Some Considerations on Epistemic and Practical
Reasoning in Abstract Argumentation
Pietro Baroni and Massimiliano Giacomin
Dep. of Information Engineering, University of Brescia, Brescia, Italy
{massimiliano.giacomin,pietro.baroni}@unibs.it
Abstract. In this short paper we discuss two approaches for integrating
epistemic and practical reasoning in abstract argumentation, showing
their commonalities and differences both from a technical and conceptual
perspective.
Keywords: Abstract Argumentation, Semantics, Epistemic and Prac-
tical Reasoning
1 Introduction
Abstract argumentation provides a general account of argumentation where ar-
guments are simply represented as nodes of a directed graph AF = (A, →),
called abstract argumentation framework [7], and binary attacks between them
correspond to the edges of the graph, i.e. an argument a attacks an argument
b if (a, b) ∈→, also denoted as a → b. The issue is then to determine a justi-
fication status for the arguments in A. To this purpose, several argumentation
semantics identify for each argumentation framework a number of extensions,
each intuitively conceived as a set of arguments that can survive the conflict
together. Most semantics embed a notion of defense, i.e. admissible sets of argu-
ments are required to counterattack the arguments against them, and extensions
are defined as admissible sets satisfying additional constraints that reflect the
intuitions and the degree of skepticism specific to the semantics [3]. More specif-
ically, a set of arguments Args is admissible if ¬∃a, b ∈ Args : a → b, and for any
b such that b → a with a ∈ Args, there is an argument c ∈ Args such that c → b.
A complete extension is then an admissible set Args including all arguments it
defends, i.e. if ∀b such that b → a there is c ∈ Args such that c → b, then
a ∈ Args. For the sake of the present paper, we need to recall grounded (GR)
and preferred (PR) semantics only. Given an AF , grounded semantics identifies
as its unique extension, denoted as GRAF , the least (w.r.t. ⊆) complete exten-
sion, while preferred semantics identifies as its extensions the maximal (w.r.t.
⊆) complete extensions, denoted as EPR (AF ).
Abstract argumentation frameworks capture a variety of reasoning situa-
tions, typically based on conflicting information affected by uncertainty and
incompleteness. In particular, a distinction has been advocated in [9] between
epistemic and practical arguments. While epistemic arguments concern reason-
ing about what to believe, practical arguments concern reasoning about what
2 P. Baroni, M. Giacomin
to do, involving goals, desires and intentions. This distinction impacts on the
semantics adopted to evaluate argument justification.
On the grounds that conflicts between epistemic arguments mainly arises
from uncertainty and incompleteness of information, grounded semantics is pro-
posed in [9] to deal with epistemic arguments, since it enforces a skeptical behav-
ior ensuring that any indecision about arguments prevents their justification. To
exemplify this idea, a case concerning how to reach a remote small town is de-
scribed in [9]. Suppose Mary warns that there will be a railway strike, while Bob
does not believe there will be such a strike. Two conflicting arguments estrike
and e¬strike then arise and none of them can be justified, thus the question
concerning whether the train will be available remains undecided.
Turning to practical arguments, in this case conflicts between them arise
from the fact that distinct goals cannot all be fulfilled. The decision can then be
based on meta-level considerations, e.g. in the framework of value-based argu-
mentation [6] each argument supports a value and an attack succeeds only if the
value supported by the attacked argument is not strictly preferred to the value
associated to the attacking argument. Continuing the example above, assume
that John has to give a talk in the remote town and, in order to reach it, he
can either take the train or drive the car. This situation can be modeled by
two mutually conflicting practical arguments ptrain and pcar . If the train, differ-
ently from the car, allows John to work on a paper he has to submit, then the
value supported by ptrain (i.e. reaching the destination and working) is strictly
preferred w.r.t. the value supported by pcar (i.e. reaching the destination only),
thus ptrain attacks pcar but not vice versa, and ptrain turns out to be justified.
This outcome corresponds to a general result in the context of value-based ar-
gumentation frameworks, i.e. if values are totally and strictly ordered and there
are no attack cycles between arguments supporting the same value, then the re-
sulting framework has a unique grounded and preferred extension [6]. However,
when values do not allow to discriminate between conflicting arguments, one is
led to make an arbitrary choice between them. On this basis, a very credulous
approach is advocated in [9] for practical arguments, i.e. selecting a preferred
extension at random. For instance, if the available alternatives for John are the
car and a crowded bus (where working on the paper is impossible), then we have
two mutually conflicting arguments pcar and pbus , but differently from the case
of estrike and e¬strike either of them should be justified.
