It is a mark of an educated person to look for precision in each kind of inquiry just to the extent that the nature of the subject allows it.


The difficult part in an argument is not to defend one's opinion but rather to know it.

Andre Maurois

All human errors stem from impatience,
a premature breaking off of a methodological approach,
an ostensible pinning down of an ostensible matter.

Franz Kafka

This project is has been transformed into AGORA-net: Participate - Deliberate. Please visit to see its continuation.

Last modified: Mar 20, 2012

First published: Feb 2008

Logical Argument Mapping (LAM): A Manual

In order to understand someone's position or thesis, it is good to know this person's justification for this thesis or position. This is especially important for ethical problems. Since ethical decisions can be based on a variety of ethical principles and moral considerations, there are often good arguments for conflicting positions.

Justifications can be represented in the form of arguments. For example, if I want to argue for the thesis "Paul is responsible for what he did," I might provide as a justification for this thesis the reason "Paul is a rational being."

What is an argument? An argument is defined as a set of statements--a claim and one or more reasons--where the reasons jointly provide support (not necessarily conclusive) for the claim, or are at least intended to support the claim. In my example, the statement "Paul is responsible for what he did" would be the claim, and the justification "Paul is a rational being" is the reason.

Logical Argument Mapping (LAM) and the corresponding web-based software system "AGORA: Participate - Deliberate" are built on the idea that the visualization of arguments in graphical form facilitates the structuring of complex justifications and debates, and stimulates self-reflection. The reason for the former is that argument mapping helps us to represent entire argumentations, that is chains of arguments, including objections, counter-, and counter-counter-arguments. Based on the graphical structure of argument maps, the central claim, the structure of justifications, controversial points, open ends, and the status of complex debates are immediately visible. On an argument map, everything is clearly located at a certain position. Everything is part of a structure.

The reason for the second assumption that argument mapping stimulates self-reflection is the fact that we have to create this structure. We have to reflect on the adequacy of a certain structure, and we have to revise it if necessary. This helps us to reflect on our own thinking about an issue, and on that of others when we are using LAM to represent or reconstruct given arguments.

What distinguishes LAM and the AGORA approach from other argument visualization tools is the fact that it guides the user to represent arguments in the form of deductively valid arguments.

What is a deductively valid argument? An argument is "deductively valid" if and only if it follows an argument scheme that is deductively valid. An argument scheme is deductively valid if and only if it is impossible for any argument following this scheme to have true premises and a false conclusion. See, for example, the deductively valid argument scheme that is called modus ponens:

-- p

-- If p, then q

-- Therefore, q

Every argument that is formulated according to this scheme will be deductively valid (as long as p and q are variables that represent propositions, and "if p, then q" is understood as material implication, that is as something like a law of nature that connects an event described by q as a necessary consequence of an event described by p). For example:

-- Paul is a rational being

-- if Paul is a rational being, then Paul is responsible for what he did

-- therefore, Paul is responsible for what he did

This example shows that it is possible to transform any argument into a deductively valid argument simply by introducing a fitting additional premise like the "if-then" statement in this example. I call this additional premise an "enabler." The "enabler" in an argument is the premise that guarantees that the reason provided is sufficient to justify the claim. The enabler "enables" the reason to produce the claim with logical necessity. Thus, the simple argument "Paul is a rational being, therefore he is responsible for what he did" can be transformed into a deductively valid argument by constructing the enabler "if Paul is a rational being, then Paul is responsible for what he did."

In contrast to classical deduction, in LAM deductively valid arguments are interpreted as defeasible deductions. Even though -- as in classical deductive validity -- a conclusion will be necessarily true in case the premises are true, in LAM both the enabler and the reason of an argument are only believed to be true by the person proposing the argument, and only as long as there is no information to the contrary. If information comes up that would either defeat or question one of the premises, this information will be connected to this premise as an "objection," and the status of every proposition that depends on this defeated or questioned premise will change from "undefeated" to "defeated" or "questioned" (see here for an example). This way, an entire deductive argument can be defeated by defeating one of its premises.

LAM and the AGORA system use seven deductively valid argument schemes: modus ponens; modus tollens; disjunctive syllogism; not-both syllogism; conditional syllogism; equivalence; and constructive dilemma (see here for details). This list is the result of a compromise between completeness and practicality. There are more deductively valid argument schemes, but these turned out to be the ones whose validity is easily comprehensible, and that are sufficient to represent most of the arguments that we are using every day (after a fitting enabler has been introduced).

Why should it make sense to transform arguments into defeasible deductions? There are three reasons for this fundamental design decision:

1. A thesis about human cognition: Critical reflection and learning can be better achieved with those systems of representation that provide a clear normative standard of argument construction that constrains the freedom of expression; a standard that challenges the user to be more specific than he would be otherwise, to slow down and think more thoroughly.

2. A consideration from argumentation theory: In order to locate any possible objection against an argument precisely, anything that can be criticized in an argument must be represented. The easiest way to achieve this form of completeness is to present an argument in deductively valid form. Looking at a deductively complete argument reminds us that we do not only have to reflect on the question whether the reasons we provide are acceptable and justified, but also the inferential relation between reason and claim.

3. An educational and computational argument: Learning needs scaffolding, and software tools that are designed to support autonomous learning--either individually or in groups--should guide the user in a step-by-step process. This can be much easier achieved by software tools whose means of expression are limited to deductive argument schemes.

Logical Argument Mapping is not deductive reasoning. Logical Argument Mapping is the process of constructing arguments in deductive form, assessing the acceptability of the premises as they need to be formulated to achieve this deductive form, and revising these premises and/or the structure of the argument as long as it takes to construct the best possible argument. A reconstruction of an argument in logical form can show us how its premises would need to look like if the goal were to guarantee the truth of the conclusion. The point is to get the content of the premises right and to formulate them in their strongest possible form.

For an example of how such a process of revising and improving an argument might work, see the "Tweety can fly" example here.


Logical Argument Mapping (LAM) can be used--in individual, collaborative, and competitive settings--for the following purposes:

-- Justifying claims in order to represent knowledge

-- Justifying norms, proposals, and decisions in ethics and policy making

-- Visualizing webs of mutually supporting beliefs and values

-- Reflecting on one's own thinking and sensemaking

-- Revealing unknowns, opportunities, and conflict possibilities in planning and decision making

-- Deciding controversies, or understanding someone else's position

-- Deliberating on a problem or decision

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The AGORA project develops an interactive and web-based software version of Logical Argument Mapping.

To enter the AGORA world, and to read more, click here.