eyeprolog

Illegitimate reasoning

Can a program spot a bad argument?

“If it rained, the street is wet. The street is wet. So it rained.” That sounds reasonable and is wrong. This example describes arguments as data, recognizes four classic fallacies by their shape, and reports each one with its conclusion and a short reason, while leaving a valid argument alone.

Run it in the playground · Source

The question

Which of these arguments are illegitimate, which fallacy does each commit, and why?

Affirming the consequent: from “if A then B” and “B”, conclude “A”.
Denying the antecedent: from “if A then B” and “not A”, conclude “not B”.
Hasty generalization: a universal claim from too small a sample.
False dilemma: only two options presented when a third exists.

A fifth argument uses modus ponens (“if A then B”, “A”, so “B”), which is valid and must not be flagged.

Arguments as data

argument(arg_affirming_consequent).
implication(arg_affirming_consequent, rain, street_wet).
observed(arg_affirming_consequent, street_wet).
concludes(arg_affirming_consequent, rain).

argument(arg_modus_ponens).
implication(arg_modus_ponens, subscription_paid, access_allowed).
observed(arg_modus_ponens, subscription_paid).
concludes(arg_modus_ponens, access_allowed).

Each argument is described by its parts: the implication it relies on, what was observed, and what it concludes. The program reasons about arguments; it does not reason with them.

The rules

fallacy(A, affirming_consequent) :-
  argument(A),
  implication(A, Antecedent, Consequent),
  observed(A, Consequent),
  concludes(A, Antecedent).

fallacy(A, hasty_generalization) :-
  argument(A),
  sample_size(A, N),
  required_sample_size(A, Min),
  (N < Min),
  concludes(A, all(_, _)).

Each fallacy is a pattern over the parts. The modus ponens argument observes the antecedent and concludes the consequent, so it matches no pattern.

The answer

eyeprolog examples/illegitimate-reasoning.pl

fallacy(arg_affirming_consequent, affirming_consequent).
fallacy(arg_denying_antecedent, denying_antecedent).
fallacy(arg_hasty_generalization, hasty_generalization).
fallacy(arg_false_dilemma, false_dilemma).
type(arg_affirming_consequent, illegitimate_reasoning).
...

19 answers in all: four fallacies, their types, conclusions and reasons, plus the sample sizes and the omitted alternative. arg_modus_ponens appears nowhere.

The reason

eyeprolog --proof examples/illegitimate-reasoning.pl

step(fallacy(arg_affirming_consequent, affirming_consequent),
     rule(26),
     ['A' = arg_affirming_consequent, 'Antecedent' = rain, 'Consequent' = street_wet],
     [argument(arg_affirming_consequent),
      implication(arg_affirming_consequent, rain, street_wet),
      observed(arg_affirming_consequent, street_wet),
      concludes(arg_affirming_consequent, rain)]).

The diagnosis cites the exact rule and the four facts that match it: rain implies a wet street, the street was observed wet, and the argument concluded rain. A reader can verify the judgement from the evidence alone.

The check

condition('C1', resolution, ok, 39).
condition('C5', re_decision, ok, 1).
condition('C7', relevance, ok, 59).
verdict(checked).

39 steps replay against their clauses, and the one built-in comparison (3 < 30 for the sample size) is recomputed. Nothing is trusted.

Try it

Set the required sample size of arg_hasty_generalization to 3. The hasty generalization disappears from the output, because 3 < 3 fails.
Add a false-dilemma-shaped argument with no omitted_alternative/2 fact and predict whether it is flagged.
Add a pattern for circular reasoning: an argument that concludes one of its own premises.

Learn more in The Art of EyeProlog, Chapter 14.

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