The question then arises as to how to manage epistemic and practical ar-
guments combined together. For instance, in the running example John may
evaluate the three options corresponding to the train, the car and the (crowded)
bus, taking into account the possibility of the railway strike. In the next section
we review two approaches for integrating epistemic and practical reasoning, i.e.
one introduced by Prakken in [9] and an approach first proposed in [10] and
then recasted, as sketched in [8], as an instance of a framework for combining
argumentation semantics based on decomposability [1]. The paper then provides
a comparison between these approaches and finally outlines some perspectives
for further research.
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pcar
e¬strike
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ptrain e¬strike
On Epistemic and Practical pcr train
estrike Reasoning
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3
(a) (b)
Fig. 1. Representation of the running example and a variation.
2 Two approaches for epistemic and practical arguments
2.1 Prakken’s approach
As in [9], we assume that the set of arguments A of the AF is partitioned into
a set of epistemic arguments Ae and a set of practical arguments Ap , where
epistemic arguments can attack the practical ones but not viceversa.
The viable practical options are identified in [9] as follows. First, the grounded
extension GRAF is computed, then all arguments that are attacked by epistemic
arguments that are not in turn attacked by (arguments of) GRAF are removed
from A. Finally, each practical option is derived from a preferred extension of
the resulting argumentation framework.
Figure 1(a) depicts the argumentation framework modeling John’s prob-
lem where the options of taking the train, taking the crowded bus and driving
the car are considered, and the contradictory epistemic arguments concerning
the strike are taken into account. In this case, GRAF = ∅, leading to remove
estrike , e¬strike and ptrain . Thus, the resulting preferred extensions are {pbus }
and {pcar }, i.e. either the bus or the car should be chosen. Note that without
argument estrike , the unique preferred extension would be {e¬strike , ptrain }, i.e.
the train should be chosen since it allows John to work while traveling.
2.2 Decomposability-based approach
The formal treatment of this approach requires a labelling-based definition of
argumentation semantics, where each extension E is replaced by a corresponding
labelling, i.e. a total function from A to {in, out, undec}, such that an argument
a is labelled in iff a ∈ E; it is labelled out iff ∃ b ∈ E such that b → a; it
is labelled undec if neither of the above conditions holds. Thus, a semantics S
returns for any AF a set of labellings LS (AF ) instead of a set of extensions.
Given an AF = (A, →), the general approach to combine semantics intro-
duced in [8] considers a partition P = {P1 , . . . , Pn } of A with associated seman-
tics S(Pi ). Each set Pi identifies the sub-framework AF ↓Pi = (Pi , → ∩(Pi ×Pi )),
where the semantics S(Pi ) is locally applied. The local computation of S(Pi ) is
expressed by a local function FS(Pi ) , which assigns to the arguments in Pi a set
of labellings on the basis of AF ↓Pi , of the set Pi inp = {a ∈ / Pi | ∃b ∈ Pi : a → b}
including the external arguments attacking Pi (playing S the role of input ar-
guments), of the labels externally assigned to them1 ( j=1...n,j6=i Lab Pj )↓Pi inp ,
and of the attack relation Pi R =→ ∩(Pi inp × Pi ) from the input arguments of
Pi inp to Pi . Then theS resulting labelling are {Lab P1 ∪ . . . ∪ Lab Pn | Lab Pi ∈
FS(Pi ) (AF ↓Pi , Pi inp , ( j=1...n,j6=i Lab Pj )↓Pi inp , Pi R )}.
1
More precisely, given a labelling L and a set of arguments Args, L↓Args , L∩(Args ×
{in, out, undec}).
4 P. Baroni, M. Giacomin
In order to apply this general schema to epistemic and practical arguments,
we consider the partition {Ae , Ap } with S(Ae ) = GR and S(Ap ) = PR (note
however that the framework can easily be generalized to other semantics). As
shown in [1], the relevant local functions can be identified by applying each
semantics S to a standard argumentation framework where the input arguments
are added to AF ↓Pi and the input labelling is enforced through the addition
of arguments attacking out-labelled arguments and self-attacks for all undec-
labelled arguments.
For instance, Figure 1(b) depicts an argumentation framework represent-
ing a variation of the running example where also the train is crowded (and
thus does not allow John to work), and as a consequence the three options are
equally preferable. The application of GR to AF ↓{estrike ,e¬strike } (with empty
input arguments) yields both epistemic arguments undecided. Thus, the local
application of PR to AF ↓{pcr−train ,pbus ,pcar } yields the two preferred labellings
{(pcr−train , undec), (pbus , in), (pcar , out)} and {(pcr−train , undec), (pbus , out),
(pcar , in)}. It can be checked that Prakken’s approach gives the same outcome,
identifying as extensions the sets {pbus } and {pcar }. Intuitively, since the avail-
ability of the train is uncertain, either the train or the car should be considered.
