=Paper=
{{Paper
|id=Vol-2381/xaila2018_paper_6
|storemode=property
|title=A Dialogical Framework for Disputed Issues in Legal Interpretation
|pdfUrl=https://ceur-ws.org/Vol-2381/xaila2018_paper_6.pdf
|volume=Vol-2381
|authors=Tomasz Żurek
|dblpUrl=https://dblp.org/rec/conf/jurix/AraszkiewiczZ18
}}
==A Dialogical Framework for Disputed Issues in Legal Interpretation==
https://ceur-ws.org/Vol-2381/xaila2018_paper_6.pdf
A Dialogical Framework for Disputed
Issues in Legal Interpretation
Michał ARASZKIEWICZa,1 and Tomasz ZUREKb
a
Department of Legal Theory, Jagiellonian University in Kraków, Poland
b
Institute of Computer Science, Maria Skłodowska-Curie University in Lublin, Poland
Abstract. We present a dialogical framework modelling the exchange of arguments
concerning legal interpretation. The framework may be used to model legal debates
on interpretation of statutes or contracts with the use of structured argumentation.
We introduce the notion of abduction move that generates the set of sentences (and
arguments based thereon) that would justify the choice of a given deliberated
conclusion.
Keywords. Argumentation, Interpretation, Justification, Hybrid systems
1. Introduction
Major part of legal disputes has essentially dialogical setting of certain type: trials
involve exchange of please between parties to the litigation, negotiations consist in
posing options and commitments of the parties, members of legal doctrine comment on
judicial decisions and publications of other scholars. Each type of legal discourse may
be accounted for a dialogue consisting in presenting arguments for and against a given
thesis, also if this dialogue is only “virtual” in the sense it involves only one physical
agent. Therefore it is not surprising that the dialogical features of legal reasoning have
been modelled in the field of AI and Law since the early days, to mention three-ply
argument in HYPO [2], the model of Pleadings Game [5] or the model for assessing
conflicting arguments developed by Prakken and Sartor [7]. The present contribution
offers a first dialogical framework to model debates on legal interpretation of relevant
sources (statutes or contracts). The focus of the model is on the transparency of
argumentation moves and on the explainability of the solution, encompassed by the
specific abduction move that leads to the generation of potential elements of reasoning
which would support a decision in favour of each of the deliberated conclusions.
1
Corresponding Author. The writing of this paper was supported by the project K/DSC/004874.
2. The Model of Agents Arguing on Interpretation
The model outlined below represents the process of argumentation of relevant agents
involved in a dispute on the meaning of contractual provisions. As a point of departure,
we adopt the notion of Interpreting Agent as defined in [3], developed, amended and
partially restricted for the sake of realization of the purposes of this paper. We do not
define any specific logical language or argumentation system for this model, because it
may in principle be implemented in different existing well-developed formal systems
such as Carneades [5] and ASPIC+ [6] in environments that enable artificial agents
interaction, for instance via dialogue protocols [1]. The presented model may be used for
testing of expressive power of the abovementioned formal systems.
Definition 1. Interpreting Agent. Each Interpreting Agent (IA) is a tuple , where:
• KB(IA)t is the knowledge base of the Agent at the time t,
• preferences(IA)t is the set of the Agent’s preferences and goals at the time
t,
• authority(IA)t, c - Authority – is the characterization of the formal status of
statements used by an agent, at the time t and in the context of the case c.
The typical agent vested with non-empty authority(IA)t, c is the Judge [4].
By IA we denote the set of all agents.
Definition 2. Argument. Let L be a defined language being able to express terms and
let SL be the set of all sentences of the language L. Then for any Γ, Ω ⊆ SL an ordered
pair < Γ, Ω> is an argument if and only if:
• PRO < Γ, Ω> - the set of sentences A provides reason for the acceptance of the
set of sentences Ω, or
• CON < Γ, Ω> - the set of sentences A provides reason for the rejection of the
set of sentences Ω.
We will use the symbol ARG as a variable that may adopt the values PRO or CON. For
the structures of interpretive arguments see [8].
Definition 3. Authorship Relation. The relation of authorship is a subset of a Cartesian
product: R ⊆ IA × ARG , i.e. a set of pairs: (ia, A), where ia ∈ IA and
A ∈ ARG.
By ARGia we denote the set of all arguments created by agent ia. If A ∈ ARGia t and A=
< Γ, Ω> then by conc(A) we denote the conclusion of argument A (Ω).
Definition 4. Interpretive Statements. Let s and t be terms of the language L. An
Interpretive Statement is a sentence in L expressing a relation “is interpreted as” between
a pair of terms of L: s • t [3].
Definition 5. Incompatibility. Let α and β be the statements of the language L. The two
statements are incompatible INC (α , β) if they cannot be accepted together by an agent
IA taking into account the structure of the agent. Hence, the notion of incompatibility is
agent-relative.
