Nowadays it has been extended to a general framework for the study of meaning, knowledge, and inference constituted during interaction.
The philosopher and mathematician Paul Lorenzen (Erlangen-Nürnberg-Universität) was the first to introduce a semantics of games for logic in the late 1950s.
Jaakko Hintikka (Helsinki, Boston) developed a little later to Lorenzen a model-theoretical approach known as GTS.
The philosophical development of dialogical logic continued especially in the fields of argumentation theory, legal reasoning, computer science, applied linguistics, and artificial intelligence.
The new results in dialogical logic began on one side, with the works of Jean-Yves Girard in linear logic and interaction; on the other, with the study of the interface of logic, mathematical game theory and argumentation, argumentation frameworks and defeasible reasoning, by researchers such as Samson Abramsky, Johan van Benthem, Andreas Blass, Nicolas Clerbout, Frans H. van Eemeren, Mathieu Fontaine, Dov Gabbay, Rob Grootendorst, Giorgi Japaridze, Laurent Keiff, Erik Krabbe, Alain Leconte, Rodrigo Lopez-Orellana, Sébasten Magnier, Mathieu Marion, Zoe McConaughey, Henry Prakken, Juan Redmond, Helge Rückert, Gabriel Sandu, Giovanni Sartor, Douglas N. Walton, and John Woods among others, who have contributed to place dialogical interaction and games at the center of a new perspective of logic, where logic is defined as an instrument of dynamic inference.
In other words, according to the conception of the dialogical framework, the intertwining of the right to ask for reasons, on the one hand, and the obligation to give them, on the other, provides the roots of knowledge, meaning and truth.
The interaction between the two players P and O is spelled out by challenges and defences, implementing Robert Brandom's take on meaning as a game of giving and asking for reasons.
Defense: X A[x/t] (The defender chooses) Any play (dialogue) starts with the Proponent P stating a thesis (labelled move 0) and the Opponent O bringing forward some initial statement (if any).
Note: This last clause is known as the Last Duty First condition, and makes dialogical games suitable for intuitionistic logic (hence this rule's name).
In order to cast the notion of validity within the dialogical framework we need to define what a winning strategy is.
In dialogical logic validity is defined in relation to winning strategies for the proponent P. Branches are introduced by O's choices such as when she challenges a conjunction or when she defends a disjunction.
Most of these developments are a result of studying the semantic and epistemological consequences of modifying the structural rules and/or of the logical constants.
In fact, they show how to implement the dialogical conception of the structural rules for inference, such as weakening and contraction.
[note 7] This new approach to dialogues with content, called immanent reasoning,[12] is one of the results of the dialogical perspective on Per Martin-Löf's constructive type theory.