The Argument Mapping Tool of the
Carneades Argumentation System
DIAGRAMMING EVIDENCE:
VISUALIZING CONNECTIONS IN
SCIENCE AND HUMANITIES’
University of Windsor,
April 25 & 26, 2014.
Douglas Walton
CRRAR
The Advent of Defeasible Logic
• Argumentation has long been used to study defeasible reasoning,
and recently formal and computational argumentation systems
have been built in artificial intelligence and multiagent computing
that show how nonmonotonic reasoning can be modeled in
argumentation-theoretic terms.
• The basic model is a tree structure representing a connected
sequence of argumentation both pro and con an ultimate
conclusion. An evaluation shows the conclusion as accepted if the
pro-arguments supporting it are not defeated by the con arguments
against it.
• Other devices may also be used, such as a priority ordering on
rules, a system for assigning standards of proof to arguments, and
defeasible argumentation schemes that provide tentative support
for a conclusion in the absence of counterarguments or the posing
of critical questions to rebut or undercut the argument.
The DefLog System
•
•
•
•
•
Bart Verheij in 1999 began to build an automated argument
assistant called ArguMed that helps a user to construct an
argument diagram in order to analyze and evaluate a given
argument (Verheij, 2003, 320).
The development of this system was guided by his parallel research
on the logical system called DefLog (Verjeij, 2003) that represents
the underlying structure of the reasoning displayed by ArguMed.
ArguMed (http://www.ai.rug.nl/~verheij/aaa/argumed3.htm) is
available at no cost on the Internet.
The ultimate conclusion, called the issue in ArguMed, appears in a
text box at the top of the diagram, and the premises supporting it
form arguments that can be linked together, and that lead by
arrows to the conclusion.
The user can input statements directly into the boxes shown on the
screen in a way comparable to other argument mapping tools.
An Example of an ArguMed Map
The System ASPIC+
• ASPIC+ is built on a logical language containing a contrariness
function, a set of strict and defeasible inference rules, and an
ordering of this set of inference rules (Prakken, 2010).
• Suppose that we have the goal of increasing productivity because
we think that increasing productivity is good. And suppose we think
that reducing taxes is the way to increase productivity. Then we
should conclude that taxes should be reduced.
• However we also accept the premises that reducing taxes increases
inequality, that increasing inequality is bad, and that equality is
more important than productivity. Then we should conclude that
we should not reduce taxes.
• The second argument defeats the first one, even though the
conclusion of the first argument was acceptable before the second
argument was considered.
Abstract Argumentation Frameworks
• ASPIC+ is built on the basis of abstract argumentation
frameworks (Dung, 1995). An abstract argumentation
framework is a structure used to determine which
arguments can be accepted among a set of arguments
in which some arguments defeat others.
• The proponent starts with the argument he wants to
prove and when the opponent has his turn, he must
provide a defeating counterargument.
• An abstract argumentation framework (AF) is defined
as a pair (Args, Def ), where Args is a set of arguments
and Def ⊆ Args × Args is a binary relation of defeat.
Undercutters and Rebutters
• ASPIC+ works by determining the success of rebutting
and undercutting attacks that compare conflicts in
arguments at the points where they conflict.
• ASPIC+ is based on the system of (Pollock, 1995) where
an important distinction was drawn between two kinds
of refutations called rebutting defeaters and
undercutting defeaters (often referred to as rebutters
versus undercutters).
• A rebutter gives a reason for denying a claim by
arguing that the claim is false whereas an undercutter
defeater attacks the inferential link between the claim
and the reason supporting it (Pollock, 1995, 40).
Famous Example
• Pollock used a famous example (1995, 41) to illustrate his
distinction. According to the example, if I see an object that looks
red to me, that is a reason for thinking it is red, but if I know that
the object is illuminated by a red light, that is an undercutter,
because red objects look red in red light too.
• This is not a reason for thinking the object is not red, but it is a
reason for undercutting the argument that it is red. Despite the
attacking argument, the object may be red, for all we know.
• As an undercutter it acts like a critical question that casts an
argument into doubt rather than strongly refuting it.
