Piecha, [2013] “Three Lectures on Dialogues”
This article presents three lectures on the dialogical semantics of intuitionistic logic. Dialogical logic is an interpretation of logical formulas devised by Paul Lorenzen and his student/collaborator Kuno Lorenz in the 1950s. It is based on the idea of a game between a player and an opponent, where the validity of a formula is determined by the player being able to form a winning strategy against any opponent’s behavior. In fact, it is a precursor to game semantics.
The lectures are organized as follows:
- Introduction to Lorenzen’s dialogues for propositional logic: formulas, attacks/defenses, positions, D-dialogues, strategies, completeness, and classical generalizations.
- Extension of propositional logic to Horn clauses in the style of logic programming: E-dialogues, Prolog-style definitional reasoning (resolution + unification).
- An alternative interpretation of implication and the corresponding new form of E-dialogues, introducing additional asymmetry between the permissible moves of the player and the opponent.