3 Comparing the two approaches
In order to analyze the relationship between the two approaches, it is convenient
to partition the arguments of A on the basis of the labelling assigned by GR ap-
plied to the whole AF . In particular, we partition Ae into ine , oute and undece ,
where le denotes the subset of Ae including arguments labelled l according to
GR. We also partition Ap into inp , outp , undec←e p and undec∼ p , where inp and
←e
outp have the same meaning as above, undecp includes those arguments of Ap
that are labelled undec by GR and are attacked by an argument of undece , and
undec∼ p includes the remaining arguments of Ap that are labelled undec.
The following observations concerning Prakken’s approach are relatively easy
to prove: i) oute , undece , outp and undec←e p are removed from A, thus they
do not belong to any preferred extension; ii) ine and inp belong to all pre-
ferred extensions. A direct consequence of the first observation is that after
removal undec∼ p does not receive attacks from external arguments, and due
to the property of directionality of PR [4] the set of preferred extensions is
{ine ∪ inp ∪ E | E ∈ EPR (AF ↓undec∼ p
)}.
As to the decomposability-based approach, using the results in [1] it is pos-
sible to prove that a corresponding outcome is yielded for all arguments but
undec∼ p . In particular, any obtained labelling assigns the label in to the argu-
ments in ine and inp , the label out to the arguments in oute and outp , and the
label undec to the arguments in undece and undec←e p . Differences only concern
the arguments of undec∼ p . Taking into account decomposability of PR [1], it
can be shown that the labellings restricted to undec∼ p can be obtained by lo-
cally applying PR into the argumentation framework AF ↓undec∼ p
by taking into
account the input arguments of undec∼ p in undec ←e
p . Due to a monotony prop-
On Epistemic and Practical Reasoning 5
erty of the local function of preferred semantics, it can be shown that for any
labelling obtained by the decomposability-based approach there is an extension
of Prakken’s approach which (not necessarily strictly) includes all arguments la-
belled in. Intuitively, the decomposability-based approach is more skeptical wrt
Prakken’s proposal.
From a conceptual point of view, this difference can be appreciated in the
case of Figure 1(a), where the decomposability-based approach returns a unique
labelling with all arguments undecided. While this may seem undesirable, we
believe the outcome more closely corresponds to the direction of the attacks.
In particular, while in Figure 1(b) there is no preference towards the train and
thus it is perfectly sensible to choose between the car and the bus, in the case
of Figure 1(a) leaving the train out of consideration would prevent a possible
alternative which is stricly more preferred than the car and the bus.
4 Perspectives for further research
We believe the considerations pointed out in this short paper open the way to
several interesting investigations. A first direction is applying different semantics
besides GR and PR, such as [2]. Another interesting question is how to handle
a gradual evaluation of practical arguments given different degrees of strength
for epistemic arguments, possibly exploiting a probabilistic approach [5].
References
1. P. Baroni, G. Boella, F. Cerutti, M. Giacomin, L. W. N. van der Torre, and S. Vil-
lata. On the input/output behavior of argumentation frameworks. Artificial In-
telligence, 217:144–197, 2014.
2. P. Baroni and M. Giacomin. Resolution-based argumentation semantics. In Fron-
tiers in Artificial Intelligence and Applications, pages 25–36, 2008.
3. P. Baroni and M. Giacomin. Skepticism relations for comparing argumentation
semantics. Int. Journal of Approximate Reasoning, 50(6):854–866, 2009.
4. P. Baroni, M. Giacomin, and B. Liao. On topology-related properties of abstract
argumentation semantics. A correction and extension to Dynamics of argumenta-
tion systems: A division-based method. Artif. Intell., 212:104–115, 2014.
5. P. Baroni, M. Giacomin, and P. Vicig. On rationality conditions for epistemic
probabilities in abstract argumentation. In Frontiers in Artificial Intelligence and
Applications, pages 121–132, 2014.
6. T.J.M. Bench-Capon. Persuasion in practical argument using value-based argu-
mentation frameworks. Journal of Logic and Computation, 13(3):429–448, 2003.
7. P. M. Dung. On the acceptability of arguments and its fundamental role in
nonmonotonic reasoning, logic programming, and n-person games. Artif. Intell.,
77(2):321–357, 1995.
8. M. Giacomin. Handling heterogeneous disagreements through abstract argumen-
tation (extended abstract). In Proc. of PRIMA 2017, pages 3–11, 2017.
9. H. Prakken. Combining sceptical epistemic reasoning with credulous practical
reasoning. In Proc. of COMMA 2006, pages 311–322. IOS Press, 2006.
10. T. Rienstra, A. Perotti, S. Villata, D.M. Gabbay, and L. van der Torre. Multi-sorted
Argumentation, pages 215–231. Springer Berlin Heidelberg, 2012.