• The use of three kinds of counterarguments that can be used to
attack any given argument is highly characteristic of ASPIC+. The
three kinds of counterarguments are undercutters, rebutters and
premise attacks.
The Carneades
Argumentation System
• Thomas F. Gordon (Fraunhofer Fokus)
• There are many software packages to assist with
argument diagramming (Scheuer et al., 2010),
based on informal logic models of argument.
• Carneades provides a number of software tools,
including argument diagramming, based on a
formal, computational model of argument.
• Carneades is named after the Greek skeptical
philosopher (Gordon and Walton, 2006) and is
open source software, available at
http://carneades.github.com/.
Why Carneades is a
Formal, Computational
Model of Argument
• computational, because the model consists of
mathematical structure whose operations are all
computable
• formal, because there is a formal calculus for
computable functions (lambda calculus)
Argument Graphs
• Definition (Argument Graph) An argument graph is a bipartite,
directed, labeled graph, consisting of statement nodes and
argument nodes connected by premise and conclusion edges.
Formally, an argument graph is a structure ⟨𝑆, A, P, 𝐶⟩, where:
• 𝑆 is a set of statement nodes,
• 𝐴 is a set of argument nodes,
• 𝑃 is a set of premises, and
• 𝐶 is a set of conclusions.
Argument Maps
• In Carneades argument maps, statement nodes are shown as
propositions in text boxes.
• Argument nodes are displayed as circles, with a + or – sign
inside the circle, to distinguish pro and con arguments,
respectively.
• Premises and conclusions are visualized as lines and arrows,
respectively, connecting statement and argument nodes.
Single Argument
Linked Argument
Convergent Argument
Divergent Argument
Serial Argument
The Role of the Audience
• Argument graphs are evaluated, relative to audiences,
to determine the acceptability of statements in a stage.
• Audiences are modelled as a set of assumptions and an
assignment of weights to argument nodes.
• Where L is a propositional language, an audience is a
structure <assumptions, weight>, where assumptions
⊆ L is a consistent set of literals assumed to be
acceptable by the audience and weight is a partial
function mapping arguments to real numbers in the
range 0.0...1.0, representing the relative weights
assigned by the audience to the arguments.
Acceptability
Acceptability
Acceptability
Premise Attack
Rebutter
An Example of an Undercutter
• Messerli (2012) found there was a close significant
linear correlation between chocolate consumption per
capita and the number of Nobel laureates in a country.
• He found some theory-based biochemical evidence in
the scientific observation that flavonoids present in
cocoa are known to improve blood flow to the brain.
• He used the form of argument called argument from
correlation to cause.
Argument from Correlation to Cause
[Scheme in Carneades]
id: correlation-to-cause
strict: false
direction: pro
conclusion: Event E1 causes event E2.
premises:
 Events E1 and E2 are correlated.
assumptions:
 There exists a theory explaining how event E1 causes event E2.
exceptions:
 Event E3 causes events E1 and E2.
Undercutter
Undercutter
In, Out and Undecided
• Statements which have been accepted or
rejected by the audience are in or out,
respectively.
• The values of the remaining statement nodes are
computed using proof standards and the weights
assigned by the audience to the argument nodes.
• This example shows how values can be
propagated along an argumentation tree
structure to prove an ultimate conclusion (the
statement shown at the extreme left of the map).
Propagation 1
Propagation 2
Propagation 3
Propagation 4
Propagation 5
Propagation 6
Propagation 7
Propagation 8
Standards and Schemes
• Conflicts between pro and con arguments are
resolved using proof standards, such as
preponderance of the evidence and beyond
reasonable doubt, inspired by the legal domain.
• Carneades also formalizes argumentation
schemes.
• Schemes can be used to construct or reconstruct
arguments, as well as to check whether
arguments are “valid”, i.e. whether they properly
instantiate the types of argument deemed
normatively appropriate for the type of dialogue.
Choosing a Scheme
DMP
• This form of argument can be used for evaluating
defeasible inferences like the Tweety argument: If
Tweety is a bird, Tweety flies; Tweety is a bird;
therefore Tweety flies.
• This form of argument was called defeasible
modus ponens (DMP) by Walton (2002).
