstream task. For example, ADA [30]
uses neural classifiers and LSTMs to mine quantified BAFs from textual reviews, and then reasons
with them (under gradual semantics) to provide recommendations for movies, evaluated against
review aggregations measures. Also, DEAr [31] uses AutoEncoders for feature selection from
tabular data to extract AAFs, and then reasons with them (under extension-based semantics) to
provide explainable classifications from tabular inputs. Further, Local-HDP-ABL [32] deploys
(possibly neural) feature selection methods with images to extract BAFs for reasoning over the
images for explainable classification. In these methods the two components (AF extraction and
symbolic, argumentative reasoning) are decoupled within a pipeline, and the argumentative
reasoning provides “delayed” feedback to the AF extraction by the NN.
Integrated methods. Finally, argumentative reasoning over AFs has been integrated within
NNs as a form of inductive bias, to guide the learning within the NNs. Specifically, NSAM [33]
Paper Formalism Learning Setting
DAX [26, 27, 28] BAFs Translation of NNs (MLPs, CNNs) to AFs
SpArX [11, 29] Weighted BAFs Translation of MLPs to AFs
ADA [30] Quantified BAFs AFs learnt by NNs → argumentative reasoning
DeAr [31] AAFs AFs learnt by AEs → argumentative reasoning
Local-HDP-ABL [32] BAFs AFs learnt by NNs → argumentative reasoning
NSAM [33] probabilistic semi-AAFs Reasoning with AFs as inductive bias
Table 1
NAL approaches based on argumentation frameworks (AFs) of various kinds
Paper Formalism Learning Setting
CIL2 P[35] Propositional LP Translation of NNs to LP
NeSyFOLD[36] Stratified LP LP learnt from pre-trained CNN
FFNSL[37] ASP LP learnt from pre-trained NNs
NeurASP[38] Probabilistic ASP e2e training of NNs via user-defined rules
DeepProbLog[39] Probabilistic Stratified LP e2e training of NNs via user-defined rules
NeuroLog[40] Abductive LP e2e training of NNs via user-defined rules
embed2sym[41] ASP e2e training of NNs via user-defined rules
pix2rule[42] ASP e2e learning of ASP
Table 2
Neuro-symbolic approaches based on non-monotonic rules (mappable to AFs)
defines argumentation Boltzmann machines (a form of NNs capturing argumentative knowl-
edge, in the form of probabilistic semi-abstract AFs), trained on instances of the argumentative
knowledge applicable to given data, to make predictions that can be explained argumentatively.
Related work in logic programming. We include neuro-symbolic paradigms integrating
forms of non-monotonic LPs and ASPs, as those have a natural understanding in CA terms. We
omit instead neuro-symbolic methods focusing on positive logic programs (e.g. see overview
in [34]), as they support monotonic reasoning only and are not relevant to an argumentative
viewpoint. The LP works are summarised in Table 2. CIL2 P [35] extracts LPs from MLPs, for
the purposes of explainability. Some methods follow a pipeline approach, learning LPs from
NNs pre-trained for feature extraction on images: NeSyFOLD [36] generates stratified LPs from
CNNs, and FFNSL [37] learns ASPs. Other methods integrate reasoning with LPs/ASPs provided
by humans, for the purpose of training NNs end-to-end (e2e) to benefit from the knowledge
represented in the LPs/ASPs and learn from it as well as from unstructured data such as images:
NeurASP [38] represents knowledge in the form of probabilistic ASPs, DeepProbLog [39] uses
probabilistic stratified LPs (i.e. ProbLog programs), NeuroLog [40] makes use of abductive LP
to supervise the e2e training process, and embed2sym [41] integrates clustering for feature
extraction with ASPs. Finally, pix2rule [42] learns ASPs e2e, through a training regime that
processes both images and ASPs, by including a differentiable layer in NNs from which ASP
rules can be extracted.
3. Challenges
We conclude by discussing the role that NAL could have in the future development of neuro-
symbolic systems in three settings: 1) the NN component is pre-trained, AFs are learnt; 2) AFs
are predefined, the NN component is learnt; 3) both components are learnt e2e.
NNs pre-trained, AFs learnt. The simplest way in which CA could be used is within a
simple pipeline architecture: an AF is extracted (or learnt) from a pre-trained NN. This approach
is very close to standard CA-based forms of XAI as discussed earlier [30, 31, 32]. A more
advanced variant of this pipeline architecture could be implemented by representing pre-trained
NN modules symbolically as (probabilistic) neural predicates, similarly to [36, 39]. With this
representation, together with suitable background knowledge by domain experts, we could
learn symbolic concepts as ABAFs (e.g. as suggested in [43]) or as probabilistic ABAFs [44].
Predefined AFs, NNs learnt. In this type of systems NNs are trained e2e: the input to NNs
is labeled by symbolic concepts for which we provide a suitable background knowledge defined
by means of AFs. In this context, ABA frameworks could be used to guide the training of NNs,
again extending the work done in the area of LP and ASP [36, 39]. The ability of ABAFs to
formalise various kinds of knowledge/reasoning (e.g. default theories, ontologies, and temporal
logics) would be a plus for achieving better accuracy and reliability with smaller data sets.
NNs and AFs both learnt. The most challenging task is to construct systems that are com-
posed of neural modules and symbolic modules where both components are learnt at the same
time, while training is done e2e on their composition. A critical sub-task is learning latent
concepts, that is, the symbolic concepts associated with the output of the neural component.
Initial work in this direction, for LP/ASP, could provide a starting point. For example, [45]
design an approach based on so-called policy functions, similar to reinforcement learning, to
learn symbolic knowledge which could be seen as a collection of facts (and thus monotonic).
While this work makes quite strong hypotheses on the form of the symbolic knowledge to be
learnt, it would be interesting to explore whether the approach could be generalised to learn
(non-monotonic) AFs. Furthermore, the aforementioned [42] – proposing a specific approach
for e2e learning of relations and rules from images – could provide a fruitful starting point to
learn AFs.
Although CA-based approaches have not been considered in this setting, they might be
advantageous. First, the features of ABAFs useful for learning the two components separately
can also be useful for their combined learning. For example, in this more complex scenario we
could exploit ABAFs, following an iterative approach, for a variety of tasks such as: represent
rich background knowledge, use that knowledge to generate suitable neural model templates,
to train them, and extract new knowledge from trained neural models. Further, for this more
complex task, we need representation and reasoning mechanisms that cope with the non-
monotonicity of knowledge extraction and learning. To this aim, the ability of CA to support
various forms of non-monotonic reasoning and to represent the learnt symbolic knowledge in
the form of defeasible rules, could play a key role. Notably, we believe that abduction, which
can be realised naturally in CA, could be useful for learning latent concepts.
4. Acknowledgments
We would like to thank the anonymous reviewers for constructive criticism. We also thank
support from the Royal Society, UK (IEC\R2\222045 - International Exchanges 2022 Cost Share).
M. Proietti is a member of the INDAM-GNCS research group, Italy. F. Toni was partially funded
by the European Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation programme (grant agreement No. 101020934) and by J.P. Morgan and the Royal
Academy of Engineering under the Research Chairs and Senior Research Fellowships scheme.
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