Definition 6. Argument ordering. The expression in L ARGi > ARGj means that the
set of arguments ARGi is stronger than the set of arguments ARGj. In practical
argumentation the compared sets of arguments will most often be singletons. The
argument ordering relations may follow from the Knowledge Base of IAs by default or
they may be subject of dispute between the agents.
As an argumentation process we understand the dynamic process of argument
invention, exchange, justification, and attack.
In particular, the framework should be capable enough to represent the
argumentation moves.
Definition 7. Argumentation Moves. Each IA is entitled to perform the following
argumentation moves:
• assertion(α) – asserting a statement α
• questioning(α) – demanding an agent A who asserted α to provide justification
for α
• providing support for α - asserting such β that PRO <β, α>
• undermining attack on the argument ARG <α, β> – asserting such γ that CON
< γ, α >
• rebutting attack on the argument ARG <α, β> – asserting such γ that CON < γ,
β > or such γ that PRO < γ, δ > where INC (δ , β ).
• undercutting attack on the argument ARG <α, β> - asserting such γ that CON
< γ, ARG <α, β> >
• retract(M) – retraction of a previously made move M.
• abduction(D, KB) – generation of a set of sentences D from the set KB(IAt) and
arguments based on them that would lead to assignment of priority to one of the
competing conclusions, were these sentences asserted by a given agent.
The idea of the abduction move is the generation of different sets of sentences could
provide justification for the final conclusion. The abduction move may then motivate the
user of the system to look for additional evidence or suggest the direction of
argumentation with regard to legal matters. If a given agent is not sure what move should
be made in order to obtain the justification status of a given conclusion, the abduction
move shall indicate the possible solution.
Definition 8. Justified formula.
A formula α is:
• weakly justified iff there is at least one sound argument PRO <Γ, α>
• strongly justified iff there is at least one sound argument PRO <Γ, α> and PRO
<Γ, α> is stronger than any argument CON <Ω, α> or any argument PRO <Ω,
β> such that INC (α, β).
• undoubtedly justified iff there is at least one argument PRO <Γ, α> and there
is no arguments CON <Ω, α>
More fine-grained notions of justification may be defined, cf. standards of proof in [6].
Definition 9. Sound argument.
An argument A that is not attacked is sound.
An argument A is sound if the arguments constructed to undermine or undercut A are
unsound.
An argument is unsound if it is undermined or undercut by a sound argument.
The abduction move may be constrained in different manners, such that the number of
other moves necessary to obtain weak or strong justification for a given conclusion.
3. Conclusions
We outlined a model of intelligent agents based on argumentation and explicit
knowledge stored in the agent’s knowledge base. The model itself has abstract character,
but it may be fruitfully applied to the interpretation of statutes and contracts. Such model
should be capable of enabling agents involve in a dialogue concerning interpretation of
statutory or contractual provisions and suggesting them possible solutions to the
interpretive problems by means of abduction. Such systems, being able to explain the
reason for the suggested solutions should complement the developed ML systems based
on statistical methods.
4. References
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(AIMSA'06),J. Euzenat and J. Domingue (Eds.). Springer-Verlag, Berlin, Heidelberg, 2006, 13-23.
DOI=http://dx.doi.org/10.1007/11861461_4
[2] K. Ashley, Modeling legal argument. Reasoning with Cases and Hypotheticals. MIT Press, Cambridge:
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[3] M. Araszkiewicz, T. Zurek, Comprehensive Framework Embracing the Complexity of Statutory
Interpretation, in: A. Rotolo (ed.), JURIX 2015: The Twenty-Eighth Annual Conference, IOS Press,
Amsterdam 2015, 145-148.
[4] M. Araszkiewicz, T. Zurek, Interpreting Agents, in: F. Bex, S. Villata (eds.), JURIX 2016: The Twenty-
Ninth Annual Conference, IOS Press, Amsterdam 2016, 13-22.
[5] T.F. Gordon, The Pleadings Game. An Artificial Intelligence Model of Procedural Justice. Springer:
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[6] T. F. Gordon, , H. Prakken, D. Walton, The Carneades model of argument and burden of proof. Artificial
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[7] H. Prakken, G. Sartor, A Dialectical Model of Assessing Conflicting Arguments in Legal Reasoning.
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[8] S. Modgil and H. Prakken, “The aspic+ framework for structured argumentation: A tutorial,” Argument
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[9] D. Walton, G. Sartor, F. Macagno, Statutory Interpretation as Argumentation. In: Bongiovanni G.,
Postema G., Rotolo A., Sartor G., Valentini C., Walton D. (eds) Handbook of Legal Reasoning and
Argumentation. Springer, Dordrecht, 2018.