• An example (Copi and Cohen, 1998, p. 363) also
illustrates DMP: if he has a good lawyer then he
will be acquitted; he has a good lawyer; therefore
he will be acquitted.
Form of DMP
• Using a concept from defeasible logic called defeasible
implication, or the defeasible conditional as it might be
called, we can represent DMP is having the following form.
Major Premise: A => B
Minor Premise: A
Conclusion: B
• The first premise states the defeasible conditional, ‘If A is
true then generally, but subject to exceptions, B is true’.
• DMP is a scheme in DefLog, ASPIC+ and CAS.
Argument Construction
• Ballnat and Gordon (2010) provided a method of argument
invention for Carneades, and Walton and Gordon (2012)
have shown how the method can be applied in informal
logic.
• To use the system, an arguer first provides input on the
premises he assumes the audience already accepts or not.
• Then the system searches for minimal subsets of the
remaining premises which together with the assumed
premises are sufficient to (defeasibly) prove a given claim.
• The arguer can then focus his attention on trying to
construct arguments that support the premises in one of
the minimal sets found.
Menu for Finding an Argument
Instantiating a Scheme
Cycle in a Graph
The RAS Triangle
• Blair (2012, 87) wrote that when he and Ralph Johnson
first wrote their textbook Logical Self-defense (first
edition, 1977), they used the relevance-sufficiencyacceptability (RSA) triangle to determine whether an
argument is a good one.
• According to the RSA principle, an argument is a good
one if its grounds (or premises) singly or in
combination meet three criteria.
1. The premises have to be individually acceptable.
2. Taken together the premises have to be sufficient to
support the claim that is the conclusion of the argument.
3. The argument needs to be relevant as a support for the
conclusion.
Sufficiency
• Carneades is built around the idea of modelling sufficiency
by using proof standards to aggregate pro and con
arguments.
• The conclusion of an argument is in (acceptable) if has been
accepted by the audience or it satisfies the proof standard
appropriate for the type of dialogue.
• Proof standards have a legal flavor, and the notions of proof
standards and burdens of proof modelled in Carneades are
motivated by our interest in legal applications.
• Several legal standards of proof exist, for example the
preponderance of the evidence standard and the beyond
reasonable doubt standard.
Conclusions
• Carneades has been used to illustrate some of the
capabilities of current AI argumentation systems, but other
systems such as DefLog and ASPIC+ are comparable.
• These systems can be used to assist with making argument
diagrams, but they can also be used to evaluate arguments,
and to construct new arguments from a knowledge base to
prove a conclusion.
• They incorporate argumentation schemes and dialectical
features of argumentation that can use standards of proof
to model burden of proof shifts.
• Argument invention is something that is fundamental to
rhetoric. The notion of audience is basic for Carneades to
evaluate and construct arguments.
Some References
Ballnat, S. and Gordon, T. F. (2010). Goal Selection in Argumentation Processes,
Computational Models of Argument: Proceedings of COMMA 2010, ed. P. Baroni.
Blair, J. A. (2001). Walton’s Argumentation Schemes for Presumptive Reasoning: A
Critique and Development, Argumentation, 5, 365-379.
Blair, J. A. (2012). Groundwork in the Theory of Argumentation. Dordrecht: Springer.
Gordon, T. F., and Walton, D. (2009). Proof Burdens and Standards. In Argumentation
in Artificial Intelligence, I. Rahwan and G. Simari, Eds. Springer-Verlag, Berlin, Germany,
2009, 239-260.
Johnson, R. H. (2009). Some Reflections on the Informal Logic Initiatives, Studies in
Logic, Grammar and Rhetoric, 16 (29), 17-46.
Tindale, C. W. (1999). Acts of Arguing: A Rhetorical Model of Argument. Albany: State
University of New York Press.
Wadler, P. (2014). University of Edinburgh, Propositions as Types [preprint]:
http://homepages.inf.ed.ac.uk/wadler/topics/recent.html
Walton, D. and Gordon T. F. (2012). The Carneades Model of Argument Invention,
Pragmatics & Cognition, 20(1), 1-31.