In the second half of the twentieth century, different systems of logic were constructed to give a formal representation of argumentative dialogue.

— In addition to his historical presentation, discussion and critique of the “standard treatment of fallacies” Charles L. Hamblin proposed a “formal dialectic” (1970)

— Paul Lorenzen and Kuno Lorenz developed a *dialogical logic* (Lorenzen, Lorenz, 1978).

— Else Barth and Jan L. Martens constructed a *formal dialectic* for the analysis of argument (Barth, Martens, 1977).

— Jaakko Hinttika studied the *semantic of questions*, and the logic of *information-seeking dialogs* (1981).

— Taking Hamblin’s work as a starting point, Douglas Walton and John Woods developed a logical approach to fallacies (Woods, Walton 1989) and to argumentative dialogues (Walton 1989).

The dialogical logic (*Dialogische Logik)* of Lorenzen and the school of Erlangen was developed as a contribution to formal logic. This model extended to apply to the definition of rational dialogue, is a precursor of the pragma-dialectic approach to argument.

# 1. Logical dialogue game

The logical contribution consists in a method of no longer defining logical connectives by the traditional method of truth tables, but by means of permissible or prohibited moves in a “dialogical game”. Consider, for example, the connector “&”, “and”. It can be defined by the truth table method. In dialogical games, “&” is defined by the following moves:

(a) First round:

Proponent: **P & Q
**Opponent: Attacks

**P**

Proponent: Defends

**P**

If the proponent defends **P** successfully, he wins round (a). If his or her defense fails, the game is over, and the proponent has lost the game. In the language of truth tables, this corresponds to the truth-table line “if **P** is false, then the conjunction ‘**P & Q**’ is false”. In other words, the line “if **P** is false, then the conjunction ‘**P & Q**’ is false” is excluded.

If the proponent won round (a), in relation to **P**, the game continues.

(b) Second round, the opponent attacks **Q**.

Proponent: **P & Q
**Opponent: Attacks

**Q**

Proponent: Defends

**Q**

If the proponent defends **Q** successfully, he wins round (**b**), and, as round (**a**) has already been won, the game is won for the proponent. If his or her defense fails, the game is over, the proponent lost the game, and the opponent won it.

In the language of truth-tables, this translates as “**P & Q**” is true: the proponent won; and “**P & Q**” is false: the opponent won.

# 2. Dialogue logic rules and Pragma-Dialectical rules

Dialogical logic uses three kinds of rules (van Eemeren *& al.* 1996, p. 258)

— *Starting rule*: the proponent starts by asserting a thesis.

— *General rules* on legal and illegal moves in dialogue (see above).

— *Closing rule*, or winning rule, determining who has won the game.

Similar rules apply in Pragma-Dialectic:

— The starting rule corresponds to “Rule 1. *Freedom* — “The parties must not interfere with the free expression or questioning of points of view” (van Eemeren, Grootendorst, Snoeck Henkemans 2002, 182-183).

— The closing rule, or the winning rule corresponds to “Rule 9. *Closing* — If a point of view has not been conclusively defended, the advancing party must withdraw it. If a point of view has been conclusively defended, the other party must withdraw the doubts it has expressed with respect to that point of view” (*ibid*.).

The other rules are intended to ensure the smooth running of an argumentative dialogue in ordinary language aimed at eliminating differences of opinion.

# 3. A contribution to the theory of rationality

In a work entitled *Logical Propaedeutic: Pre-School of Reasonable Discourse *([1967] / 1984), Kamlah and Lorenzen aim to provide “the building blocks and rules for all rational discourse” (quoted in van Eemeren *& al* 1996, p. 248). Their basic assumption is that, “in order to prevent them from speaking at cross purposes in interminable monologues, the interlocutors’ linguistic usage in a discussion or conversation must comply with certain norms and rules. Only when they share a number of fixed postulates with respect to linguistic usage can they conduct a meaningful discussion” (van Eemeren *& al.* 1996, p. 253). The goal of the enterprise is therefore the construction of an “ortholanguage” (Lorenzen & Schwemmer, 1975, p. 24; quoted in* id*., p. 253), defining the rational dialogical behavior capable of resolving inter-individual contradictions.

There is obviously a great difference between this approach and the interactional approaches to speech in interaction that began to develop at the same time.